Table of contents

  1. December 2006
  2. November 2006
  3. October 2006
  4. September 2006
  5. August 2006
  6. July 2006
  7. June 2006
  8. May 2006
  9. April 2006
  10. March 2006
  11. February 2006
  12. January 2006

December 2006

Dec 28, 2006 (2nd)

By Yousuke Koide / GMP-ECM

(10621-1)/9 = (1)621<621> = 33 · 37 · 277 · 757 · 333667 · 11055043 · 1970554717<10> · 109908191603107<15> · 203864078068831<15> · 440334654777631<15> · 11111111111111111111111<23> · 1595352086329224644348978893<28> · 30483187506704565749803762042596649<35> · 823799348530495507269035013254489287846904557<45> · 11033517351146841676953477818524172302174982813132058195800613488154982399<74> · C346

C346 = P40 · C306

P40 = 3343594428384401477244840930119560710799<40>

C306 = [450377923741970808148950296226613032400566155131568499041822243047158328146539757935075382025095148527133551625501785016893572159399932122711365422556992408548848991871421391458636588324840594526713717497745060394412424048730385747613423456947185389836707759125364034009038282054167764539431128404447755521<306>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 28, 2006

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(2·10157-11)/9 = (2)1561<157> = 1307 · 227076523 · 41803616430887<14> · C132

C132 = P57 · P76

P57 = 133550863188163178037852511255596245705285448630017952863<57>

P76 = 1341155421012836738800447933210092150861764010961882722169751753291060047181<76>

Number: trial
N=179112464145748746805374846504014682308278110369127593030548399981364056346062044214134328695106803134333980305291396012181814029203
  ( 132 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=133550863188163178037852511255596245705285448630017952863 (pp57)
 r2=1341155421012836738800447933210092150861764010961882722169751753291060047181 (pp76)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 73.93 hours.
Scaled time: 38.15 units (timescale=0.516).
Factorization parameters were as follows:
n: 179112464145748746805374846504014682308278110369127593030548399981364056346062044214134328695106803134333980305291396012181814029203
m: 10000000000000000000000000000000
c5: 200
c0: -11
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3000001)
Primes: RFBsize:216816, AFBsize:217237, largePrimes:5721932 encountered
Relations: rels:5704445, finalFF:502337
Max relations in full relation-set: 0
Initial matrix: 434118 x 502337 with sparse part having weight 34615373.
Pruned matrix : 404026 x 406260 with weight 25796728.
Total sieving time: 58.92 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 13.86 hours.
Time per square root: 0.43 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 73.93 hours.
 --------- CPU info (if available) ----------

Dec 26, 2006 (2nd)

By Yousuke Koide / GMP-ECM

(10591-1)/9 = (1)591<591> = 3 · 37 · 52009 · 2316842929<10> · 3707079392784283<16> · 79040479805615687465683<23> · 7478417919783613513048627<25> · 3599474961483053310878605135585111374469138078226023233589649293<64> · 750914105302558436752000930239222531800507092216032215426336586609291356367521996611125219417012181327241<105> · C343

C343 = P47 · P296

P47 = 14969825042462452779165494832955385273042368237<47>

P296 = 93696223430042503515209992685260973400653568450838728238629096649817396148168839486303968426912972256207993383920531938149701226310489022341502001395015749564990023360486520540430751646613322259497452737670770634148247428397820336451859675947344796100737871536080988501102119909768537672914822587<296>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 26, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

10173+9 = 1(0)1729<174> = 72 · 132 · 2515573 · 501355609 · 980959509182183<15> · C139

C139 = P56 · P84

P56 = 43621013613880185555572860857609538355052262229723114093<56>

P84 = 223762640416341510155833285985486831687028975194572884766702131594185801601877826383<84>

Number: 10009_173
N=9760753183879009646135889360607373608838812644875806219835912669099476964166309210938898210949322811535458367356231635756270419228754515619
  ( 139 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=43621013613880185555572860857609538355052262229723114093 (pp56)
 r2=223762640416341510155833285985486831687028975194572884766702131594185801601877826383 (pp84)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 366.05 hours.
Scaled time: 245.99 units (timescale=0.672).
Factorization parameters were as follows:
name: 10009_173
n: 9760753183879009646135889360607373608838812644875806219835912669099476964166309210938898210949322811535458367356231635756270419228754515619
m: 10000000000000000000000000000000000
c5: 1000
c0: 9
skew: 4
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10800001)
Primes: RFBsize:501962, AFBsize:500591, largePrimes:6442805 encountered
Relations: rels:6897642, finalFF:1125193
Max relations in full relation-set: 0
Initial matrix: 1002620 x 1125193 with sparse part having weight 66333627.
Pruned matrix : 895561 x 900638 with weight 50940551.
Total sieving time: 312.96 hours.
Total relation processing time: 1.54 hours.
Matrix solve time: 51.22 hours.
Time per square root: 0.33 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 366.05 hours.
 --------- CPU info (if available) ----------

Dec 25, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(22·10186-1)/3 = 7(3)186<187> = 7 · 67 · 331 · C182

C182 = P31 · C151

P31 = 5679860644357315055141531091607<31>

C151 = [8316927375912425675232689124341181802299980314993069805942537621415770313404508190180998100214135140699510365051647362171567079564114595515698728073621<151>]

Dec 25, 2006

By Alexander Mkrtychyan / ggnfs-0.77.1-20060513-win32 snfs

(79·10200-7)/9 = 8(7)200<201> = C201

C201 = P77 · P125

P77 = 12552959240238880156671133611977244215193772311428177779302543233603334526387<77>

P125 = 69925964147484466181286398935166368644230263837598388909290350401694329924977506307770282327347615709798206665285899283888971<125>

r1 = 69925964147484466181286398935166368644230263837598388909290350401694329924977506307770282327347615709798206665285899283888971 (p125)
r2 = 12552959240238880156671133611977244215193772311428177779302543233603334526387 (p77)

n: 877777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777
m: 10000000000000000000000000000000000000000
c5: 79
c0: -7
skew: 1
type: snfs
rlim: 30000000
alim: 30000000
lbpr: 30
lbpa: 30
mfbr: 54
mfba: 54
rlambda: 2.2
alambda: 2.2

sieved special-q: [13m;200m)

processed with different FBs:
lbpr/lbpa(m): 30/30, 40/40, 25/28, 10/30, 8/25

with 30m/30m

largePrimes: 5432730 , relations: 9596734, finalFF:4164004
Pruning matrix with wt=0.400
Initial matrix is 3717752 x 4164004 with sparse part having weight 98074369.
(total weight is 260467550)
Matrix pruned to 3156845 x 3175497 with weight 74485702.
Solved successfully.
Factorization found on 0,1,2,3,5,6,7,8,12,15 dependencies.
---
with 8m/25m
relations: 9337677

Matrix loaded: it is 1956035 x 1966635.
Original matrix had 2259738 columns.
Matrix difficulty is about 6309811.90
---
with 10m/30m

rels:8711565, initialFF:0, finalFF:2623788
Pruning matrix with wt=0.300                                                 
Initial matrix is 2524472 x 2634693 with sparse part having weight 187685347.
(total weight is 319960393)                                                  
Matrix pruned to 2459960 x 2472646 with weight 173289624.                    
Total elapsed time: 4296.44 seconds.
Solved: 715000 seconds.
Found only trivial dependencies
---

CPU RAM*
Process:          (GHz days**)(Max RSS)
----------------- ---------- ---------
gnfs-lasieve4I14e    2590       135MB
procrels             0.04       ??MB
matbuild             0.51       711MB
matsolve            59.80       393MB
sqrt                 0.10       ??MB
----------
total 2650.45

* data for successful factorization, w/o unsuccessful time
**1GHz day ~= 1 day on P3 1GHz

It's the largest number factored by GGNFS in our tables so far. Congratulations!

See also Records.

Dec 23, 2006

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(29·10151+7)/9 = 3(2)1503<152> = 32 · 11 · 28597727 · 11536947310113791<17> · C126

C126 = P57 · P70

P57 = 270934293156900183594932829079733518732282549735324741973<57>

P70 = 3641110758838558932109472437657733441598489296771623913270689827230257<70>

Number: trial
N=986501769751909411961170002152524580143175098932585822837399053431527946681209013531212654513345836260634733596897677783477061
  ( 126 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=270934293156900183594932829079733518732282549735324741973 (pp57)
 r2=3641110758838558932109472437657733441598489296771623913270689827230257 (pp70)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 44.89 hours.
Scaled time: 24.11 units (timescale=0.537).
Factorization parameters were as follows:
n: 986501769751909411961170002152524580143175098932585822837399053431527946681209013531212654513345836260634733596897677783477061
m: 1000000000000000000000000000000
c5: 290
c0: 7
skew: 1
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176383, largePrimes:5285780 encountered
Relations: rels:5059326, finalFF:406032
Max relations in full relation-set: 0
Initial matrix: 352752 x 406032 with sparse part having weight 40051505.
Pruned matrix : 328838 x 330665 with weight 26384199.
Total sieving time: 34.60 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 9.43 hours.
Time per square root: 0.44 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 44.89 hours.
 --------- CPU info (if available) ----------

Dec 21, 2006 (2nd)

By Bruce Dodson / GMP-ECM

(10329-1)/9 = (1)329<329> = 239 · 4649 · 35121409 · 1964089881669809395643<22> · 316362908763458525001406154038726382279<39> · C255

C255 = P44 · P212

P44 = 37633698993045258670863410188544865190871951<44>

P212 = 12175990136267618100062412451321121844977125961935799309046323782610299025911626168118737338968216243867796848803259561923384268932593679164283019843448278074106680143267046033732670400418363798167958964008153787<212>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 21, 2006

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 gnfs

(8·10189-71)/9 = (8)1881<189> = 17 · 521 · 30259 · 1773229 · 625516159 · 74065325249<11> · 345781643941<12> · 292088948280678446566609<24> · C120

C120 = P57 · P64

P57 = 222819387861185833526742714383975148891821116287140753681<57>

P64 = 1793981384058924893821212283538113799870047038762128239533917597<64>

Number: trial
N=399733833830372570282527388178208665038615477184692436745428272043328591004926149531322290011212791187921050965128424557
  ( 120 digits)
Divisors found:
 r1=222819387861185833526742714383975148891821116287140753681 (pp57)
 r2=1793981384058924893821212283538113799870047038762128239533917597 (pp64)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 137.34 hours.
Scaled time: 70.59 units (timescale=0.514).
Factorization parameters were as follows:
name: trial
n: 399733833830372570282527388178208665038615477184692436745428272043328591004926149531322290011212791187921050965128424557
skew: 103810.45
# norm 3.61e+16
c5: 24480
c4: -297199816
c3: -1382502805553921
c2: 583359676691979072
c1: 4891292481911117734813456
c0: -805602083914226446018861456
# alpha -5.79
Y1: 1319152663103
Y0: -110304165081665752089315
# Murphy_E 2.71e-10
# M 677867400259774854722433970520922671737645589615500042774504931605111288385311259262026269508935052221438696083141795
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 1
)
Primes: RFBsize:315948, AFBsize:315861, largePrimes:7647100 encountered
Relations: rels:7663422, finalFF:728749
Max relations in full relation-set: 0
Initial matrix: 631890 x 728749 with sparse part having weight 70820634.
Pruned matrix : 559071 x 562294 with weight 47741797.
Total sieving time: 115.87 hours.
Total relation processing time: 1.98 hours.
Matrix solve time: 18.16 hours.
Time per square root: 1.33 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 137.34 hours.
 --------- CPU info (if available) ----------

Dec 20, 2006

By Yousuke Koide / GMP-ECM

(10519-1)/9 = (1)519<519> = 3 · 37 · 347 · 1039 · 14533 · 21528169344472027<17> · 46194618816084982100679234312974236345786346173<47> · 32198046775720891593420454244946597764673353202694265726843479376953223792923910764829129134957786957553803<107> · C337

C337 = P41 · C297

P41 = 27556151204359553942685920311502726470093<41>

C297 = [216514826332371848322762555578613448056021292727337050311807751933401214900332242367650030603068301186552949610544037767579778110246878949700183394024838083707712222016266792473767108010610363941458066189164465028096213015007237587114703846104214458455026790737791798829124341877208532765964548801<297>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 19, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(4·10195-1)/3 = 1(3)195<196> = 919 · 2815092622300365139319<22> · C171

C171 = P37 · C135

P37 = 1616772208578912506305058572743036521<37>

C135 = [318773126025054291670957797550571273589430793561728712537650216394184484148701462662385921621852455278537160766090492754352887897550493<135>]

Dec 13, 2006

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 gnfs

(22·10189-1)/3 = 7(3)189<190> = 11419757 · 211184184100965653310251<24> · 5247840149796055570797016942289983138483<40> · C120

C120 = P58 · P63

P58 = 1826310899844750455890038379870677364429281210698126055419<58>

P63 = 317269164063171180914353224226880162452791136883719201604270747<63>

Number: test
N=579432132513201923188799315527338302692526852393619136492994578653670372434846049946697734504501561737781423227202527993
  ( 120 digits)
Divisors found:
 r1=1826310899844750455890038379870677364429281210698126055419 (pp58)
 r2=317269164063171180914353224226880162452791136883719201604270747 (pp63)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 168.31 hours.
Scaled time: 86.51 units (timescale=0.514).
Factorization parameters were as follows:
name: test
n: 579432132513201923188799315527338302692526852393619136492994578653670372434846049946697734504501561737781423227202527993
skew: 139462.11
# norm 3.25e+16
c5: 11580
c4: 229069215
c3: -1035517698637270
c2: -4821042319501375108
c1: 5743668297144006940945468
c0: 55004793579072396798085029760
# alpha -5.73
Y1: 318511853737
Y0: -137993553767881193160243
# Murphy_E 2.72e-10
# M 554922421292239917976551006198690292058518776280396076817314663820096833353889847215255004097124190281310884136455988765
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 1
)
Primes: RFBsize:315948, AFBsize:315877, largePrimes:7704379 encountered
Relations: rels:7756750, finalFF:729214
Max relations in full relation-set: 0
Initial matrix: 631903 x 729214 with sparse part having weight 72647660.
Pruned matrix : 559034 x 562257 with weight 50370839.
Total sieving time: 127.06 hours.
Total relation processing time: 2.11 hours.
Matrix solve time: 37.62 hours.
Time per square root: 1.52 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 168.31 hours.
 --------- CPU info (if available) ----------

Dec 9, 2006

By Yousuke Koide / GMP-ECM

(10525-1)/9 = (1)525<525> = 3 · 31 · 37 · 41 · 43 · 71 · 151 · 239 · 271 · 1933 · 4201 · 4649 · 21401 · 25601 · 79801 · 123551 · 2906161 · 10838689 · 35120401 · 435288001 · 30703738801<11> · 182521213001<12> · 625437743071<12> · 102598800232111471<18> · 18525843918490695886751<23> · 57802050308786191965409441<26> · 991474271662986957800680951<27> · 15763985553739191709164170940063151<35> · 54442267778748734853078961420361450411594669214709944589849727424959801<71> · C219

C219 = P43 · P177

P43 = 4401268665169140025731821222935000987130551<43>

P177 = 186243861617073980885505452610064684612129749201325732764290050555482397120222194754557152744180256772035732524938930620412706217059111157975741996041453725977078102648969888751<177>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 8, 2006

By Yousuke Koide / GMP-ECM

101570+1 = 1(0)15691<1571> = 101 · 3541 · 27961 · 94201 · 207241 · 364241 · 725341 · 3868481 · 5925181 · 7136984465461<13> · 9897542032658521861<19> · 3299894113715127521683201<25> · 28415783195151364586816438858689<32> · [34843277171045295933029273038354723106623942274167877028468403719880416626983967470194597426602476866146739051545997293765790832960699270182751148635492102757666140991780660761728507665838983382655047656132036840522542926670514159867455052679491682106619196393145144395922810075309<281>] · [22454709964066403559107101299163638986979610188692082356449728640968571102518022328651101898576409756577035423368397079217553950196221899081834254023564051072964208366536065240044733114930488490539175912345498307317005607293206687629316616437519512562887849697996400007055383520476112350625041785437433893185759269495528644287257542976626237862359274712053307068223025288940257963206877937004269547005395381663694800169300862181761155654556259088046735158689970456248973987896515914817649250776568167679167984601501635401188978971528638514795642673555900381<557>] · C601

C601 = C38 · C563

P38 = 29761675926781160150142940130769922081<38>

C563 = [54841596780936737488692802484103764893199543412517314910884339498475336340544513602803847141138049993277365711938350078305449521112799665314971784100223901313322213997598891691233982281136056563235763737920054337537589252252790187317793498535722907064286141023558151521345566500495986225152292478101551514112242118800165474543307117844620528591910013208031795692971895367931479213070339699089203649858831044946218140074943673591335814874740780675614559538251147498039991524177044527768326798950790851469961736228988133391948595383324310690985581463715403740244041<563>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 6, 2006

By JMB / GGNFS-0.77.1-20060513-pentium4 gnfs

(52·10162-7)/9 = 5(7)162<163> = 103 · 381011 · 946681999961618639<18> · 1221459109676013540068392985396141510503<40> · C99

C99 = P49 · P50

P49 = 8438134055835129687391374189732897448405262542547<49>

P50 = 15088866711043141207643579503789954343073186607831<50>

Number: N
N=127321880058410134937874685456288398513745339782992258022290739921523427135877001437678981240885557
  ( 99 digits)
Divisors found:
 r1=8438134055835129687391374189732897448405262542547 (pp49)
 r2=15088866711043141207643579503789954343073186607831 (pp50)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 10.37 hours.
Scaled time: 12.47 units (timescale=1.202).
Factorization parameters were as follows:
name: N
n: 127321880058410134937874685456288398513745339782992258022290739921523427135877001437678981240885557
skew: 9643.08
# norm 6.38e+13
c5: 21120
c4: 311152786
c3: -7904505190150
c2: -20055983778161829
c1: 316396256294438203240
c0: 657038077305820350429725
# alpha -5.88
Y1: 6126630781
Y0: -5702173808368634646
# Murphy_E 3.90e-09
# M 48616991791541821940847763123385691274109460482888757071970272973892514502053664826490013542985493
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 25000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1325001)
Primes: RFBsize:135072, AFBsize:134685, largePrimes:3786279 encountered
Relations: rels:3726881, finalFF:343538
Max relations in full relation-set: 28
Initial matrix: 269840 x 343538 with sparse part having weight 23488350.
Pruned matrix : 210003 x 211416 with weight 11580736.
Total sieving time: 9.46 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 0.60 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 10.37 hours.
 --------- CPU info (if available) ----------

Dec 5, 2006 (2nd)

By Yousuke Koide / GMP-ECM

101275+1 = 1(0)12741<1276> = 7 · 11 · 13 · 103 · 211 · 241 · 251 · 2161 · 4013 · 5051 · 9091 · 87211 · 102001 · 2254201 · 787223761 · 21993833369<11> · 291078844423<12> · 5516286288241<13> · 78875943472201<14> · 377526955309799110357<21> · 4270914986978327797975291<25> · 165564988462016408581266824201<30> · 201069283252703294533187911388251<33> · 216219010761333454086082249502131<33> · 10000099999999989999899999000000000100001<41> · 73610520788177438692703784333146668068451<41> · 160220794821014452066741918303580917664386555934641<51> · 175137725562337579790651749196120587807233668420015131<54> · 18103293041473682932576480240232418518560200896635102620265398137792101055968813301676929657920974523594103092467214576079129177678145686917465120573429118444647478671055435116260002205526892422444318067914692401<212> · C640

C640 = P31 · C610

P31 = 3228529113769803189332045176651<31>

C610 = [3097354754631152192863055596837469549881472079730729195187714434409989364909503064765447683515430510986536639597179836264932430193956149762360195438774298995821874636636744698536172506813008082807457406388860537959687636020341319784853558770432005208387396767738134036084111618022251571529736556157719626027902604153147271712627114289805521341260481893644390068847368181889709948803734022640623304583086765402879268652929209712202498645521483975053530060875008047953984644164792100095547532556321890446631612021472043959384922289262541118564945552603412445599209736618237653298506605224325056728379017839070851<610>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Dec 5, 2006

By Chris Monico / GGNFS-0.80.1

(8·10166-71)/9 = (8)1651<166> = 383 · 2887 · 55815703 · C153

C153 = P66 · P88

P66 = 141560894710474867768362601769154727182998709670386480583402999463<66>

P88 = 1017424571164532619839800754370275756667350476653199232325748520042742652983871482885049<88>

Dec 4, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(52·10162-7)/9 = 5(7)162<163> = 103 · 381011 · 946681999961618639<18> · C138

C138 = P40 · C99

P40 = 1221459109676013540068392985396141510503<40>

C99 = [127321880058410134937874685456288398513745339782992258022290739921523427135877001437678981240885557<99>]

Dec 4, 2006

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 gnfs

(2·10197+7)/9 = (2)1963<197> = 1621 · 141974874916545385999<21> · 2232227063658151482511<22> · 43577960060843625073819999006811<32> · C120

C120 = P54 · P67

P54 = 451432857691895875961752904940309204980009605290656993<54>

P67 = 2198844637377041314605159450464334723319742368211499399632756249129<67>

Number: test
N=992630718271618283341033880453341958342128797919820395767331503484855179680778194512437518931403483604755119718794009097
  ( 120 digits)
Divisors found:
 r1=451432857691895875961752904940309204980009605290656993 (pp54)
 r2=2198844637377041314605159450464334723319742368211499399632756249129 (pp67)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 129.21 hours.
Scaled time: 116.03 units (timescale=0.898).
Factorization parameters were as follows:
name: test
n: 992630718271618283341033880453341958342128797919820395767331503484855179680778194512437518931403483604755119718794009097
skew: 62269.20
# norm 1.52e+16
c5: 49140
c4: 7968213204
c3: -633335444221141
c2: -28081596552590686164
c1: 1107218209111382214603576
c0: 3534481494395924396324930335
# alpha -5.71
Y1: 2082926580031
Y0: -115098657175494752776662
# Murphy_E 2.89e-10
# M 504697680091632283507625193131377291428449168427719895603688346894281193132345617680896109259306414785276999124103053047
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 1
)
Primes: RFBsize:315948, AFBsize:316002, largePrimes:7651339 encountered
Relations: rels:7660346, finalFF:709798
Max relations in full relation-set: 0
Initial matrix: 632033 x 709798 with sparse part having weight 68225438.
Pruned matrix : 571453 x 574677 with weight 49175844.
Total sieving time: 117.39 hours.
Total relation processing time: 2.46 hours.
Matrix solve time: 8.63 hours.
Time per square root: 0.73 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 129.21 hours.
 --------- CPU info (if available) ----------

Dec 3, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

10167+9 = 1(0)1669<168> = 7 · 13 · 53 · 877 · 107171 · C156

C156 = P63 · P93

P63 = 578285490464535003292508528455551062720454372885574351763458327<63>

P93 = 381472790189423991118742839850166453080558585132743676617075753578582424625410729307533832287<93>

Number: 10009_167
N=220600179573565709368504340113503800147035985155837573658020885780015632167763060253476327002737780573173682022539160307617346454159538787082518830731603849
  ( 156 digits)
SNFS difficulty: 167 digits.
Divisors found:
 r1=578285490464535003292508528455551062720454372885574351763458327 (pp63)
 r2=381472790189423991118742839850166453080558585132743676617075753578582424625410729307533832287 (pp93)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 178.55 hours.
Scaled time: 109.27 units (timescale=0.612).
Factorization parameters were as follows:
name: 10009_167
n: 220600179573565709368504340113503800147035985155837573658020885780015632167763060253476327002737780573173682022539160307617346454159538787082518830731603849
m: 1000000000000000000000000000000000
c5: 100
c0: 9
skew: 3
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 6400001)
Primes: RFBsize:348513, AFBsize:348501, largePrimes:5953601 encountered
Relations: rels:6095608, finalFF:780802
Max relations in full relation-set: 0
Initial matrix: 697078 x 780802 with sparse part having weight 58659671.
Pruned matrix : 635534 x 639083 with weight 45096830.
Total sieving time: 153.34 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 24.20 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,167,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 178.55 hours.
 --------- CPU info (if available) ----------

November 2006

Nov 30, 2006

By Yousuke Koide / GMP-ECM

10693+1 = 1(0)6921<694> = 72 · 112 · 13 · 19 · 23 · 127 · 463 · 2689 · 4093 · 8317 · 8779 · 24179 · 52579 · 459691 · 590437 · 648649 · 909091 · 5274739 · 7444361 · 599144041 · 7093127053<10> · 183411838171<12> · 167940794674423<15> · 4539402627853030477<19> · 4924630160315726207887<22> · 136094982876222218559943<24> · 189772422673235585874485732659<30> · 141122524877886182282233539317796144938305111168717<51> · 803956626149925031112757148192164970057208483589704631288984124647169634536861236854805849361<93> · C340

C340 = P37 · C304

P37 = 1992239470584165788605948879953926371<37>

C304 = [4603184964734402473011132054574871768101384322818910046547748531884259027958267080342140972683398434286257762067178960349541200528618030240830132851782792895996117549551271815944610220256799485207702831103176523404549814416087930733678705878813258634914133639328074562923421485980890386223188429086045853<304>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 25, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1

10181+9 = 1(0)1809<182> = 192 · 663883229598790612639169<24> · C155

C155 = P34 · P122

P34 = 1972852879967879178904902617372213<34>

P122 = 21149806574944880773112316633222849030124545193584976920415264370446417132428148912879467226040854694780865097353747249277<122>

Nov 25, 2006

(25·10153-1)/3 = 8(3)153<154> = 13 · 135197 · 2146571139152631849772721<25> · C124

C124 = P37 · P87

P37 = 5393541826404464811149133316798078361<37>

P87 = 409533101044409088462546935359683563035408954430106138774390557254932874425892524573013<87>

Number: test
N=2208833909780146430450526784619613274824795703886149452683911106599445833442442008509253921427912994781563034774490439871693
  ( 124 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=5393541826404464811149133316798078361 (pp37)
 r2=409533101044409088462546935359683563035408954430106138774390557254932874425892524573013 (pp87)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 45.70 hours.
Scaled time: 20.70 units (timescale=0.453).
Factorization parameters were as follows:
n: 2208833909780146430450526784619613274824795703886149452683911106599445833442442008509253921427912994781563034774490439871693
m: 5000000000000000000000000000000
c5: 8
c0: -1
skew: 1
type: snfsFactor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1
)
Primes: RFBsize:176302, AFBsize:176058, largePrimes:5486213 encountered
Relations: rels:5409505, finalFF:403557
Max relations in full relation-set: 0
Initial matrix: 352425 x 403557 with sparse part having weight 25966191.
Pruned matrix : 321474 x 323300 with weight 19571072.
Total sieving time: 40.29 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 4.61 hours.
Time per square root: 0.41 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 45.70 hours.
 --------- CPU info (if available) ----------

Nov 22, 2006 (2nd)

By Yousuke Koide / GMP-ECM

10948+1 = 1(0)9471<949> = 73 · 137 · 170641 · 259121 · 73921249 · 99990001 · 57340465299866278297<20> · 52201702278536187174995982385190339542840861545149808159731432186088602525064098418072959548867561425890781539716300154490510721563835995312133388810104710726015330140180100712831208243369704593632493581391545465384002703669518350982143743148868128174561205103289746036643410805299221918913812703969<299> · C600

C600 = P34 · C566

P34 = 7766457159337484152304096869413649<34>

C566 = [13160605651726332711824188828231198974781817449170107220843017244925292787555978722379682670875489051063645457879559843216704892378318231053991874231132340342953316014469870226734932565533810812418846304981368619810054475856949401252258566231884568535957089879450035409745536613986710956990658406048668451352905354578528814334680077095374009876604796822907072341585310879826779147173972597386594702857046340165047037357564066043359340376061087990248909603666034420683949986454993266279058626732208248361954284400688841746207803537487889583649311294163392186504195737<566>]

10951+1 = 1(0)9501<952> = 7 · 11 · 13 · 3536453 · 12361733 · 23801700277<11> · 38405613853<11> · 68009240067498931554643059611689714176253<41> · [3057680777939340873709128976697248022108596412174873961787759431938025628869678008257542334571156935185136195428088353104791656344052255750374564165542466009514157472101863859769365418973638732536985785497459589011510554591776547201190016880328515272743477435703<262>] · C612

C612 = P33 · C580

P33 = 102570756454098763233742574501743<33>

C580 = [1172012803769621719252365058938965506852034255538255007373757985097563509193496805313736730077703309259876626566612185446011310800300769994399386653021937694266520577838243385384774401385492842581044381509749875841324524047036304574190605332513109880751219408698204055258625861509987926962423351385639646591127710298342927544330033130259244488289180348708388102537736901822082292342772957838450752598706597561798689276191118701886297433227752846591987632088979079350694789923207263820430089623986825840706751833030361951318310171887323357204388747832176545729713142420913287917917<580>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 22, 2006

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 gnfs

(8·10190-71)/9 = (8)1891<190> = 31 · 130631 · 1819798107166331261<19> · 79551780549152904467<20> · 516691240715476214463353437<27> · C119

C119 = P53 · P67

P53 = 13300943125012238261994582238288397549590803371621527<53>

P67 = 2206240654687068048051269685385242576181184555049501743077860013517<67>

Number: test
N=29345081468082457331289864149984090927414031492921287709615885718403229306209097275348874449736436951154902266428180459
  ( 119 digits)
Divisors found:
 r1=13300943125012238261994582238288397549590803371621527 (pp53)
 r2=2206240654687068048051269685385242576181184555049501743077860013517 (pp67)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 115.85 hours.
Scaled time: 102.41 units (timescale=0.884).
Factorization parameters were as follows:
name: test
n: 29345081468082457331289864149984090927414031492921287709615885718403229306209097275348874449736436951154902266428180459
skew: 165490.48
# norm 8.52e+16
c5: 23520
c4: 4956381832
c3: -2588841180336804
c2: -98228419725155829003
c1: 24426972850082958580741534
c0: 329035407253681913013070439181
# alpha -6.99
Y1: 6596018737759
Y0: -65950451013578676648460
# Murphy_E 3.21e-10
# M 10717586801923053861335544256814480236621499124251542442465227226576716907432907631440614918980170118495814277857599813
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 1
)
Primes: RFBsize:315948, AFBsize:315630, largePrimes:7562889 encountered
Relations: rels:7550887, finalFF:707603
Max relations in full relation-set: 0
Initial matrix: 631657 x 707603 with sparse part having weight 58660544.
Pruned matrix : 568239 x 571461 with weight 40931424.
Total sieving time: 99.73 hours.
Total relation processing time: 2.04 hours.
Matrix solve time: 13.35 hours.
Time per square root: 0.72 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 115.85 hours.
 --------- CPU info (if available) ----------

Nov 21, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

10165+9 = 1(0)1649<166> = 1117 · 29009 · 658851377041905167825719734691<30> · C128

C128 = P45 · P84

P45 = 405476469408529846096552458965513686928349281<45>

P84 = 115521003954448422975067155610313660368992451637991336302242072977588854951379884143<84>

Number: 10009_165
N=46841048825978561356978747541657395628214092574365582530196085768744223145586011443337758767687268157082158826887686500017351183
  ( 128 digits)
SNFS difficulty: 165 digits.
Divisors found:
 r1=405476469408529846096552458965513686928349281 (pp45)
 r2=115521003954448422975067155610313660368992451637991336302242072977588854951379884143 (pp84)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 109.42 hours.
Scaled time: 66.75 units (timescale=0.610).
Factorization parameters were as follows:
name: 10009_165
n: 46841048825978561356978747541657395628214092574365582530196085768744223145586011443337758767687268157082158826887686500017351183
m: 1000000000000000000000000000000000
c5: 1
c0: 9
skew: 2
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 4800001)
Primes: RFBsize:348513, AFBsize:348501, largePrimes:5792990 encountered
Relations: rels:5968131, finalFF:784837
Max relations in full relation-set: 0
Initial matrix: 697078 x 784837 with sparse part having weight 37403878.
Pruned matrix : 623951 x 627500 with weight 27859202.
Total sieving time: 92.53 hours.
Total relation processing time: 0.64 hours.
Matrix solve time: 15.99 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 109.42 hours.
 --------- CPU info (if available) ----------

Nov 18, 2006

GGNFS, ECM

10164+7 = 1(0)1637<165> = 23 · 379 · 7309 · 12698886469366937367312361817<29> · C129

C129 = P59 · P70

P59 = 89521774571891440725766027916492942543621141376778475868817<59>

P70 = 1380640691183467041940805484295021196494682231216695693196237567677271<70>

Number: N
N=123597404720906723070603691171193332824198996716018877260358883611797898401587603600800822151252138669606949349037994378388558407
  ( 129 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=89521774571891440725766027916492942543621141376778475868817 (pp59)
 r2=1380640691183467041940805484295021196494682231216695693196237567677271 (pp70)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 108.96 hours.
Scaled time: 196.45 units (timescale=1.803).
Factorization parameters were as follows:
name: 10^164+7
n: 123597404720906723070603691171193332824198996716018877260358883611797898401587603600800822151252138669606949349037994378388558407
skew: 1
c5: 10000
c4: 0
c3: 0
c2: 0
c1: 0
c0: 7
m: 100000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 47
mfba: 47
rlambda: 2.4
alambda: 2.4
qintsize: 10000Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 47/47
Sieved algebraic special-q in [2000000, 3440001)
Primes: RFBsize:283146, AFBsize:283882, largePrimes:5478274 encountered
Relations: rels:5452413, finalFF:639994
Max relations in full relation-set: 28
Initial matrix: 567092 x 639993 with sparse part having weight 49903993.
Pruned matrix : 517836 x 520735 with weight 38625421.
Total sieving time: 102.91 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 5.64 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,47,47,2.4,2.4,100000
total time: 108.96 hours.
 --------- CPU info (if available) ----------

10189+7 = 1(0)1887<190> = 59 · 2131 · C184

C184 = P37 · C148

P37 = 3159054500600988812343025556881597237<37>

C148 = [2517719943928015933161812602621927145881018065738612169370878161327571268215304182048198373665295635371013719764424373030947660451097961657183402859<148>]

Nov 17, 2006

ECM, GGNFS gnfs, GGNFS snfs

10198+7 = 1(0)1977<199> = 53 · 571 · 2311139052889<13> · C182

C182 = P40 · C142

P40 = 8981676309068044990065102914772467010071<40>

C142 = [1591858814267617896078250031041439073424924024742250415820682638458770032616911002606947871751429467343698998106474368448419328480312019748431<142>]

10167+7 = 1(0)1667<168> = 383 · 829 · 11591207077<11> · 73347288818135303<17> · 141440849542595046487975537469003983<36> · C100

C100 = P43 · P57

P43 = 2767384195308432800998826640296194868680403<43>

P57 = 946432516737087044441832532380571281421477140914013266779<57>

Number: Job
N=2619142388744198489221178578867314405367094314526442514421260482505307467083353062573172058928231937
  ( 100 digits)
Divisors found:
 r1=2767384195308432800998826640296194868680403 (pp43)
 r2=946432516737087044441832532380571281421477140914013266779 (pp57)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 8.60 hours.
Scaled time: 15.90 units (timescale=1.850).
Factorization parameters were as follows:
name: Job
n: 2619142388744198489221178578867314405367094314526442514421260482505307467083353062573172058928231937
skew: 8767.84
# norm 1.44e+14
c5: 39960
c4: 10073859
c3: -20284580639278
c2: -124696502742194
c1: 640938381477089277548
c0: -70909371893625224570160
# alpha -6.23
Y1: 8282152207
Y0: -9189813678694628131
# Murphy_E 3.31e-09
# M 1501514031735999265463075416290939630348073546891187053019114908450105058567508383777968256834056499
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 10000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1000001)
Primes: RFBsize:135072, AFBsize:135190, largePrimes:3875502 encountered
Relations: rels:3862298, finalFF:368646
Max relations in full relation-set: 28
Initial matrix: 270344 x 368646 with sparse part having weight 27249881.
Pruned matrix : 197174 x 198589 with weight 13002163.
Total sieving time: 7.84 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 0.56 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
gnfs,99,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 8.60 hours.
 --------- CPU info (if available) ----------

10162+7 = 1(0)1617<163> = 373 · 2897560744807<13> · 284650192636237<15> · C133

C133 = P53 · P81

P53 = 10547001703389742749894012224851142970616143003250831<53>

P81 = 308189700406341423181147659113543127355444178794088410677400174480962049420222271<81>

Number: N
N=3250477295152857483616387321204676144778298388584513349964512256612201623520987517912245791751948647147902352423129220799543585457201
  ( 133 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=10547001703389742749894012224851142970616143003250831 (pp53)
 r2=308189700406341423181147659113543127355444178794088410677400174480962049420222271 (pp81)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 79.92 hours.
Scaled time: 146.58 units (timescale=1.834).
Factorization parameters were as follows:
name: 10^162+7
n: 3250477295152857483616387321204676144778298388584513349964512256612201623520987517912245791751948647147902352423129220799543585457201
skew: 1
c5: 100
c4: 0
c3: 0
c2: 0
c1: 0
c0: 7
m: 100000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 47
mfba: 47
rlambda: 2.4
alambda: 2.4
qintsize: 10000Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 47/47
Sieved algebraic special-q in [2000000, 3100001)
Primes: RFBsize:283146, AFBsize:283097, largePrimes:5323478 encountered
Relations: rels:5295599, finalFF:640531
Max relations in full relation-set: 28
Initial matrix: 566309 x 640530 with sparse part having weight 39852777.
Pruned matrix : 512205 x 515100 with weight 29578204.
Total sieving time: 75.32 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 4.22 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,47,47,2.4,2.4,100000
total time: 79.92 hours.
 --------- CPU info (if available) ----------

Nov 16, 2006 (2nd)

ECM, GGNFS snfs

10184+7 = 1(0)1837<185> = 3623 · 14947 · 87049 · 81831577 · 27032969027<11> · 82572781465758823<17> · C137

C137 = P41 · P96

P41 = 13812625427379003182132914528083742520447<41>

P96 = 840787078677037174391304726181032112104649288083138093961703021109819735570348848562966541610497<96>

10178+7 = 1(0)1777<179> = 9779956187<10> · 15061360829503<14> · C155

C155 = P32 · C124

P32 = 28611712108180931576351076849383<32>

C124 = [2372766658386071479394164140981662985967236676580748175830928608025753371979903404338599883260199063087303313743132894406989<124>]

10159+7 = 1(0)1587<160> = 53 · 112071623517499016299<21> · 742724173649744073677<21> · C117

C117 = P57 · P60

P57 = 354663760028666201445811359498151123731853622090995334671<57>

P60 = 639122480641374580716319914410982978520319328839614482642443<60>

Number: N
N=226673582103118334143885828835544134495812108823761215777923161449519382625786039701855765820567862409213621214041253
  ( 117 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=354663760028666201445811359498151123731853622090995334671 (pp57)
 r2=639122480641374580716319914410982978520319328839614482642443 (pp60)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 79.32 hours.
Scaled time: 144.21 units (timescale=1.818).
Factorization parameters were as follows:
name: 10^159+7
n: 226673582103118334143885828835544134495812108823761215777923161449519382625786039701855765820567862409213621214041253
skew: 1
c5: 10000
c4: 0
c3: 0
c2: 0
c1: 0
c0: 7
m: 10000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 47
mfba: 47
rlambda: 2.4
alambda: 2.4
qintsize: 10000Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 47/47
Sieved algebraic special-q in [2000000, 3010001)
Primes: RFBsize:283146, AFBsize:283882, largePrimes:5284168 encountered
Relations: rels:5264200, finalFF:647445
Max relations in full relation-set: 28
Initial matrix: 567093 x 647445 with sparse part having weight 36687284.
Pruned matrix : 507077 x 509976 with weight 26304945.
Total sieving time: 75.21 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 3.76 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,47,47,2.4,2.4,100000
total time: 79.32 hours.
 --------- CPU info (if available) ----------

Nov 16, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

10163+9 = 1(0)1629<164> = 19 · 223 · 5851 · 88411 · 2701583 · 341165536047659<15> · C130

C130 = P62 · P69

P62 = 21282218145805492933175466817926209552898014184560253546079961<62>

P69 = 232597357666536071396985516556630866129009673684071188821993975702361<69>

Number: 10009_163
N=4950187705997164365857621953071374136800891903657774027127968403552641352310285897052129258301158018266953244295705051113242487921
  ( 130 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=21282218145805492933175466817926209552898014184560253546079961 (pp62)
 r2=232597357666536071396985516556630866129009673684071188821993975702361 (pp69)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 108.09 hours.
Scaled time: 72.85 units (timescale=0.674).
Factorization parameters were as follows:
name: 10009_163
n: 4950187705997164365857621953071374136800891903657774027127968403552641352310285897052129258301158018266953244295705051113242487921
m: 100000000000000000000000000000000
c5: 1000
c0: 9
skew: 2
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4650001)
Primes: RFBsize:315948, AFBsize:315061, largePrimes:5821181 encountered
Relations: rels:5959009, finalFF:712522
Max relations in full relation-set: 0
Initial matrix: 631076 x 712522 with sparse part having weight 38928691.
Pruned matrix : 568676 x 571895 with weight 30046734.
Total sieving time: 93.04 hours.
Total relation processing time: 0.55 hours.
Matrix solve time: 14.28 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 108.09 hours.
 --------- CPU info (if available) ----------

Nov 15, 2006 (4th)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

10198+9 = 1(0)1979<199> = 225961 · 124678768297051697<18> · C176

C176 = P40 · C136

P40 = 9690036302476528221435163969533038158217<40>

C136 = [3663098565111345395412929971728350097530716199796536338138921821753864966157300030614431362264492489238686784881314038315456171995557481<136>]

Nov 15, 2006 (3rd)

ECM, GGNFS gnfs

10167+7 = 1(0)1667<168> = 383 · 829 · 11591207077<11> · 73347288818135303<17> · C135

C135 = P36 · C100

P36 = 141440849542595046487975537469003983<36>

C100 = [2619142388744198489221178578867314405367094314526442514421260482505307467083353062573172058928231937<100>]

10172+7 = 1(0)1717<173> = 53 · 191938429 · 331415043556425612418268467<27> · 29849566288772955116003809849<29> · C107

C107 = P36 · P72

P36 = 519653203407133915489828689837558457<36>

P72 = 191222214126927932611849860371304656786463312566330254859420091542285581<72>

Number: Job
N=99369236133662997498046538437800014670090090351377956564066351892312953445624960793469992991788770475708517
  ( 107 digits)
Divisors found:
 r1=519653203407133915489828689837558457 (pp36)
 r2=191222214126927932611849860371304656786463312566330254859420091542285581 (pp72)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 42.52 hours.
Scaled time: 77.09 units (timescale=1.813).
Factorization parameters were as follows:
name: Job
n: 99369236133662997498046538437800014670090090351377956564066351892312953445624960793469992991788770475708517
skew: 32421.20
# norm 1.79e+14
c5: 4320
c4: -163080001
c3: -12032430761768
c2: 161855080600218078
c1: 6064058439032775643530
c0: -35072402530886590558603860
# alpha -5.01
Y1: 3652301983
Y0: -470276921272562053703
# Murphy_E 1.43e-09
# M 87827777070393059920832879408730568231186274136573932948700867604413699478459017235755435042804514255498026
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2600001)
Primes: RFBsize:183072, AFBsize:183374, largePrimes:4651120 encountered
Relations: rels:4941887, finalFF:559453
Max relations in full relation-set: 28
Initial matrix: 366521 x 559453 with sparse part having weight 52068998.
Pruned matrix : 243802 x 245698 with weight 30090006.
Total sieving time: 39.81 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 2.37 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 42.52 hours.
 --------- CPU info (if available) ----------

Nov 15, 2006 (2nd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 snfs, gnfs

(4·10179-1)/3 = 1(3)179<180> = 1997 · C176

C176 = P48 · P56 · P73

P48 = 253295417124993861031296281669624054174266850009<48>

P56 = 81068109172017008610971560943119572493804243852629380849<56>

P73 = 3251496537693114498458159549987550518732739228349528825468592962030431329<73>

I had to do 2 runs of ggnfs. the first time with snfs crashed but gave me the factor (no output info):

r1 = 81068109172017008610971560943119572493804243852629380849

the second run gave:

Number: test
N=823589171795450761291859546035443959370517761467932302810461890880519047747545879286033387788030175748017974504417531961
  ( 120 digits)
Divisors found:
 r1=253295417124993861031296281669624054174266850009 (pp48)
 r2=3251496537693114498458159549987550518732739228349528825468592962030431329 (pp73)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 165.08 hours.
Scaled time: 79.07 units (timescale=0.479).
Factorization parameters were as follows:
name: test
n: 823589171795450761291859546035443959370517761467932302810461890880519047747545879286033387788030175748017974504417531961
skew: 46590.16
# norm 3.33e+16
c5: 84360
c4: -8202502714
c3: -1387888129134160
c2: 11428243751837448755
c1: 653112455495502668312670
c0: -1357104695023944835862993736
# alpha -5.75
Y1: 1171896562859
Y0: -99521041163549129211445
# Murphy_E 2.83e-10
# M 548991466575707693749971971104244681063225514790280051859897817838862609292117688812115775794054142884095234452671759882
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4530001)
Primes: RFBsize:315948, AFBsize:315899, largePrimes:7613366 encountered
Relations: rels:7587614, finalFF:708900
Max relations in full relation-set: 0
Initial matrix: 631935 x 708900 with sparse part having weight 75263515.
Pruned matrix : 573365 x 576588 with weight 52935839.
Total sieving time: 116.62 hours.
Total relation processing time: 2.12 hours.
Matrix solve time: 44.85 hours.
Time per square root: 1.49 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 165.08 hours.
 --------- CPU info (if available) ----------

Nov 15, 2006

ECM, GGNFS

10172+7 = 1(0)1717<173> = 53 · 191938429 · 29849566288772955116003809849<29> · C134

C134 = P27 · C107

P27 = 331415043556425612418268467<27>

C107 = [99369236133662997498046538437800014670090090351377956564066351892312953445624960793469992991788770475708517<107>]

10160+7 = 1(0)1597<161> = 5189 · 13931 · C153

C153 = P39 · P115

P39 = 122227155285903457182666321837042118481<39>

P115 = 1131791252435748089591200016536616025548232549159948520144370768984943188816711312258317968241365841533122026175233<115>

Number: N
N=138335625162691341167897685422270671661929201791407611881807314548748014866486962233917823022226979738077817358213143076843544579810311147393164053781073
  ( 153 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=122227155285903457182666321837042118481 (pp39)
 r2=1131791252435748089591200016536616025548232549159948520144370768984943188816711312258317968241365841533122026175233 (pp115)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 56.43 hours.
Scaled time: 102.87 units (timescale=1.823).
Factorization parameters were as follows:
name: 10^160+7
n: 138335625162691341167897685422270671661929201791407611881807314548748014866486962233917823022226979738077817358213143076843544579810311147393164053781073
skew: 1
c5: 1
c4: 0
c3: 0
c2: 0
c1: 0
c0: 7
m: 100000000000000000000000000000000
type: snfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 47
mfba: 47
rlambda: 2.4
alambda: 2.4
qintsize: 10000Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 47/47
Sieved algebraic special-q in [2000000, 2670001)
Primes: RFBsize:283146, AFBsize:283082, largePrimes:5150741 encountered
Relations: rels:5142908, finalFF:651842
Max relations in full relation-set: 28
Initial matrix: 566294 x 651842 with sparse part having weight 31982635.
Pruned matrix : 495098 x 497993 with weight 21734435.
Total sieving time: 53.34 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 2.81 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,47,47,2.4,2.4,100000
total time: 56.43 hours.
 --------- CPU info (if available) ----------

10163+7 = 1(0)1627<164> = 751 · 65793577 · 27552936913<11> · C142

C142 = P29 · P114

P29 = 41544031117073918433594752857<29>

P114 = 176807234786569338582523829881595287129675124275481575083841952162459544421538630230247564397123546438974833341401<114>

10190+7 = 1(0)1897<191> = 197 · 8317 · 127747 · 2829317 · 72279887 · 142368179 · 32918013164986911675034336901<29> · C128

C128 = P33 · P40 · P56

P33 = 539949550351081895686956255135631<33>

P40 = 1228769056329366897148936730013579567923<40>

P56 = 75135865542155053300373496564980174488903912122130011293<56>

Number: Job
N=92324626598724059947748948540572122551209847634089980073675521676448234822325379449790050554439
  ( 95 digits)
Divisors found:
 r1=1228769056329366897148936730013579567923 (pp40)
 r2=75135865542155053300373496564980174488903912122130011293 (pp56)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 7.99 hours.
Scaled time: 14.24 units (timescale=1.783).
Factorization parameters were as follows:
name: Job
n:  92324626598724059947748948540572122551209847634089980073675521676448234822325379449790050554439
m:  6052030409229541070633
deg: 4
c4: 68819760
c3: 523795266544
c2: 139484912789525633
c1: -2180424713438310492
c0: -186745021330265119032750
skew: 1635.250
type: gnfs
# adj. I(F,S) = 54.627
# E(F1,F2) = 3.776995e-05
# GGNFS version 0.77.1-20060513-athlon-xp polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1163561373.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 10000
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 710001)
Primes: RFBsize:92938, AFBsize:92932, largePrimes:1912725 encountered
Relations: rels:2016957, finalFF:253729
Max relations in full relation-set: 28
Initial matrix: 185949 x 253729 with sparse part having weight 21506926.
Pruned matrix : 157656 x 158649 with weight 11234793.
Total sieving time: 7.51 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.37 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 7.99 hours.
 --------- CPU info (if available) ----------

Nov 14, 2006

Table 10n+7 was extended up to 200. Remaining 27 composite numbers passed GMP-ECM 5e4, 200 times.

Nov 13, 2006

By Yousuke Koide / GMP-ECM

10833+1 = 1(0)8321<834> = 11 · 103 · 197 · 4013 · 609757 · 909091 · 1868879293<10> · 21993833369<11> · 548804832033845773<18> · 5673320472670315859129<22> · 5076141624365532994918781726395939035533<40> · 103746647830421551242486430622636901002236971549990724717454338463<66> · C649

C649 = P33 · C616

P33 = 319824888758480762691339433102367<33>

C616 = [9343574757071792228077434930303221486762476778121423097668652970221821077208958882520710694973513468637733064223309368796024481695602816312019386654632567213658969755944051068351580955006486536290343866440351081883829574626125117079334890962510199844585257226508476000771679651748353042521718234285875124709637675154006541487681538322505116765623644263842843482492186160214527982947155983758385307885977270250086778447914204388035736686604684225936655586388904938583434467168465052464330580158448779970125201984020099036622848607669011680030732134695357973131485493571097432551074841523783382709012137194976990504023<616>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 11, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

10159+9 = 1(0)1589<160> = 499 · C157

C157 = P41 · P116

P41 = 25186187487813621841913773118823816536903<41>

P116 = 79567739936888292295596294112639084452134355303693380058498429690502044773614914416009946349393011410085895946365397<116>

Number: 10009_159
N=2004008016032064128256513026052104208416833667334669338677354709418837675350701402805611222444889779559118236472945891783567134268537074148296593186372745491
  ( 157 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=25186187487813621841913773118823816536903 (pp41)
 r2=79567739936888292295596294112639084452134355303693380058498429690502044773614914416009946349393011410085895946365397 (pp116)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 76.30 hours.
Scaled time: 51.50 units (timescale=0.675).
Factorization parameters were as follows:
name: 10009_159
n: 2004008016032064128256513026052104208416833667334669338677354709418837675350701402805611222444889779559118236472945891783567134268537074148296593186372745491
m: 100000000000000000000000000000000
c5: 1
c0: 90
skew: 2.46
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3700001)
Primes: RFBsize:283146, AFBsize:283222, largePrimes:5625429 encountered
Relations: rels:5626182, finalFF:634517
Max relations in full relation-set: 0
Initial matrix: 566432 x 634517 with sparse part having weight 41516401.
Pruned matrix : 514796 x 517692 with weight 29630223.
Total sieving time: 63.99 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 11.68 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 76.30 hours.
 --------- CPU info (if available) ----------

Nov 11, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

10196+9 = 1(0)1959<197> = 409 · 24509 · 24568382659368173<17> · C173

C173 = P47 · C126

P47 = 44401499461295046411183451748843306897700065477<47>

C126 = [914485651586525533357484598772878668557145673386605657821723195587345693907083602731033750236232276619318600012074196323998309<126>]

Nov 10, 2006 (2nd)

By JMB / GGNFS-0.77.1-20060513-athlon-xp

10164+3 = 1(0)1633<165> = 31 · 72661 · 34398655802053<14> · C145

C145 = P37 · P108

P37 = 4075389007177818510425958607451799493<37>

P108 = 316684198450990245853796446126980851388377309015444532754266605694332398770449162432993865124395996668140177<108>

Number: Job
N=1290611301114084388660783119477994372937028016800687221470364447812500253084007981362043316535746405003945717855762764937726394301548860221530261
  ( 145 digits)
SNFS difficulty: 164 digits.
Divisors found:
 r1=4075389007177818510425958607451799493 (pp37)
 r2=316684198450990245853796446126980851388377309015444532754266605694332398770449162432993865124395996668140177 (pp108)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 100.00 hours.
Scaled time: 183.40 units (timescale=1.834).
Factorization parameters were as follows:
name: 10164+3
n: 1290611301114084388660783119477994372937028016800687221470364447812500253084007981362043316535746405003945717855762764937726394301548860221530261
skew: 2
c5: 10000
c4: 0
c3: 0
c2: 0
c1: 0
c0: 3
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
qintsize: 20000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3560001)
Primes: RFBsize:216816, AFBsize:215581, largePrimes:6043156 encountered
Relations: rels:6143733, finalFF:509004
Max relations in full relation-set: 28
Initial matrix: 432461 x 509004 with sparse part having weight 61390523.
Pruned matrix : 403943 x 406169 with weight 47820336.
Total sieving time: 95.02 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 4.55 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,164,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 100.00 hours.
 --------- CPU info (if available) ----------

Nov 10, 2006

By JMB / GMP-ECM 6.1.1 B1=11000000

10185+9 = 1(0)1849<186> = 7 · 13 · 229846571 · 1275374768743384691<19> · 2601396325020582930122538337721<31> · C127

C127 = P34 · P93

P34 = 4277579851308146456603644470753277<34>

P93 = 336882235159639253303716540858681759020527027546821580356810549616254660757873213006852842127<93>

Nov 9, 2006

By JMB / GGNFS-0.77.1-20060513-athlon-xp

10161+3 = 1(0)1603<162> = 13384170461<11> · 821803718884451141<18> · C133

C133 = P35 · P38 · P61

P35 = 55689458843269071823219640216823151<35>

P38 = 31215643436669954814773315727432097321<38>

P61 = 5229921251194894076800387430777663894801697083886414650870293<61>

Number: Job
N=9091602483434276582331722452653348048116352758006019425620053354886938383960657549356599224903299469115788497391900843527220038162003
  ( 133 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=55689458843269071823219640216823151 (pp35)
 r2=31215643436669954814773315727432097321 (pp38)
 r3=5229921251194894076800387430777663894801697083886414650870293 (pp61)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 72.01 hours.
Scaled time: 131.70 units (timescale=1.829).
Factorization parameters were as follows:
name: 10^161+3
n: 9091602483434276582331722452653348048116352758006019425620053354886938383960657549356599224903299469115788497391900843527220038162003
skew: 1
c5: 10
c4: 0
c3: 0
c2: 0
c1: 0
c0: 3
m: 100000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
qintsize: 20000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [1250000, 2670001)
Primes: RFBsize:183072, AFBsize:183096, largePrimes:3724852 encountered
Relations: rels:3939067, finalFF:424694
Max relations in full relation-set: 28
Initial matrix: 366234 x 424694 with sparse part having weight 49131957.
Pruned matrix : 345897 x 347792 with weight 38131203.
Total sieving time: 68.36 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 3.38 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,2500000,2500000,26,26,47,47,2.3,2.3,100000
total time: 72.01 hours.
 --------- CPU info (if available) ----------

10163+3 = 1(0)1623<164> = 13 · 17 · 23 · 1249 · C157

C157 = P48 · P110

P48 = 117231589899843222398103253015079733333423108013<48>

P110 = 13436086681281923664269307468592392032596002915199098937195994818328776362541162076537167449224244474925441693<110>

Number: Job
N=1575133803678788003843956534497714244580791526788221842474963641973976584375901271873292456510949463879582910869321071651734135685491143258891984726872586009
  ( 157 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=117231589899843222398103253015079733333423108013 (pp48)
 r2=13436086681281923664269307468592392032596002915199098937195994818328776362541162076537167449224244474925441693 (pp110)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 82.88 hours.
Scaled time: 151.59 units (timescale=1.829).
Factorization parameters were as follows:
name: 10^163+3
n: 1575133803678788003843956534497714244580791526788221842474963641973976584375901271873292456510949463879582910869321071651734135685491143258891984726872586009
skew: 2
c5: 1000
c4: 0
c3: 0
c2: 0
c1: 0
c0: 3
m: 100000000000000000000000000000000
type: snfs
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
qintsize: 20000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3140001)
Primes: RFBsize:216816, AFBsize:216791, largePrimes:5926753 encountered
Relations: rels:5958971, finalFF:493581
Max relations in full relation-set: 28
Initial matrix: 433673 x 493581 with sparse part having weight 56882975.
Pruned matrix : 410829 x 413061 with weight 45472614.
Total sieving time: 78.17 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 4.35 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 82.88 hours.
 --------- CPU info (if available) ----------

Nov 8, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

10156+9 = 1(0)1559<157> = 149 · 12577 · 17257 · C146

C146 = P42 · P46 · P59

P42 = 383981700070505184610830877165967851949977<42>

P46 = 1245447807805174631186627010827838254868677573<46>

P59 = 64659942178328230286420137484904735606524156752097366805889<59>

Number: 10009_156
N=30922270259706918541273994104183262432014945588155444494107881550493940763192232543551971147645731712248062829627325026727144031780555472245719869
  ( 146 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=383981700070505184610830877165967851949977 (pp42)
 r2=1245447807805174631186627010827838254868677573 (pp46)
 r3=64659942178328230286420137484904735606524156752097366805889 (pp59)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 51.11 hours.
Scaled time: 31.23 units (timescale=0.611).
Factorization parameters were as follows:
name: 10009_156
n: 30922270259706918541273994104183262432014945588155444494107881550493940763192232543551971147645731712248062829627325026727144031780555472245719869
m: 10000000000000000000000000000000
c5: 10
c0: 9
skew: 2
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216791, largePrimes:5577567 encountered
Relations: rels:5506820, finalFF:485813
Max relations in full relation-set: 0
Initial matrix: 433674 x 485813 with sparse part having weight 32645438.
Pruned matrix : 399323 x 401555 with weight 25027274.
Total sieving time: 43.95 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 6.64 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 51.11 hours.
 --------- CPU info (if available) ----------

Nov 8, 2006

By JMB / GGNFS-0.77.1-20060513-athlon-xp

10158+3 = 1(0)1573<159> = 19 · 181 · 42367021 · C147

C147 = P41 · P107

P41 = 56562887171939352687533078968873450917397<41>

P107 = 12134121153120891677860517234609605899226468109948574988494138769478971577913168918124640360449818429183421<107>

Number: Job
N=686340925714619629813773407842849504154136513898346137695447647130283089746715169548133228993215230649747386989970687059844292811941864550032875137
  ( 147 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=56562887171939352687533078968873450917397 (pp41)
 r2=12134121153120891677860517234609605899226468109948574988494138769478971577913168918124640360449818429183421 (pp107)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 73.73 hours.
Scaled time: 136.77 units (timescale=1.855).
Factorization parameters were as follows:
name: 10^158+3
n: 686340925714619629813773407842849504154136513898346137695447647130283089746715169548133228993215230649747386989970687059844292811941864550032875137
skew: 1
c5: 1000
c4: 0
c3: 0
c2: 0
c1: 0
c0: 3
m: 10000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
qintsize: 20000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [1000000, 2480001)
Primes: RFBsize:148933, AFBsize:149150, largePrimes:2286233 encountered
Relations: rels:2556588, finalFF:336729
Max relations in full relation-set: 28
Initial matrix: 298149 x 336729 with sparse part having weight 39120057.
Pruned matrix : 285932 x 287486 with weight 31441874.
Total sieving time: 71.27 hours.
Total relation processing time: 0.11 hours.
Matrix solve time: 2.27 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,2000000,2000000,25,25,46,46,2.3,2.3,100000
total time: 73.73 hours.
 --------- CPU info (if available) ----------

10159+3 = 1(0)1583<160> = 27481 · 21857807 · 50342736358471<14> · C134

C134 = P57 · P77

P57 = 365088561996659184739622906690610283957025786636979183011<57>

P77 = 90578648466036397927895461652215642063389691714124448760625362551232618315489<77>

Number: Job
N=33069228516066127828095467188710501944989981714508049208067552235661273476089033705608855208287520512577078328935684044968578266957379
  ( 134 digits)
SNFS difficulty: 159 digits.
Divisors found:
 r1=365088561996659184739622906690610283957025786636979183011 (pp57)
 r2=90578648466036397927895461652215642063389691714124448760625362551232618315489 (pp77)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 67.02 hours.
Scaled time: 123.99 units (timescale=1.850).
Factorization parameters were as follows:
name: 10^159+3
n: 33069228516066127828095467188710501944989981714508049208067552235661273476089033705608855208287520512577078328935684044968578266957379
skew: 1
c5: 10000
c4: 0
c3: 0
c2: 0
c1: 0
c0: 3
m: 10000000000000000000000000000000
type: snfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 47
mfba: 47
rlambda: 2.3
alambda: 2.3
qintsize: 20000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 47/47
Sieved algebraic special-q in [1250000, 2510001)
Primes: RFBsize:183072, AFBsize:182136, largePrimes:3638522 encountered
Relations: rels:3804343, finalFF:422771
Max relations in full relation-set: 28
Initial matrix: 365272 x 422771 with sparse part having weight 42045423.
Pruned matrix : 343496 x 345386 with weight 31618122.
Total sieving time: 63.83 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 2.94 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,159,5,0,0,0,0,0,0,0,0,2500000,2500000,26,26,47,47,2.3,2.3,100000
total time: 67.02 hours.
 --------- CPU info (if available) ----------

Nov 7, 2006 (2nd)

By JMB / GGNFS-0.77.1-20060513-athlon-xp

10154+3 = 1(0)1533<155> = 7 · 3963860422906687<16> · C138

C138 = P69 · P70

P69 = 149423443005462551721301379502643750647745574130417390277014997318813<69>

P70 = 2411930932482573111391518332280642017351271749416029057705410264299159<70>

Number: Job
N=360399024222921909270235911303974311261988445519545605666583983972180980784491046755349332963748845118776491140122019197845700079530778267
  ( 138 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=149423443005462551721301379502643750647745574130417390277014997318813 (pp69)
 r2=2411930932482573111391518332280642017351271749416029057705410264299159 (pp70)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 45.44 hours.
Scaled time: 79.88 units (timescale=1.758).
Factorization parameters were as follows:
name: 10^154+3
n: 360399024222921909270235911303974311261988445519545605666583983972180980784491046755349332963748845118776491140122019197845700079530778267
skew: 1
c5: 10000
c4: 0
c3: 0
c2: 0
c1: 0
c0: 3
m: 1000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
qintsize: 20000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [1000000, 1860001)
Primes: RFBsize:148933, AFBsize:148285, largePrimes:2191969 encountered
Relations: rels:2400183, finalFF:341909
Max relations in full relation-set: 28
Initial matrix: 297282 x 341909 with sparse part having weight 30111148.
Pruned matrix : 280747 x 282297 with weight 22030937.
Total sieving time: 43.61 hours.
Total relation processing time: 0.10 hours.
Matrix solve time: 1.66 hours.
Time per square root: 0.07 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2000000,2000000,25,25,46,46,2.3,2.3,100000
total time: 45.44 hours.
 --------- CPU info (if available) ----------

Nov 7, 2006

By JMB / GGNFS-0.77.1-20060513-pentium4

10153+3 = 1(0)1523<154> = 29 · 67 · C150

C150 = P42 · P109

P42 = 376761827601512787036094285501223811506077<42>

P109 = 1366030211688845889671647585845412059913391266235993559996651995578056259930708624299661596143715652351500473<109>

Number: N
N=514668039114770972722593926917138445702521873391662377766340710241893978383942357179619145651055069480185280494081317550180133813690169840452907874421
  ( 150 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=376761827601512787036094285501223811506077 (pp42)
 r2=1366030211688845889671647585845412059913391266235993559996651995578056259930708624299661596143715652351500473 (pp109)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 43.84 hours.
Scaled time: 39.81 units (timescale=0.908).
Factorization parameters were as follows:
name: 10^153+3
n: 514668039114770972722593926917138445702521873391662377766340710241893978383942357179619145651055069480185280494081317550180133813690169840452907874421
skew: 1
c5: 1000
c4: 0
c3: 0
c2: 0
c1: 0
c0: 3
m: 1000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
qintsize: 20000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [1000000, 1840001)
Primes: RFBsize:148933, AFBsize:149150, largePrimes:2192600 encountered
Relations: rels:2396730, finalFF:336011
Max relations in full relation-set: 28
Initial matrix: 298149 x 336011 with sparse part having weight 30541850.
Pruned matrix : 283874 x 285428 with weight 23315534.
Total sieving time: 40.28 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 3.09 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2000000,2000000,25,25,46,46,2.3,2.3,100000
total time: 43.84 hours.
 --------- CPU info (if available) ----------

Nov 6, 2006 (4th)

By JMB / GGNFS-0.77.1-20060513-pentium4

10148+3 = 1(0)1473<149> = 7 · 5107 · 2157481 · 330473699221<12> · C126

C126 = P44 · P83

P44 = 10179078449976201273125762528418361136218099<44>

P83 = 38542844162420837355114416087578812267010926136810640691082927212474664077128617153<83>

Number: N
N=392330634414488974731222398448381945764017396400978605812774161961346108149639752235416711259679426819944874434795840080452147
  ( 126 digits)
SNFS difficulty: 148 digits.
Divisors found:
 r1=10179078449976201273125762528418361136218099 (pp44)
 r2=38542844162420837355114416087578812267010926136810640691082927212474664077128617153 (pp83)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 57.98 hours.
Scaled time: 52.13 units (timescale=0.899).
Factorization parameters were as follows:
name: 10^148+3
n: 392330634414488974731222398448381945764017396400978605812774161961346108149639752235416711259679426819944874434795840080452147
skew: 1
c5: 1000
c4: 0
c3: 0
c2: 0
c1: 0
c0: 3
m: 100000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
qintsize: 25000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [750000, 3225001)
Primes: RFBsize:114155, AFBsize:114347, largePrimes:2340638 encountered
Relations: rels:2602625, finalFF:264638
Max relations in full relation-set: 28
Initial matrix: 228568 x 264638 with sparse part having weight 32674494.
Pruned matrix : 218631 x 219837 with weight 25690126.
Total sieving time: 55.13 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 2.20 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,148,5,0,0,0,0,0,0,0,0,1500000,1500000,25,25,46,46,2.3,2.3,100000
total time: 57.98 hours.
 --------- CPU info (if available) ----------

10150+3 = 1(0)1493<151> = 4993 · 909599715918703<15> · C132

C132 = P58 · P75

P58 = 1312781142610220555791731442886796814088531285959604282653<58>

P75 = 167724222837335381788066096688395065923446964535816909617221682818743071569<75>

Number: N
N=220185196899808391220278424731994458406334096942740234561275226231125986856866486145907394280837878238350277133007976381084084192557
  ( 132 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=1312781142610220555791731442886796814088531285959604282653 (pp58)
 r2=167724222837335381788066096688395065923446964535816909617221682818743071569 (pp75)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 48.22 hours.
Scaled time: 44.70 units (timescale=0.927).
Factorization parameters were as follows:
name: 10^148+3
n: 220185196899808391220278424731994458406334096942740234561275226231125986856866486145907394280837878238350277133007976381084084192557
skew: 1
c5: 1
c4: 0
c3: 0
c2: 0
c1: 0
c0: 3
m: 1000000000000000000000000000000
type: snfs
rlim: 2000000
alim: 2000000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
qintsize: 50000
Factor base limits: 2000000/2000000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [1000000, 2050001)
Primes: RFBsize:148933, AFBsize:148825, largePrimes:2182381 encountered
Relations: rels:2406623, finalFF:361245
Max relations in full relation-set: 28
Initial matrix: 297822 x 361245 with sparse part having weight 30716807.
Pruned matrix : 259122 x 260675 with weight 20259735.
Total sieving time: 45.43 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 2.21 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,2000000,2000000,25,25,46,46,2.3,2.3,100000
total time: 48.22 hours.
 --------- CPU info (if available) ----------

Nov 6, 2006 (3rd)

By Hoogendoorn / GNFS

10372+1 = 1(0)3711<373> = 73 · 137 · 1489 · 700849 · 11110153 · 99990001 · 5419392721<10> · 640543322297<12> · 1220725699657<13> · 27908132670449<14> · 42367299139993<14> · 384705444182230291105649<24> · 16584440161215846282167330487128069170776821649169<50> · 97645954668018846467287180866355758374263120864803042536883990817097<68> · C143

C143 = P68 · P76

P68 = 23140616853203983900922551785166946660605063239337678349130406077337<68>

P76 = 1194053240550935343606131291791034479414833114386116350011658511441777011841<76>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 6, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

10154+9 = 1(0)1539<155> = 532 · 173 · C149

C149 = P56 · P93

P56 = 61663679403222757509249170662209857982446222255631728629<56>

P93 = 333712690670157588584103442128065072187953963434123029832366265075137324719065556444993079553<93>

Number: 10009_154
N=20577952370271443769716250614766327061859382620272987116144020973049055780655490094802626569840541447082766582228468773986175731597651644075504622837
  ( 149 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=61663679403222757509249170662209857982446222255631728629 (pp56)
 r2=333712690670157588584103442128065072187953963434123029832366265075137324719065556444993079553 (pp93)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 46.83 hours.
Scaled time: 31.57 units (timescale=0.674).
Factorization parameters were as follows:
name: 10009_154
n: 20577952370271443769716250614766327061859382620272987116144020973049055780655490094802626569840541447082766582228468773986175731597651644075504622837
m: 10000000000000000000000000000000
c5: 1
c0: 90
skew: 2.46
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:216791, largePrimes:5594606 encountered
Relations: rels:5553568, finalFF:488763
Max relations in full relation-set: 0
Initial matrix: 433671 x 488763 with sparse part having weight 29962612.
Pruned matrix : 393661 x 395893 with weight 22762725.
Total sieving time: 40.33 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 5.95 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 46.83 hours.
 --------- CPU info (if available) ----------

Nov 6, 2006

By JMB / GMP-ECM 6.0.1 B1=11000000

10149+3 = 1(0)1483<150> = 31 · 409 · 36299 · 68161 · 15786109931<11> · C126

C126 = P39 · P87

P39 = 384564861922004165543203544546821681061<39>

P87 = 525097150223725778038006971456374587050144448028021793732567240767742167666853365031593<87>

Nov 5, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(4·10163-1)/3 = 1(3)163<164> = 13 · 1617029653<10> · 4089127132463729329999260241<28> · C126

C126 = P44 · P82

P44 = 28707745798935503163763288419355671086157031<44>

P82 = 5403158344513526647772426770905270937762013647747568800406619329811247104567363907<82>

(22·10164-1)/3 = 7(3)164<165> = 302310500269409<15> · 5356131642213641307217<22> · C129

C129 = P38 · P92

P38 = 19880083080642109940248774655855594509<38>

P92 = 22781313294600518394371135010929040796865768981345365259606629590515987330582853978145551929<92>

Nov 5, 2006

By JMB / GGNFS-0.77.1-20060513-pentium4

10147+3 = 1(0)1463<148> = 17 · 2797246489<10> · C137

C137 = P56 · P81

P56 = 33108811339229359436324412647303299386888839796775859569<56>

P81 = 635150657593861735194302722673849771111790656208078860699275923576820452341058299<81>

Number: N
N=21029083294262633671806153503575132464951006198960260283809320282565328457608252837898295818594576069027076635542747249450985536866013131
  ( 137 digits)
SNFS difficulty: 147 digits.
Divisors found:
 r1=33108811339229359436324412647303299386888839796775859569 (pp56)
 r2=635150657593861735194302722673849771111790656208078860699275923576820452341058299 (pp81)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 49.41 hours.
Scaled time: 41.85 units (timescale=0.847).
Factorization parameters were as follows:
name: 10^147+3
n: 21029083294262633671806153503575132464951006198960260283809320282565328457608252837898295818594576069027076635542747249450985536866013131
skew: 3
c5: 100
c4: 0
c3: 0
c2: 0
c1: 0
c0: 3
m: 100000000000000000000000000000
type: snfs
rlim: 1500000
alim: 1500000
lpbr: 25
lpba: 25
mfbr: 46
mfba: 46
rlambda: 2.3
alambda: 2.3
qintsize: 25000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [750000, 750000)
Primes: RFBsize:114155, AFBsize:114062, largePrimes:2364569 encountered
Relations: rels:2647538, finalFF:270674
Max relations in full relation-set: 28
Initial matrix: 228281 x 270674 with sparse part having weight 33459960.
Pruned matrix : 216513 x 217718 with weight 25537184.
Total sieving time: 46.63 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 2.27 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,147,5,0,0,0,0,0,0,0,0,1500000,1500000,25,25,46,46,2.3,2.3,100000
total time: 49.41 hours.
 --------- CPU info (if available) ----------

Nov 4, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

10153+9 = 1(0)1529<154> = 89 · C152

C152 = P63 · P89

P63 = 952968475741213558173290137369408967511606469763002925432064241<63>

P89 = 11790479267890275373671218734902940171749839873008160665577378805343748249303568644645441<89>

Number: 10009_153
N=11235955056179775280898876404494382022471910112359550561797752808988764044943820224719101123595505617977528089887640449438202247191011235955056179775281
  ( 152 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=952968475741213558173290137369408967511606469763002925432064241 (pp63)
 r2=11790479267890275373671218734902940171749839873008160665577378805343748249303568644645441 (pp89)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 37.55 hours.
Scaled time: 22.98 units (timescale=0.612).
Factorization parameters were as follows:
name: 10009_153
n: 11235955056179775280898876404494382022471910112359550561797752808988764044943820224719101123595505617977528089887640449438202247191011235955056179775281
m: 1000000000000000000000000000000
c5: 1000
c0: 9
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:175423, largePrimes:5312210 encountered
Relations: rels:5104149, finalFF:395224
Max relations in full relation-set: 0
Initial matrix: 351792 x 395224 with sparse part having weight 34367720.
Pruned matrix : 330997 x 332819 with weight 25228972.
Total sieving time: 32.45 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 4.65 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 37.55 hours.
 --------- CPU info (if available) ----------

Nov 3, 2006

By Yousuke Koide / GMP-ECM

10697+1 = 1(0)6961<698> = 11 · 103 · 4013 · 21993833369<11> · 184952466900411703<18> · 2670502781396266997<19> · 3404193829806058997303<22> · C623

C623 = P36 · C588

P36 = 165525666279467793827703089744624213<36>

C588 = [359308269096977993468093022170028740789105888937019217440271136286307204483028607858609615266113376516383023083848873449534549812651676704385372391699541362333520709239824241861826048462909768049054998600630004856083526307688205397516081320883180154956234677233733708022746446335764039000144525507020153228092177960020254012635565656955544446401735609511013569408383142528271068437721625972496891588748833444695155776023844893509719346662131705237949421619292292987308359772640486630794121781644687628562377035413028618766356654036959027614880581534111595840593306457044705296820387620249<588>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 2, 2006 (2nd)

By Chris Monico / GGNFS-08

(8·10161-71)/9 = (8)1601<161> = 3 · 13 · 532 · 180073 · 209738761 · C143

C143 = P50 · P93

P50 = 51115477509159931763794507652915563600336098152047<50>

P93 = 420292278186894375636799893551544441041889854586442640683219972715067693082843449444417750241<93>

Nov 2, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4

10150+9 = 1(0)1499<151> = 322132274449397<15> · C136

C136 = P43 · P93

P43 = 6485315883937021911089291466838963163589677<43>

P93 = 478668255410426241114341996907533012450905011400520344471359974267559844215862172691771363961<93>

Number: 10009_150
N=3104314839949660628761284448066712660067595495580808482022733961156681326684053029198082216491817414591705050127114942813910431229430597
  ( 136 digits)
SNFS difficulty: 150 digits.
Divisors found:
 r1=6485315883937021911089291466838963163589677 (pp43)
 r2=478668255410426241114341996907533012450905011400520344471359974267559844215862172691771363961 (pp93)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 30.86 hours.
Scaled time: 20.83 units (timescale=0.675).
Factorization parameters were as follows:
name: 10009_150
n: 3104314839949660628761284448066712660067595495580808482022733961156681326684053029198082216491817414591705050127114942813910431229430597
m: 1000000000000000000000000000000
c5: 1
c0: 9
skew: 1.55
type: snfs
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [750000, 1650001)
Primes: RFBsize:114155, AFBsize:114062, largePrimes:2660088 encountered
Relations: rels:2608863, finalFF:256764
Max relations in full relation-set: 0
Initial matrix: 228281 x 256764 with sparse part having weight 19959461.
Pruned matrix : 219518 x 220723 with weight 14982825.
Total sieving time: 29.28 hours.
Total relation processing time: 0.18 hours.
Matrix solve time: 1.31 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,150,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000
total time: 30.86 hours.
 --------- CPU info (if available) ----------

Nov 1, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1

10144+9 = 1(0)1439<145> = 3510171520019041<16> · C129

C129 = P45 · P84

P45 = 343319428714803493135074217320184461540413041<45>

P84 = 829799713580309012101243243527869721960794456291028171104017893615600289042582210489<84>

Number: 10009_144
N=284886363614099255967532873170574356025189075001931636327243695405714234954473049582554837281255866762695290468589842291862587049
  ( 129 digits)
SNFS difficulty: 145 digits.
Divisors found:
 r1=343319428714803493135074217320184461540413041 (pp45)
 r2=829799713580309012101243243527869721960794456291028171104017893615600289042582210489 (pp84)
Version: GGNFS-0.77.1
Total time: 20.78 hours.
Scaled time: 12.41 units (timescale=0.597).
Factorization parameters were as follows:
name: 10009_144
n: 284886363614099255967532873170574356025189075001931636327243695405714234954473049582554837281255866762695290468589842291862587049
m: 100000000000000000000000000000
c5: 1
c0: 90
skew: 2.46
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Sieved special-q in [650000, 2550001)
Relations: rels:2850045, finalFF:254863
Initial matrix: 200113 x 254863 with sparse part having weight 28420798.
Pruned matrix : 194157 x 195221 with weight 17535297.
Total sieving time: 18.93 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 1.49 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,145,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 20.78 hours.
 --------- CPU info (if available) ----------

Nov 1, 2006

By Chris Monico / GGNFS-08

(8·10158-71)/9 = (8)1571<158> = 3 · 19 · C158

C158 = P34 · P47 · P77

P34 = 9664697394220315840642753734651277<34>

P47 = 14494535430151793717771340261148093622724469909<47>

P77 = 11132175926860369123565167768321340729065242118076195884675837389472472816681<77>

SNFS difficulty: 158 digits.
Divisors found:
 r1=9664697394220315840642753734651277 (pp34)
 r2=14494535430151793717771340261148093622724469909 (pp47)
 r3=11132175926860369123565167768321340729065242118076195884675837389472472816681 (pp77)
Version: GGNFS-08
Total time: 49.61 hours.

October 2006

Oct 31, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1

10143+9 = 1(0)1429<144> = 7 · 13 · C142

C142 = P59 · P83

P59 = 14123789326633390707175391575607972980529708650840213007567<59>

P83 = 77804976659407440945486259813469379792634366567097067716248415916074333006508991397<83>

Number: 10009_143
N=1098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901099
  ( 142 digits)
SNFS difficulty: 143 digits.
Divisors found:
 r1=14123789326633390707175391575607972980529708650840213007567 (pp59)
 r2=77804976659407440945486259813469379792634366567097067716248415916074333006508991397 (pp83)
Version: GGNFS-0.77.1
Total time: 14.91 hours.
Scaled time: 8.92 units (timescale=0.598).
Factorization parameters were as follows:
name: 10009_143
n: 1098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901098901099
m: 10000000000000000000000000000
c5: 1000
c0: 9
skew: 1
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Sieved special-q in [650000, 1950001)
Relations: rels:2708264, finalFF:268021
Initial matrix: 199881 x 268021 with sparse part having weight 25165854.
Pruned matrix : 191247 x 192310 with weight 13144682.
Total sieving time: 13.45 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 1.15 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
snfs,143,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 14.91 hours.
 --------- CPU info (if available) ----------

Oct 31, 2006

By Chris Monico / GGNFS-08

(8·10154-71)/9 = (8)1531<154> = 66931 · 582031 · 174515111 · 69342185953<11> · C125

C125 = P38 · P87

P38 = 31716109421076795373899516364671743827<38>

P87 = 594516036272926696957983957018200081631523371414648045151308665913465157064353040222081<87>

Number: c125
N=18855735659017004221926364859533618632308778279455693268834359906070907088429160187428975507074831009421689650151349620843987
  ( 125 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=31716109421076795373899516364671743827 (pp38)
 r2=594516036272926696957983957018200081631523371414648045151308665913465157064353040222081 (pp87)
Version: GGNFS-08
Total time: 35.90 hours.
Scaled time: 59.48 units (timescale=1.657).

Oct 30, 2006 (2nd)

By JMB / GGNFS-0.77.1-20060513-athlon-xp gnfs

(4·10181-13)/9 = (4)1803<181> = 3 · 827188008473580331<18> · 10341603447151033621<20> · 1860973789180998551990153<25> · C119

C119 = P48 · P72

P48 = 726067165586600200426994691694728588706768743169<48>

P72 = 128170200259701857704179587352956111803036733849614320791625723061356983<72>

Number: Job
N=93060174015228656729616238454217002066624174075285843608385241945839383503618594794008152364953724591856137946551699127
  ( 119 digits)
Divisors found:
 r1=726067165586600200426994691694728588706768743169 (pp48)
 r2=128170200259701857704179587352956111803036733849614320791625723061356983 (pp72)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 109.54 hours.
Scaled time: 200.90 units (timescale=1.834).
Factorization parameters were as follows:
name: (4*10^181-13)/9
n: 93060174015228656729616238454217002066624174075285843608385241945839383503618594794008152364953724591856137946551699127
skew: 35804.230469
# norm 1.52E+016
c5: 22320
c4: -269603043
c3: -52175301422496
c2: -15944797089324958901
c1: -131609207918808280745515
c0: 7642729809721080297442975
#alpha -5.140000
Y1: 1270960327241
Y0: -83948695108610829227264
# Murphy_E 3.07E-010
# M 90961936046725712570246445405155753284738409683224429212522550955092555241968797291283361669678102998864944648970158616
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 10000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1750000, 3130001)
Primes: RFBsize:250150, AFBsize:250327, largePrimes:5911345 encountered
Relations: rels:5922142, finalFF:563897
Max relations in full relation-set: 28
Initial matrix: 500555 x 563897 with sparse part having weight 60164839.
Pruned matrix : 453510 x 456076 with weight 46325804.
Total sieving time: 103.43 hours.
Total relation processing time: 0.52 hours.
Matrix solve time: 5.35 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,48,48,2.5,2.5,60000
total time: 109.54 hours.
 --------- CPU info (if available) ----------

Oct 30, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(43·10154-7)/9 = 4(7)154<155> = 19 · C154

C154 = P66 · P88

P66 = 698263010678625674370967526486806265752943801620969881754577082577<66>

P88 = 3601250309102059914245749920964728989234812179604000200365723315889504010401022986601979<88>

Number: 47777_154
N=2514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883
  ( 154 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=698263010678625674370967526486806265752943801620969881754577082577 (pp66)
 r2=3601250309102059914245749920964728989234812179604000200365723315889504010401022986601979 (pp88)
Version: GGNFS-0.77.1
Total time: 68.58 hours.
Scaled time: 40.26 units (timescale=0.587).
Factorization parameters were as follows:
name: 47777_154
n: 2514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883040935672514619883
m: 10000000000000000000000000000000
c5: 43
c0: -70
skew: 1.1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1500000, 3200001)
Relations: rels:5765318, finalFF:550075
Initial matrix: 432277 x 550075 with sparse part having weight 49724344.
Pruned matrix : 410491 x 412716 with weight 27468631.
Total sieving time: 61.33 hours.
Total relation processing time: 0.45 hours.
Matrix solve time: 6.59 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 68.58 hours.
 --------- CPU info (if available) ----------

Oct 27, 2006 (2nd)

By JMB / GGNFS-0.77.1-20060513-athlon-xp gnfs

(16·10191-7)/9 = 1(7)191<192> = 3 · 629989 · 25671759360749<14> · 11323837291914005426115767<26> · 3902932380637696095354177901<28> · C119

C119 = P58 · P62

P58 = 3313559207083922318452043728233410351643032203699722342601<58>

P62 = 25020053629257740914748280168854757559710770983903542575058857<62>

Number: Job
N=82905429064960492892446546401102851207709716257923855791406358121027685128379036667899534988442001145414894295493467057
  ( 119 digits)
Divisors found:
 r1=3313559207083922318452043728233410351643032203699722342601 (pp58)
 r2=25020053629257740914748280168854757559710770983903542575058857 (pp62)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 86.96 hours.
Scaled time: 159.05 units (timescale=1.829).
Factorization parameters were as follows:
name: (16*10^191-7)/9
n: 82905429064960492892446546401102851207709716257923855791406358121027685128379036667899534988442001145414894295493467057
skew: 64828.738281
# norm 7.74E+016
c5: 17280
c4: 23663102248
c3: 1216620397219238
c2: -64977991546399907181
c1: 801562380717716146640790
c0: -7074472263971952664800082359
#alpha -6.600000
Y1: 4367385213937
Y0: -86337969377655390346892
# Murphy_E 3.08E-010
# M 25944347532134769767907568398236224281537579246278114917804371101060475961289806978069322558141325860930682671642234443
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 10000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1750000, 3040001)
Primes: RFBsize:250150, AFBsize:251085, largePrimes:5868461 encountered
Relations: rels:5909219, finalFF:607135
Max relations in full relation-set: 28
Initial matrix: 501314 x 607135 with sparse part having weight 61027499.
Pruned matrix : 421447 x 424017 with weight 42368054.
Total sieving time: 82.18 hours.
Total relation processing time: 0.58 hours.
Matrix solve time: 3.97 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,48,48,2.5,2.5,60000
total time: 86.96 hours.
 --------- CPU info (if available) ----------

Oct 27, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(43·10152-7)/9 = 4(7)152<153> = 3 · 8629 · 879522223 · C140

C140 = P31 · P37 · P73

P31 = 1430176486021512778804762093129<31>

P37 = 2634124550304617716630218784122614557<37>

P73 = 5570208680054061570851852839330927864723474994741869020269931636097026509<73>

Number: 47777_152
N=20984441024199006214282702098464189974691210272294309386562281479507447360215780310022944469827007599041064432596741706279115742469976314177
  ( 140 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=1430176486021512778804762093129 (pp31)
 r2=2634124550304617716630218784122614557 (pp37)
 r3=5570208680054061570851852839330927864723474994741869020269931636097026509 (pp73)
Version: GGNFS-0.77.1
Total time: 55.54 hours.
Scaled time: 33.10 units (timescale=0.596).
Factorization parameters were as follows:
name: 47777_152
n: 20984441024199006214282702098464189974691210272294309386562281479507447360215780310022944469827007599041064432596741706279115742469976314177
m: 1000000000000000000000000000000
c5: 4300
c0: -7
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2600001)
Relations: rels:5441857, finalFF:403012
Initial matrix: 352762 x 403012 with sparse part having weight 38799169.
Pruned matrix : 345979 x 347806 with weight 27944683.
Total sieving time: 49.59 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 5.37 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 55.54 hours.
 --------- CPU info (if available) ----------

Oct 26, 2006

By Yousuke Koide / GMP-ECM

10656+1 = 1(0)6551<657> = 353 · 449 · 641 · 1409 · 69857 · 100903134230125793<18> · C623

C623 = P34 · C590

P34 = 1949975276463991211904463972906337<34>

C590 = [50823695292702772906341828639455475186647084238747143611310950107698664508702621537825683410277773548418553874833180885510941098608107516138705610549253764670513600487368737266381728491047492823332668468416979823751543426920331292534858116250899476667931096593493578610079917954613498853005960271246538325723981011978624099775752021245226369977923645972435305810863664445813538162336277625018754170859794869301439617688692791374520418480663972891570617818368839585655305169743630905264600480140364320122421217972550689446678530923120039113856690785669930590009751858140096880310930568743361<590>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 24, 2006 (2nd)

By JMB / GGNFS-0.77.1-20060513-pentium4 gnfs

(5·10185-17)/3 = 1(6)1841<186> = 11 · 29 · 593 · 1033 · 1499 · 2882608259<10> · 3543071821004207029<19> · 1137427574791532814978635687<28> · C119

C119 = P57 · P63

P57 = 416163504929315546190282656125579228074066057762843035549<57>

P63 = 117692311104550786192947019689157514283557182010799089717768293<63>

Number: N
N=48979244692501259904533934318356529766121780019559339790576785973107299044147705538529594775240417601599059313944047857
  ( 119 digits)
Divisors found:
 r1=416163504929315546190282656125579228074066057762843035549 (pp57)
 r2=117692311104550786192947019689157514283557182010799089717768293 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 115.79 hours.
Scaled time: 158.99 units (timescale=1.373).
Factorization parameters were as follows:
name: (5*10^185-17)/3
n: 48979244692501259904533934318356529766121780019559339790576785973107299044147705538529594775240417601599059313944047857
skew: 122278.929688
# norm 1.29E+017
c5: 9600
c4: 6283065260
c3: 2000094815017190
c2: -67480579476213504922
c1: -847972170400202950243923
c0: -45718757145201865256163772173
#alpha -6.430000
Y1: 3832867280899
Y0: -87406891867936911620456
# Murphy_E 2.76E-010
# M 7581874911340103816943540432161851288274241187794851548422255318280451895893905204460717843344170291847154658792726238
type: gnfs
rlim: 3000000
alim: 3000000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 10000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2620001)
Primes: RFBsize:216816, AFBsize:216487, largePrimes:4292994 encountered
Relations: rels:4649215, finalFF:507934
Max relations in full relation-set: 28
Initial matrix: 433379 x 507934 with sparse part having weight 60887804.
Pruned matrix : 383677 x 385907 with weight 46743624.
Total sieving time: 106.56 hours.
Total relation processing time: 0.46 hours.
Matrix solve time: 8.46 hours.
Time per square root: 0.31 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,26,26,48,48,2.5,2.5,10000
total time: 115.79 hours.
 --------- CPU info (if available) ----------

Oct 24, 2006

By Dirk Augustin / Oct 14, 2006

1031810+9 = 1(0)318099<31811> is PRP. This is the only PRP for 10n+9 with 4562 < n < 39254.

Oct 21, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(52·10192-7)/9 = 5(7)192<193> = 292 · 124121 · C185

C185 = P32 · C154

P32 = 18595565132796813986844950129137<32>

C154 = [2976529499611077203351314293501630935725085943516388594718960226957377562030460064235579076244868260455936858563466712545309238934826051949497196929491361<154>]

Oct 20, 2006 (2nd)

By JMB / GGNFS-0.77.1-20060513-pentium4 gnfs

(4·10183-31)/9 = (4)1821<183> = 33 · 7 · 101450189547527<15> · 5144414891929831963<19> · 1494159724423093628331262781519<31> · C118

C118 = P46 · P73

P46 = 1766892702122215773694321824469898688927028541<46>

P73 = 1706709577193253910450975857316609717444200221315333520908743744458950411<73>

Number: N
N=3015572696584852809456973175599019254442494069685606449037092916837733527003570743285631033556963439554618401900680351
  ( 118 digits)
Divisors found:
 r1=1766892702122215773694321824469898688927028541 (pp46)
 r2=1706709577193253910450975857316609717444200221315333520908743744458950411 (pp73)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 7.89 hours.
Scaled time: 10.99 units (timescale=1.394).
Factorization parameters were as follows:
name: (4*10^183-31)/9
n: 3015572696584852809456973175599019254442494069685606449037092916837733527003570743285631033556963439554618401900680351
skew: 80655.687500
# norm 2.93E+016
c5: 44160
c4: 75823687
c3: -1227681520676813
c2: 1934855151663165448
c1: 2180936122400030909134833
c0: 8766828659110871169453784725
#alpha -6.110000
Y1: 249093839953
Y0: -36886559257510036546034
# Murphy_E 3.58E-010
# M 1645930614903737644997169554295783841518726258894790408243495281749846408113031966724666382214204881428543513397336941
type: gnfs
rlim: 3000000
alim: 3000000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 10000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 5585000
)
Primes: RFBsize:216816, AFBsize:216353, largePrimes:4290124 encountered
Relations: rels:4641865, finalFF:510826
Max relations in full relation-set: 28
Initial matrix: 433255 x 510826 with sparse part having weight 62444546.
Pruned matrix : 380371 x 382601 with weight 47424543.
Total sieving time: 0.00 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 6.64 hours.
Time per square root: 0.66 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,26,26,48,48,2.5,2.5,10000
total time: 7.89 hours.
 --------- CPU info (if available) ----------

Oct 20, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(52·10193-7)/9 = 5(7)193<194> = 3 · 1517945766670785449<19> · 7229865440639606423<19> · C157

C157 = P29 · C128

P29 = 36201349029514598526708460117<29>

C128 = [48476176164638862053734691122979671227372039614455965680139465155443601982618066197127877857347079214807473440402864044309127201<128>]

(22·10189-1)/3 = 7(3)189<190> = 11419757 · 211184184100965653310251<24> · C160

C160 = P40 · C120

P40 = 5247840149796055570797016942289983138483<40>

C120 = [579432132513201923188799315527338302692526852393619136492994578653670372434846049946697734504501561737781423227202527993<120>]

Oct 19, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(2·10163+43)/9 = (2)1627<163> = 7 · 665141705436521827<18> · 16929455156593115948878553<26> · C118

C118 = P43 · P76

P43 = 6031404599401018735875679381997121151338791<43>

P76 = 4674270295113837822854436114846620958627275146480609988485697911563517332841<76>

Number: 22227_163
N=28192415356793158638192183338666628496972623324831542589743436403638771282467070408328673563565546545108383620701535231
  ( 119 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=6031404599401018735875679381997121151338791 (pp43)
 r2=4674270295113837822854436114846620958627275146480609988485697911563517332841 (pp76)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 123.25 hours.
Scaled time: 75.30 units (timescale=0.611).
Factorization parameters were as follows:
name: 22227_163
n: 28192415356793158638192183338666628496972623324831542589743436403638771282467070408328673563565546545108383620701535231
m: 200000000000000000000000000000000
c5: 125
c0: 86
skew: 3
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 5050001)
Primes: RFBsize:315948, AFBsize:316481, largePrimes:5868108 encountered
Relations: rels:5997608, finalFF:752496
Max relations in full relation-set: 28
Initial matrix: 632494 x 752496 with sparse part having weight 52357200.
Pruned matrix : 542953 x 546179 with weight 37194109.
Total sieving time: 107.20 hours.
Total relation processing time: 0.55 hours.
Matrix solve time: 15.26 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 123.25 hours.
 --------- CPU info (if available) ----------

Oct 19, 2006

By JMB / GGNFS-0.77.1-20060513-pentium4 gnfs

(43·10175-7)/9 = 4(7)175<176> = 14939 · 4317097 · 1960212386193323<16> · 127940434931842043369211386141447<33> · C118

C118 = P39 · P79

P39 = 763897337718851240158040328891174998761<39>

P79 = 3866933145518429531145860572794691424526989665039376693712221630894313776948959<79>

Number: N
N=2953939934998311490528636347565898394866912376577013806908991905371744510519282906721459264905889799112985767185239799
  ( 118 digits)
Divisors found:
 r1=763897337718851240158040328891174998761 (pp39)
 r2=3866933145518429531145860572794691424526989665039376693712221630894313776948959 (pp79)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 54.19 hours.
Scaled time: 75.38 units (timescale=1.391).
Factorization parameters were as follows:
name: (43*10^175-7)/9
n: 2953939934998311490528636347565898394866912376577013806908991905371744510519282906721459264905889799112985767185239799
skew: 27933.439453
# norm 2.76E+016
c5: 46440
c4: 15919347198
c3: 794873662952672
c2: -16331705097650427727
c1: 72617376145568288769948
c0: -3166591147057956099235500
#alpha -6.130000
Y1: 2146726319689
Y0: -36366385004763909404629
# Murphy_E 4.21E-010
# M 1451513041968703703828818440282867894869931362701179822260165269419519531044952989144692605747778864404447562205796047
type: gnfs
rlim: 3000000
alim: 3000000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 20000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 1500000)
Primes: RFBsize:216816, AFBsize:216593, largePrimes:4196009 encountered
Relations: rels:4469126, finalFF:496294
Max relations in full relation-set: 28
Initial matrix: 433493 x 496294 with sparse part having weight 55279533.
Pruned matrix : .Bye386919 x 389150 with weight 41507429.
Total sieving time: 41.95 hours.
Total relation processing time: 0.49 hours.
Matrix solve time: 4.16 hours.
Time per square root: 7.59 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,26,26,48,48,2.5,2.5,10000
total time: 54.19 hours.
 --------- CPU info (if available) ----------

Note: Stage-1 was run on a half dozen various Win 2K/XP systems under a Win32 Service which did sieving and then reported the results via TCP to the server. The server was a Win XP system using the standard (unchanged factLat Perl script under Cygwin. After finishing enough sieving, the server then ran stage-2 to combine the relationships into a solution. The distributed solution is nearly ready for release and is undergoing final testing. This allows the usage of widely seperated sieving boxes connected via the Internet with no real limit to the number of boxes doing the sieving. The only real limit remains the ability of GGNFS running stage-2 on a single computer. (JMB)

Oct 17, 2006

By JMB / GGNFS-0.77.1-20060513-pentium4 gnfs, GMP-ECM

(28·10173-1)/9 = 3(1)173<174> = 53 · 103612676339<12> · 9737493193419986671<19> · 4029058309486985448887299<25> · C118

C118 = P46 · P72

P46 = 8534554809469539304814207677240295290372836899<46>

P72 = 169197978104796095779666677633728972685095582295334772633741546037171823<72>

Number: (28*10^173-1)/9
N=1444029417786809326216074338636756742582966400392870610411306174183091069957309374175846325040369985779578551217496877
  ( 118 digits)
Divisors found:
 r1=8534554809469539304814207677240295290372836899 (pp46)
 r2=169197978104796095779666677633728972685095582295334772633741546037171823 (pp72)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.55 hours.
Scaled time: 7.57 units (timescale=1.362).
Factorization parameters were as follows:
name: (28*10^173-1) / 9
n: 1444029417786809326216074338636756742582966400392870610411306174183091069957309374175846325040369985779578551217496877
skew: 194611.937500
# norm 2.85E+016
c5: 1680
c4: 1335413090
c3: 321482727796697
c2: -68089523444144920932
c1: -2302372693675166477282388
c0: 251690766419023337740020717303
#alpha -6.140000
Y1: 3444533872571
Y0: -61213817829518135028194
# Murphy_E 3.67E-010
# M 239252686453123260267081379725652920492612042247994112100599700325613153692251770206633906010643691349709478943063231
type: gnfs
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 10000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 480000
)
Primes: RFBsize:216816, AFBsize:216947, largePrimes:4950686 encountered
Relations: rels:5036597, finalFF:488485
Max relations in full relation-set: 28
Initial matrix: 433843 x 488485 with sparse part having weight 51885627.
Pruned matrix : 394594 x 396827 with weight 39632489.
Total sieving time: 0.00 hours.
Total relation processing time: 0.97 hours.
Matrix solve time: 4.29 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,48,48,2.5,2.5,10000
total time: 5.55 hours.
 --------- CPU info (if available) ----------

(5·10199-23)/9 = (5)1983<199> = 3 · 31277 · 34583 · 36830777 · 6174445327<10> · 6305736184704221383<19> · 724344547984221899382886622270430893<36> · C118

C118 = P41 · P78

P41 = 15858988068329679345878746056908033966491<41>

P78 = 103932934578622459308779680198050058529802658072383622797509303406164951216671<78>

Oct 16, 2006

By Yousuke Koide / GMP-ECM

(10999-1)/9 = (1)999<999> = 33 · 372 · 757 · 1999 · 333667 · 2028119 · 96455449 · 247629013 · 427437692443<12> · 440334654777631<15> · 30557051518647307<17> · 2212394296770203368013<22> · 8845981170865629119271997<25> · 90077814396055017938257237117<29> · 2503678796850536532770633167883644999<37> · [4136757950500351829215273898264330779279657730180289971062696133525101971148657576622167629405278071146511535383508907868849825502655065801803508961793912566261290961976951<172>] · C634

C634 = P35 · P599

P35 = 68885090548207172944216819625900521<35>

P599 = 16989834767951509031938751456470779957376208624594709376211656213370064684984633304388134960508271034832056618519143241563631532588441360500147367129958133789914094159571288306035042403779689292340510647516223418462257058336779201137214951212266048958064627771176958757849988307147846164903913010604988764934222058919014664774137590031035792137818601922602807016038065261064197179079525701612553643232430118896932477008910217562927802867516220097438300248900772708069422161298115050068864917478406641492193973323261629305188343912545008348449403435869162536203715623201231362280817617231040081308533<599>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 14, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(52·10189-7)/9 = 5(7)189<190> = 193 · 936953 · 4752323308811190522323273<25> · C157

C157 = P33 · P125

P33 = 221420394725445605000799427000151<33>

P125 = 30364219319826735248650667358804337247970993171027903229829909448703653062603642525176895821064372165356594333176821379499831<125>

(52·10172-7)/9 = 5(7)172<173> = 3 · 53 · 229 · 331 · 17419 · 7794933312767<13> · 574391550268011338538164911<27> · C122

C122 = P32 · P91

P32 = 14367225085697915795287524745117<32>

P91 = 4278422527553913505771834755528035916005882974401794090104527392050825146837825931010046247<91>

Oct 12, 2006

By Yousuke Koide / GMP-ECM

(10933-1)/9 = (1)933<933> = 3 · 37 · 1867 · 3733 · 339613 · 4344673058714954477761314793437392900672885445361103905548950933<64> · 2557410180456133012695296509537372979376491356924379552525114935669331084986752230647446546259197479934221837065635648510025350381215759674118823641087628274237766333894639357732286152115312924645292259846495854098673368096039697255340580355564267<247> · C608

C608 = P36 · C572

P36 = 481990095942746727246571539537397351<36>

C572 = [78968209816937478263795842683215577016210668185929748401436435310861329800142492283086732016766909763162151381418413878504379769468460785295342817558185727530083174996166240797880342488083669178503520526523380736471188636753000749537543105862022786061825823041600010019846303925381814720695174047893552825653768463736056901073303302448320439833336792060480962786440653551493748044022646053792698490482715162079526964365506374555421425625940882637068430487326265191809589604211734852371071652770674214608049631562009647437331939060116244949916713624889373626257566587128587<572>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 9, 2006 (4th)

By Bruce Dodson / GMP-ECM

(10393-1)/9 = (1)393<393> = 3 · 37 · 787 · 80173 · 109517 · 141811693 · 446790173 · 7370364319027<13> · 15594845538029429933<20> · 7317723970031057677693<22> · 131758351065116151205213<24> · 180222062287834025451247081<27> · 11983466231266295686798098306470812807267<41> · C217

C217 = P49 · P169

P49 = 1100517845115354201024243897527295703743726722437<49>

P169 = 8680060322508824594393450058221938248644256663178820249090487083301292519777205595423409349376525925423911644010932939670160279114134954869470847308423421566533831579067<169>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Oct 9, 2006 (3rd)

By Wataru Sakai / GGNFS-0.77.1-20060513-pentium4

10183-9 = (9)1821<183> = C183

C183 = P59 · P62 · P63

P59 = 49314675241585004778040302476198275634070752715382741171333<59>

P62 = 27179661213248372553517898319953454110361829996769269348594493<62>

P63 = 746070354608195431221196594309881696831382401936346066887929639<63>

Number: test
N=999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
  ( 183 digits)
SNFS difficulty: 183 digits.
Divisors found:
 r1=49314675241585004778040302476198275634070752715382741171333 (pp59)
 r2=27179661213248372553517898319953454110361829996769269348594493 (pp62)
 r3=746070354608195431221196594309881696831382401936346066887929639 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 693.77 hours.
Scaled time: 870.68 units (timescale=1.255).
Factorization parameters were as follows:
n: 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991
m: 1000000000000000000000000000000000000
c5: 1000
c0: -9
skew: 1
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 10400001)
Primes: RFBsize:501962, AFBsize:500591, largePrimes:6582409 encountered
Relations: rels:7042426, finalFF:1138240
Max relations in full relation-set: 28
Initial matrix: 1002620 x 1138240 with sparse part having weight 77666909.
Pruned matrix : 890943 x 896020 with weight 60231765.
Total sieving time: 658.07 hours.
Total relation processing time: 1.06 hours.
Matrix solve time: 34.33 hours.
Time per square root: 0.32 hours.
Prototype def-par.txt line would be:
snfs,183,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 693.77 hours.
 --------- CPU info (if available) ----------

Oct 9, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 gnfs

(2·10163+61)/9 = (2)1629<163> = 32 · 139 · 1210801 · 1115069503<10> · 725285628261153897132220859<27> · C118

C118 = P42 · P76

P42 = 761860097003061775609574934943524755379623<42>

P76 = 2381064543231869191934548798422487616615874054481195444767670889236963622749<76>

Number: 22229_163
N=1814038063877182841401857985549425415789637699634763116341145011895306527483066218905233296189598338648966492853843627
  ( 118 digits)
Divisors found:
 r1=761860097003061775609574934943524755379623 (pp42)
 r2=2381064543231869191934548798422487616615874054481195444767670889236963622749 (pp76)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 95.14 hours.
Scaled time: 58.23 units (timescale=0.612).
Factorization parameters were as follows:
name: 22229_163
n: 1814038063877182841401857985549425415789637699634763116341145011895306527483066218905233296189598338648966492853843627
skew: 54556.16
# norm 5.22e+15
c5: 35760
c4: 824980868
c3: -243975418425104
c2: 1210152699479810801
c1: 365768834554650299254910
c0: -4225460881627121993335122775
# alpha -5.23
Y1: 1134037947163
Y0: -34757594460612935108244
# Murphy_E 3.82e-10
# M 145070186104097092653043400977547244110897557992933454442252958316216359431500264754146837604667943660512937007560201
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3990001)
Primes: RFBsize:315948, AFBsize:315208, largePrimes:7659692 encountered
Relations: rels:7760879, finalFF:780547
Max relations in full relation-set: 28
Initial matrix: 631240 x 780547 with sparse part having weight 65108804.
Pruned matrix : 504499 x 507719 with weight 38951632.
Polynomial selection time: 4.43 hours.
Total sieving time: 75.34 hours.
Total relation processing time: 0.92 hours.
Matrix solve time: 13.94 hours.
Time per square root: 0.53 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 95.14 hours.
 --------- CPU info (if available) ----------

Oct 9, 2006

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(14·10153-41)/9 = 1(5)1521<154> = 3 · 11 · 88256925209<11> · 9297581956571547150667<22> · C119

C119 = P37 · P38 · P45

P37 = 5869281371990934517896039538832558131<37>

P38 = 24106869046755270050566332204861288659<38>

P45 = 406000940317690411891991058441288457615883581<45>

Number: test
N=57445072003404701363203335515060261736047876565777623202277926783180283144761034643442564878604284961558202284453114149
  ( 119 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=5869281371990934517896039538832558131 (pp37)
 r2=24106869046755270050566332204861288659 (pp38)
 r3=406000940317690411891991058441288457615883581 (pp45)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 34.66 hours.
Scaled time: 29.67 units (timescale=0.856).
Factorization parameters were as follows:
n: 57445072003404701363203335515060261736047876565777623202277926783180283144761034643442564878604284961558202284453114149
m: 2000000000000000000000000000000
c5: 875
c0: -82
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2200001)
Primes: RFBsize:176302, AFBsize:176584, largePrimes:5473280 encountered
Relations: rels:5306437, finalFF:400078
Max relations in full relation-set: 0
Initial matrix: 352952 x 400078 with sparse part having weight 33257430.
Pruned matrix : 331945 x 333773 with weight 24776358.
Total sieving time: 29.50 hours.
Total relation processing time: 0.46 hours.
Matrix solve time: 4.46 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 34.66 hours.
 --------- CPU info (if available) ----------

Oct 8, 2006

By JMB / GGNFS-0.77.1-20060513-pentium4 gnfs

10180+9 = 1(0)1799<181> = 29 · 53 · 67033 · 2271206017<10> · 5186257364017<13> · 23670431279329<14> · 1153178324949098471581835646098710369<37> · C101

C101 = P36 · P66

P36 = 280771938914481207966046774999018277<36>

P66 = 107515366282598987181603343567825994793954957702377171456669085293<66>

Number: Job
N=30187297854265955340839026475771432703339043701378522512760624169899371628725359916608624530578900161
  ( 101 digits)
Divisors found:
 r1=280771938914481207966046774999018277 (pp36)
 r2=107515366282598987181603343567825994793954957702377171456669085293 (pp66)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.51 hours.
Scaled time: 1.99 units (timescale=1.320).
Factorization parameters were as follows:
name: Job
n: 30187297854265955340839026475771432703339043701378522512760624169899371628725359916608624530578900161
skew: 14419.32
# norm 2.67e+014
c5: 30000
c4: -200576340
c3: -19944828508384
c2: -76423963274765993
c1: 1256607135224133054124
c0: -2933090521390132407939712
# alpha -6.51
Y1: 23452030007
Y0: -15868703858252830905
# Murphy_E 2.94e-009
# M 26243756146532592332210597896072185256913651889324693570901958506917004720982464758064521831519658178
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 10000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1440001)
Primes: RFBsize:135072, AFBsize:133877, largePrimes:3811261 encountered
Relations: rels:3721649, finalFF:307182
Max relations in full relation-set: 28
Initial matrix: 269029 x 307182 with sparse part having weight 22082602.
Pruned matrix : 240697 x 242106 with weight 14550235.
Total sieving time: 0.00 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 1.08 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
gnfs,100,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 1.51 hours.
 --------- CPU info (if available) ----------

Note: A mix of 4 systems (XP & 2K) with an experimental network version of GGNFS. One system local, the other 3 systems remote over the Internet. Actual real time, exactly 4.5 hours. (JMB)

Oct 7, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

10180+9 = 1(0)1799<181> = 29 · 53 · 67033 · 2271206017<10> · 5186257364017<13> · 23670431279329<14> · C137

C137 = P37 · C101

P37 = 1153178324949098471581835646098710369<37>

C101 = [30187297854265955340839026475771432703339043701378522512760624169899371628725359916608624530578900161<101>]

(4·10183-1)/3 = 1(3)183<184> = 31 · 191 · 1441447205041<13> · C168

C168 = P34 · P134

P34 = 6072305590934333145116691628161281<34>

P134 = 25727128498375098828468605178370279518924233409783280779712479401958175869912315139968289557372463400226652457116345975767906836633413<134>

Oct 7, 2006

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 gnfs

10187+9 = 1(0)1869<188> = 131 · 889796277314453<15> · 257182844103564007<18> · 534221796617984999646462038876207<33> · C120

C120 = P38 · P83

P38 = 46380071957938637799624457780838279939<38>

P83 = 13463038988859045230601743027672415432613633469191464238601408561268969782958135733<83>

Number: test
N=624416717075815956418387439219885297129632171625703612920258713290457714163614874975484756782174120692018842001812960287
  ( 120 digits)
Divisors found:
 r1=46380071957938637799624457780838279939 (pp38)
 r2=13463038988859045230601743027672415432613633469191464238601408561268969782958135733 (pp83)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 108.78 hours.
Scaled time: 95.62 units (timescale=0.879).
Factorization parameters were as follows:
name: test
n: 624416717075815956418387439219885297129632171625703612920258713290457714163614874975484756782174120692018842001812960287
skew: 82032.68
# norm 1.58e+16
c5: 26640
c4: -1892851050
c3: -665282759993338
c2: 21579123426525373733
c1: 1604607886731191767427182
c0: 12012190188221992101476024128
# alpha -5.34
Y1: 1507813949081
Y0: -118573636331197106730999
# Murphy_E 2.79e-10
# M 194582865165137178428195865785239108272202113357042784592412946166876127374665336547701087884574524171915983078141962741
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4710001)
Primes: RFBsize:315948, AFBsize:316939, largePrimes:7679259 encountered
Relations: rels:7699054, finalFF:710267
Max relations in full relation-set: 0
Initial matrix: 632966 x 710267 with sparse part having weight 73630538.
Pruned matrix : 573734 x 576962 with weight 53605846.
Total sieving time: 83.27 hours.
Total relation processing time: 1.75 hours.
Matrix solve time: 22.99 hours.
Time per square root: 0.77 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 108.78 hours.
 --------- CPU info (if available) ----------

Oct 6, 2006

By JMB / GGNFS-0.77.1-20060513-athlon-xp gnfs

(5·10162-17)/3 = 1(6)1611<163> = 164076642253592773<18> · 3467585771022759954025112257<28> · C118

C118 = P50 · P69

P50 = 13087620058046631959993084591838258467056180917457<50>

P69 = 223827837558522390339892066815882054959737192972738012418729835888593<69>

Number: Job
N=2929373696380120915420844504125371244948839260830283456490946306945700548601185908936173210016579452797771199580868001
  ( 118 digits)
Divisors found:
 r1=13087620058046631959993084591838258467056180917457 (pp50)
 r2=223827837558522390339892066815882054959737192972738012418729835888593 (pp69)
Version: GGNFS-0.77.1-20060513-athlon-xp
Total time: 47.15 hours.
Scaled time: 86.94 units (timescale=1.844).
Factorization parameters were as follows:
name: (5*10^162-17)/3 (C118)
n: 2929373696380120915420844504125371244948839260830283456490946306945700548601185908936173210016579452797771199580868001
skew: 42442.109375
# norm 1.58E+016
c5: 113220
c4: -13331106708
c3: -598331550851393
c2: 14672009091871272899
c1: 638442542548238304495483
c0: -1094640139667582557540540821
#alpha -6.560000
Y1: 2615262625259
Y0: -30378841351670209238248
# Murphy_E 4.03E-010
# M 945153404266162509028427668802199907711894421324314351187289110756934010427599444509716626073746157422304913109119527
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.5
alambda: 2.5
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1750000, 3750001)
Primes: RFBsize:250150, AFBsize:249604, largePrimes:7791659 encountered
Relations: rels:7812331, finalFF:624982
Max relations in full relation-set: 28
Initial matrix: 499838 x 624982 with sparse part having weight 63103867.
Pruned matrix : 408269 x 410832 with weight 41941917.
Total sieving time: 42.72 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 3.87 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.5,2.5,60000
total time: 47.15 hours.
 --------- CPU info (if available) ----------

Oct 5, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(88·10171-7)/9 = 9(7)171<172> = 32 · 19 · 1811 · 11839 · 824679440616849163<18> · 75641005071705113898148003<26> · C119

C119 = P50 · P70

P50 = 14605153717126806279150957554605672217739146622139<50>

P70 = 2927264666988950529424877716042538664876915437450385858565497463678093<70>

Number: 97777_171
N=42753150432087633563269806313292842264358298521714558766823452062563630797240050069307805296959170412010015283803100927
  ( 119 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=14605153717126806279150957554605672217739146622139 (pp50)
 r2=2927264666988950529424877716042538664876915437450385858565497463678093 (pp70)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 385.43 hours.
Scaled time: 235.50 units (timescale=0.611).
Factorization parameters were as follows:
name: 97777_171
n: 42753150432087633563269806313292842264358298521714558766823452062563630797240050069307805296959170412010015283803100927
m: 20000000000000000000000000000000000
c5: 55
c0: -14
skew: 3
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 11300001)
Primes: RFBsize:501962, AFBsize:502197, largePrimes:6536889 encountered
Relations: rels:7002442, finalFF:1146396
Max relations in full relation-set: 28
Initial matrix: 1004225 x 1146396 with sparse part having weight 71985085.
Pruned matrix : 881319 x 886404 with weight 54141652.
Total sieving time: 331.63 hours.
Total relation processing time: 1.33 hours.
Matrix solve time: 52.03 hours.
Time per square root: 0.43 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 385.43 hours.
 --------- CPU info (if available) ----------

Oct 2, 2006

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

(10160+71)/9 = (1)1599<160> = 3 · 6781 · 935971 · 10662763 · 54488692536470399<17> · C126

C126 = P34 · P92

P34 = 7705207815128361758535915747767663<34>

P92 = 13035257023255755892253709177324288688206891999314832662653855898078395052424282312810258233<92>

Number: test
N=100439364287797115559198333140766663985000303404901034584222277865427662296609088955539445318007939959959632657299956316919479
  ( 126 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=7705207815128361758535915747767663 (pp34)
 r2=13035257023255755892253709177324288688206891999314832662653855898078395052424282312810258233 (pp92)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 64.35 hours.
Scaled time: 56.11 units (timescale=0.872).
Factorization parameters were as follows:
n: 100439364287797115559198333140766663985000303404901034584222277865427662296609088955539445318007939959959632657299956316919479
m: 100000000000000000000000000000000
c5: 1
c0: 71
skew: 2.35
type: snfsFactor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:283453, largePrimes:5686050 encountered
Relations: rels:5720090, finalFF:636577
Max relations in full relation-set: 0
Initial matrix: 566663 x 636577 with sparse part having weight 38066033.
Pruned matrix : 514471 x 517368 with weight 28552678.
Total sieving time: 51.02 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 12.62 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 64.35 hours.
 --------- CPU info (if available) ----------

September 2006

Sep 27, 2006

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4

10173-9 = (9)1721<173> = 401 · 2528185841<10> · C161

C161 = P45 · P117

P45 = 938580727415304869460365420846237262713037883<45>

P117 = 105093292974603519781220816145515742537483095614362298755215504949519619870717052285912811121252640366779911913175797<117>

Number: 99991_173
N=98638539366573120452994767723440582424050055416812167532315793178419311373542771635535734084350490583679502593832805512478586901259119729035900095445164099717751
  ( 161 digits)
SNFS difficulty: 173 digits.
Divisors found:
 r1=938580727415304869460365420846237262713037883 (pp45)
 r2=105093292974603519781220816145515742537483095614362298755215504949519619870717052285912811121252640366779911913175797 (pp117)
Version: GGNFS-0.77.1-20060722-pentium4
Total time: 255.28 hours.
Scaled time: 222.86 units (timescale=0.873).
Factorization parameters were as follows:
n: 98638539366573120452994767723440582424050055416812167532315793178419311373542771635535734084350490583679502593832805512478586901259119729035900095445164099717751
m: 10000000000000000000000000000000000
c5: 1000
c0: -9
skew: 1
type: snfs
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3700000, 9700001)
Primes: RFBsize:501962, AFBsize:500591, largePrimes:6358041 encountered
Relations: rels:6796903, finalFF:1124380
Max relations in full relation-set: 0
Initial matrix: 1002620 x 1124380 with sparse part having weight 61398959.
Pruned matrix : 897151 x 902228 with weight 46452392.
Total sieving time: 207.68 hours.
Total relation processing time: 1.52 hours.
Matrix solve time: 45.57 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
snfs,173,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 255.28 hours.
 --------- CPU info (if available) ----------

Sep 20, 2006 (2nd)

By CWI / gnfs

10396+1 = 1(0)3951<397> = 73 · 137 · 617 · 2377 · 3169 · 16369 · 98641 · 432961 · 761113 · 99990001 · 6796152793<10> · 24387741577<11> · 99677548081<11> · 440718109921<12> · 3199044596370769<16> · 126197002179733470481<21> · 283830826522232279893972777<27> · 4987445373502665124237014313<28> · 16205834846012967584927082656402106953<38> · 7408727338313716781446937691661250885891761<43> · C141

C141 = P69 · P73

P69 = 246288943607463575049631057704872789315648893038409344335438892115177<69>

P73 = 3286441734725167632640591449151190304019453738946987847768004461574472857<73>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 20, 2006

By Yousuke Koide / GMP-ECM

(10617-1)/9 = (1)617<617> = C617

C617 = P31 · C586

P31 = 4830562365700424178611903148293<31>

C586 = [2300169270146668925037321150876838558648667950628240672650039331746387974782871253313969194853396587686058063292655000320957266896220069555631724155204278453926330052442955420796251175701773298213899837780766062880369630179988196955676879181343546242395734859492490033529658820766340472502868595502146307641275074456945435446896412683895393487125218380817138534097945963671721164306273869369942045979928375831793037151313223825888601824572075094230007167441099574805037126062025169064291518766436994915997184460232574847196621162803220266629118550960504767813084206134721484308826030427<586>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 18, 2006 (3rd)

By JMB / GGNFS-0.77.1 gnfs

(8·10156-71)/9 = (8)1551<156> = 7 · 47 · 131 · 248692069 · 9944396663<10> · 9275005532447911<16> · C117

C117 = P31 · P37 · P50

P31 = 2997698735605426418767872380233<31>

P37 = 9764529913019020615309018869039972997<37>

P50 = 30717538201460534340297361939081901505386210927107<50>

Number: Job
N=899136715284523369077591605553594215443688063801386230671576796657095902988937771674709332494070529673951870737835207
  ( 117 digits)
Divisors found:
 r1=2997698735605426418767872380233 (pp31)
 r2=9764529913019020615309018869039972997 (pp37)
 r3=30717538201460534340297361939081901505386210927107 (pp50)
Version: GGNFS-0.77.1
Total time: 41.67 hours.
Scaled time: 77.09 units (timescale=1.850).
Factorization parameters were as follows:
name: (8*10^156-71)/9
n: 899136715284523369077591605553594215443688063801386230671576796657095902988937771674709332494070529673951870737835207
skew: 26671.449219
# norm 2.20E+016
c5: 475200
c4: 25292363578
c3: -734548944339791
c2: -19516094989828822425
c1: -162675718473930164799925
c0: 455080907979280906821907451
#alpha -6.580000
Y1: 343208536379
Y0: -18004860957275713061334
# Murphy_E 4.14E-010
# M 739616504969869649068527192358617520744048083453378070391281540997102668229365593228562839239521216353745679411815636
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 3550001)
Relations: rels:6527129, finalFF:568546
Initial matrix: 500690 x 568546 with sparse part having weight 49461972.
Pruned matrix : 475185 x 477752 with weight 34016748.
Total sieving time: 37.60 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.61 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,49,49,2.4,2.4,100000
total time: 41.67 hours.
 --------- CPU info (if available) ----------

Sep 18, 2006 (2nd)

By Yousuke Koide / GMP-ECM

101070+1 = 1(0)10691<1071> = 101 · 2141 · 3541 · 6421 · 27961 · 40882343106721<14> · 10719760477926601<17> · 96252210267521261<17> · 1044374808061138338437701<25> · 2421825498886875706568085804897442030525256100180294305383840413574930314582991559155197335837338973747281007884658776715423100656032123324942160620509168628560523446063044557248001192491268292405581<199> · C381 · [45694159383400420895364062596466617852011611775786881006869558599910610477217486868157712852442098496522223654849953527635815397518621032760219197455320181715888758085627187505475337742196481586876017626037509524302125956337784834421608468635159467331874295244291090287619654281670689896547808944858108979299754064139473542218852080477844583741540567121079524887709382309414572330079377484133964448440781<404>]

C381 = P40 · C341

P40 = 2663175124735692788546303920893311173981<40>

C341 = [56025976983785216427301670566879779317040561350457827417120594801025302395071738849640118305957601394748668668688506204426236050310120629885748911472915942193623343473886452313329016411247009778894661048613349991077945420288986786603484482370957104815945360455226140581889842852067952305461502335440826258942522067467072165653391816299579621<341>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 18, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 gnfs

5·10160-1 = 4(9)160<161> = 19 · 436091 · 2329189 · 1033904918067164428884577564259<31> · C118

C118 = P49 · P69

P49 = 6893933938446466919399636517410130127156761488611<49>

P69 = 363485282102468445025331961873781689545727542437808306501301663929371<69>

Number: 49999_160
N=2505843522411995360881620202892235691372910031817756477061988171397055319833605473171594643548876245306856441524893681
  ( 118 digits)
Divisors found:
 r1=6893933938446466919399636517410130127156761488611 (pp49)
 r2=363485282102468445025331961873781689545727542437808306501301663929371 (pp69)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 101.60 hours.
Scaled time: 68.58 units (timescale=0.675).
Factorization parameters were as follows:
name: 49999_160
n: 2505843522411995360881620202892235691372910031817756477061988171397055319833605473171594643548876245306856441524893681
skew: 67698.81
# norm 1.66e+16
c5: 43680
c4: 2257503728
c3: -777745474760110
c2: -6995506859892789237
c1: 1061094916189007052816270
c0: 6870339507820636323602079525
# alpha -6.12
Y1: 1479919241581
Y0: -35623294165211846579056
# Murphy_E 3.92e-10
# M 2441904005236875944325738509808338119467647459205288901605343286851365346903917443586164924402372617797036892016430170
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4170001)
Primes: RFBsize:315948, AFBsize:315757, largePrimes:7681791 encountered
Relations: rels:7773988, finalFF:761206
Max relations in full relation-set: 28
Initial matrix: 631791 x 761206 with sparse part having weight 66536489.
Pruned matrix : 524261 x 527483 with weight 42459606.
Total sieving time: 84.05 hours.
Total relation processing time: 0.97 hours.
Matrix solve time: 16.09 hours.
Time per square root: 0.49 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 101.60 hours.
 --------- CPU info (if available) ----------

Sep 16, 2006

By JMB / GGNFS-0.77.1 gnfs

(82·10163+71)/9 = 9(1)1629<164> = 32 · 112 · 395287 · 2377426606649<13> · 150235770371064075681776231<27> · C117

C117 = P46 · P72

P46 = 1380055841093701458474306253109586399637999751<46>

P72 = 429391857648325781478819024438910645718621748253085861588269453741208257<72>

Number: Job
N=592584741265647161919373632559337423859197124960778106705162031198827682993772730378812360822463487801493429405144007
  ( 117 digits)
Divisors found:
 r1=1380055841093701458474306253109586399637999751 (pp46)
 r2=429391857648325781478819024438910645718621748253085861588269453741208257 (pp72)
Version: GGNFS-0.77.1
Total time: 44.05 hours.
Scaled time: 81.27 units (timescale=1.845).
Factorization parameters were as follows:
name: (82*10^163+71)/9
n: 592584741265647161919373632559337423859197124960778106705162031198827682993772730378812360822463487801493429405144007
skew: 18073.009766
# norm 4.72E+015
c5: 310800
c4: 16468673320
c3: -198783222359184
c2: -4542315464963551881
c1: 32947377273969925276064
c0: -76038780804607144144203495
#alpha -5.490000
Y1: 19557325663
Y0: -18032414674158987800432
# Murphy_E 4.32E-010
# M 462678572950758850991351445594612693415045523695436613693612378778682584519992700519503425655894148746364718950202916
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 3650001)
Relations: rels:6680093, finalFF:602897
Initial matrix: 500010 x 602897 with sparse part having weight 56108267.
Pruned matrix : 465300 x 467864 with weight 33835212.
Total sieving time: 40.09 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 3.48 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,49,49,2.4,2.4,100000
total time: 44.05 hours.
 --------- CPU info (if available) ----------

Sep 15, 2006

Tyler Cadigan certified 239 prime numbers by using PRIMO 2.2.0 beta 6. All the prime numbers under 2000 digits in our tables had been completely certified.

Newly certified prime numbers are: 101383+7, (101452+71)/9, (101679+71)/9, (11·101179+7)/9, (11·101596+7)/9, (11·101084+43)/9, (4·101205+17)/3, (4·101835+17)/3, (13·101443+23)/9, (13·101111+41)/9, (14·101323+31)/9, (5·101083-11)/3, (5·101296+1)/3, (5·101356+1)/3, (5·101398+7)/3, (16·101756-7)/9, 2·101370-3, 2·101488+3, 2·101819+3, (19·101344+17)/9, (19·101573+17)/9, (2·101011+7)/9, (2·101178+7)/9, (2·101217+7)/9, (2·101168+43)/9, (2·101695+43)/9, (7·101049-1)/3, (7·101006+17)/3, (22·101801-13)/9, (22·101941+23)/9, (23·101746-41)/9, (23·101277+13)/9, (23·101665+13)/9, (23·101979+13)/9, (8·101190+7)/3, (25·101241-7)/9, (25·101417+11)/9, (26·101307-71)/9, (26·101237+1)/9, 3·101137+7, (28·101505-1)/9, (28·101805+53)/9, (29·101005-11)/9, (101732-7)/3, (101918-7)/3, (31·101334+23)/9, (31·101482+41)/9, (32·101965+13)/9, (32·101052+31)/9, (32·101163+31)/9, (32·101485+31)/9, (32·101731+31)/9, (32·101970+31)/9, (11·101088-17)/3, (11·101219-17)/3, (11·101656-17)/3, (34·101185+11)/9, (35·101609-71)/9, (35·101668-71)/9, (35·101674-71)/9, (35·101127+1)/9, (35·101518+1)/9, (35·101761+1)/9, 4·101609-9, 4·101737+3, (37·101871+71)/9, (13·101040-7)/3, (13·101887-7)/3, (13·101246-1)/3, (13·101752-1)/3, (13·101860+11)/3, (4·101310+23)/9, (4·101044+41)/9, (41·101456-23)/9, (41·101217+13)/9, (41·101640+13)/9, (41·101450+31)/9, (14·101063-17)/3, (14·101509-11)/3, (14·101608+1)/3, (14·101904+1)/3, (43·101041-7)/9, (43·101089-7)/9, (43·101093-7)/9, (43·101297-7)/9, (43·101271+11)/9, (43·101412+11)/9, (44·101706-17)/9, (44·101090+1)/9, 5·101091-3, 5·101366-3, 5·101714-3, 5·101774-3, 5·101077+3, 5·101177+3, 5·101552+3, 5·101199+9, (46·101235-1)/9, (46·101727-1)/9, (46·101812-1)/9, (46·101048+17)/9, (47·101641-11)/9, (47·101646-11)/9, (47·101304+43)/9, (47·101644+43)/9, (16·101705-1)/3, (49·101799-31)/9, (49·101782+23)/9, (49·101077+41)/9, (49·101383+41)/9, (49·101566+41)/9, (49·101960+41)/9, (5·101002+31)/9, (17·101777-11)/3, (17·101252+7)/3, (17·101893+7)/3, (52·101097-61)/9, (52·101226-7)/9, (52·101324+11)/9, (52·101600+11)/9, (53·101115-71)/9, (53·101419-71)/9, (53·101689-71)/9, (53·101201+1)/9, 6·101022-7, (55·101195+53)/9, (19·101272-7)/3, (19·101008+11)/3, (19·101517+11)/3, (58·101340-31)/9, (58·101575-13)/9, (58·101234+23)/9, (58·101538+23)/9, (59·101363-41)/9, (59·101876-41)/9, (59·101332-23)/9, (59·101395-23)/9, (59·101811-23)/9, (59·101489+13)/9, (59·101488+31)/9, (2·101600-17)/3, (61·101055-43)/9, (61·101997-43)/9, (61·101193-7)/9, (61·101730-7)/9, (61·101811-7)/9, (61·101871-7)/9, (62·101027-71)/9, (62·101605-53)/9, (62·101362-17)/9, 7·101255-9, 7·101259-9, 7·101384-3, 7·101594-3, 7·101048+3, 7·101974+3, 7·101058+9, 7·101563+9, 7·101695+9, 7·101816+9, 7·101937+9, (64·101724+71)/9, (65·101132-11)/9, (65·101570-11)/9, (65·101851+61)/9, (22·101089-7)/3, (22·101607-7)/3, (22·101079-1)/3, (22·101595+17)/3, (67·101315-31)/9, (68·101346-41)/9, (68·101843+31)/9, (23·101157-11)/3, (23·101344+7)/3, (7·101067-61)/9, (71·101314-53)/9, (71·101728-53)/9, (71·101728+1)/9, (71·101876+1)/9, (71·101884+1)/9, 8·101157-9, 8·101427-9, 8·101876-7, 8·101359+3, (73·101746-1)/9, (73·101461+53)/9, (73·101614+71)/9, (74·101154+7)/9, (74·101246+7)/9, (74·101874+43)/9, (74·101067+61)/9, (25·101925-1)/3, (25·101420+17)/3, (25·101462+17)/3, (76·101614-31)/9, (76·101339-13)/9, (76·101797-13)/9, (77·101074-41)/9, (77·101211-23)/9, (77·101056+13)/9, (77·101856+31)/9, (26·101176-11)/3, (26·101473+7)/3, (79·101319-61)/9, (79·101227-43)/9, (8·101096-71)/9, (8·101419-71)/9, 9·101061-7, 9·101186-7, 9·101853-7, 9·101350+7, 9·101736+7, (82·101909+53)/9, (83·101810-11)/9, (83·101373+7)/9, (28·101025+11)/3, (28·101172+11)/3, (28·101353+11)/3, (85·101290-13)/9, (85·101915+23)/9, (86·101416-41)/9, (86·101450-41)/9, (86·101442-23)/9, (86·101721-23)/9, (29·101131-17)/3, (29·101198-17)/3, (29·101743-17)/3, (29·101872-17)/3, (29·101408+1)/3, (29·101486+1)/3, (29·101712+1)/3, (88·101031-43)/9, (88·101239-43)/9, (88·101891-7)/9, (89·101192-71)/9, (89·101260-71)/9, (89·101392-53)/9, 101107-9 and 101887-3.

Sep 14, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(4·10181-1)/3 = 1(3)181<182> = 13 · 208003 · 947369 · 6213997 · C162

C162 = P30 · C133

P30 = 422657489810930235663875844391<30>

C133 = [1981741514598812229481879734997465766050310558827137636411795585696942843981824920305180687606156525827556280138909164422933883661169<133>]

Sep 13, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 gnfs

(19·10156-1)/9 = 2(1)156<157> = 71 · 6632063 · 36137897 · 72099682374588477659537<23> · C118

C118 = P43 · P75

P43 = 4636228306457607462635241942913928692255657<43>

P75 = 371144524930028738274438333409653087743425848528036989882492056181504067359<75>

Number: 21111_156
N=1720710752267360410105609345232545624387885928118481566071559188882648454506534550677196332416770769659285549776799863
  ( 118 digits)
Divisors found:
 r1=4636228306457607462635241942913928692255657 (pp43)
 r2=371144524930028738274438333409653087743425848528036989882492056181504067359 (pp75)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 95.69 hours.
Scaled time: 58.56 units (timescale=0.612).
Factorization parameters were as follows:
name: 21111_156
n: 1720710752267360410105609345232545624387885928118481566071559188882648454506534550677196332416770769659285549776799863
skew: 67470.35
# norm 7.69e+15
c5: 8340
c4: 2693958160
c3: -247736409110981
c2: -9971288712667080996
c1: 310344041495595923871180
c0: 5692810027268370676923538416
# alpha -5.31
Y1: 297831307213
Y0: -46015927782010312498585
# Murphy_E 3.88e-10
# M 22695345206128828176637561883451475757938048504662292121030122801492708956969441634842119491414876978104227342224742
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3990001)
Primes: RFBsize:315948, AFBsize:316687, largePrimes:7668538 encountered
Relations: rels:7774387, finalFF:785989
Max relations in full relation-set: 28
Initial matrix: 632712 x 785989 with sparse part having weight 63385380.
Pruned matrix : 502602 x 505829 with weight 37903759.
Total sieving time: 80.36 hours.
Total relation processing time: 1.43 hours.
Matrix solve time: 13.36 hours.
Time per square root: 0.54 hours.
Prototype def-par.txt line would be:
gnfs,117,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 95.69 hours.
 --------- CPU info (if available) ----------

Sep 11, 2006

By JMB / GGNFS-0.77.1 gnfs

(79·10182-7)/9 = 8(7)182<183> = 115987387 · 125687914650272813477483495359<30> · 277453739305469829129656557217<30> · C117

C117 = P48 · P70

P48 = 162056010817029360137027687776827583842235554323<48>

P70 = 1339135644904339985823718669445723597191456382468572443486293907060559<70>

Number: Job
N=217014980556087308878927231813617367028075041392377799114208275145971398575415608280897569212675022064944352895246557
  ( 117 digits)
Divisors found:
 r1=162056010817029360137027687776827583842235554323 (pp48)
 r2=1339135644904339985823718669445723597191456382468572443486293907060559 (pp70)
Version: GGNFS-0.77.1
Total time: 42.65 hours.
Scaled time: 79.12 units (timescale=1.855).
Factorization parameters were as follows:
name: (79*10^182-7)/9
n: 217014980556087308878927231813617367028075041392377799114208275145971398575415608280897569212675022064944352895246557
skew: 61590.828125
# norm 2.24E+016
c5: 20880
c4: -12338727134
c3: -419279908850309
c2: 33963095371967508346
c1: 681561752337410900249080
c0: -23423277003549404626500902592
#alpha -6.490000
Y1: 2658245483993
Y0: -25313793572045121558227
# Murphy_E 4.27E-010
# M 102689576836686222011314360928127318722076257797759486725450542555420135684534362258338233999715520749962921487761097
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 3600001)
Relations: rels:6609022, finalFF:597261
Initial matrix: 500200 x 597261 with sparse part having weight 53144885.
Pruned matrix : 466084 x 468649 with weight 32422170.
Total sieving time: 38.83 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.36 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,49,49,2.4,2.4,100000
total time: 42.65 hours.
 --------- CPU info (if available) ----------

Sep 8, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 gnfs

8·10167-1 = 7(9)167<168> = 9439 · 6271129 · 106683139 · 4006996902901<13> · 288689376711364702949<21> · C117

C117 = P46 · P71

P46 = 6699442777335423652252069571185108736736497909<46>

P71 = 16346846671469550453943562736383940599589650231774542042153858211713471<71>

Number: 79999_167
N=109514763865386290777458175990679805223116309295754300737131171375962407278963151743982808794463348440192106698632139
  ( 117 digits)
Divisors found:
 r1=6699442777335423652252069571185108736736497909 (pp46)
 r2=16346846671469550453943562736383940599589650231774542042153858211713471 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 84.68 hours.
Scaled time: 56.99 units (timescale=0.673).
Factorization parameters were as follows:
name: 79999_167
n: 109514763865386290777458175990679805223116309295754300737131171375962407278963151743982808794463348440192106698632139
skew: 36968.17
# norm 4.75e+15
c5: 30660
c4: -6699269768
c3: -93580883140749
c2: 8089962192932196080
c1: 67664030510233170685222
c0: -1238997054605988332371740160
# alpha -5.37
Y1: 1305639979501
Y0: -20444727018117514523559
# Murphy_E 4.51e-10
# M 39792006408851603576345681438263979568746439464916972834789019409408685336844465229572147209599156983171569402045178
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3870001)
Primes: RFBsize:315948, AFBsize:315999, largePrimes:7638500 encountered
Relations: rels:7740528, finalFF:787770
Max relations in full relation-set: 28
Initial matrix: 632032 x 787770 with sparse part having weight 65396655.
Pruned matrix : 497525 x 500749 with weight 38439370.
Total sieving time: 69.89 hours.
Total relation processing time: 1.17 hours.
Matrix solve time: 13.17 hours.
Time per square root: 0.45 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 84.68 hours.
 --------- CPU info (if available) ----------

Sep 8, 2006

By JMB / GGNFS-0.77.1 gnfs

(73·10152-1)/9 = 8(1)152<153> = 5231 · 1054888361<10> · 183000140980702502916941<24> · C117

C117 = P47 · P71

P47 = 24501822758582821147734188172261373770858670363<47>

P71 = 32782291808142593311323070496639770907390327179373591214478907883163487<71>

Number: Job
N=803225903503251375441492928863425757906879320546286373789569303265743856991535394189124497517331138811415542970635781
  ( 117 digits)
Divisors found:
 r1=24501822758582821147734188172261373770858670363 (pp47)
 r2=32782291808142593311323070496639770907390327179373591214478907883163487 (pp71)
Version: GGNFS-0.77.1
Total time: 48.48 hours.
Scaled time: 89.70 units (timescale=1.850).
Factorization parameters were as follows:
name: (73*10^152-1)/9
n: 803225903503251375441492928863425757906879320546286373789569303265743856991535394189124497517331138811415542970635781
skew: 23007.630859
# norm 3.68E+015
c5: 84780
c4: -9423911058
c3: -132469474889920
c2: 4155757346501018329
c1: 27456603732540635947216
c0: -406511063813649227120699245
#alpha -5.050000
Y1: 231241072423
Y0: -24849001857844668661608
# Murphy_E 4.22E-010
# M 187023802232222326968134068717950088092301513770255333477897951266691344534879367302085971353460158407144614502961620
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 3550001)
Relations: rels:6514381, finalFF:562397
Initial matrix: 500042 x 562397 with sparse part having weight 49028961.
Pruned matrix : 475951 x 478515 with weight 34662345.
Total sieving time: 44.20 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 3.79 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,49,49,2.4,2.4,100000
total time: 48.48 hours.
 --------- CPU info (if available) ----------

Sep 7, 2006

By Yousuke Koide / GMP-ECM

101365+1 = 1(0)13641<1366> = 72 · 11 · 132 · 127 · 131 · 157 · 211 · 241 · 859 · 2161 · 2689 · 2731 · 6397 · 9091 · 15601 · 102103 · 216451 · 459691 · 909091 · 925081 · 4147571 · 5528251 · 21705503 · 1058313049<10> · 6097697971<10> · 29970369241<11> · 388847808493<12> · 2475034612051<13> · 1081846114760321<16> · 1661378260814161<16> · 46205575684179731<17> · 265212793249617641<18> · 18276168846821336356291<23> · 8396862596258693901610602298557167100076327481<46> · 50678387411703889101759125785290439894389920385627096501794498837<65> · 63054129911571801941639263405768461425999152026392552531582926655481271974023945336611<86> · 8912569571903773640423787742857701624820835919699625957033503601168338923351027082278688276455237261214743926133405384757726021771250608797<139> · [7348023713666465741898930375855789029789464909885364967534063144593321690065366703003692450137448338937174103088086714517623508982957303799165476749049702132200218043013256379700020843782902271375636103812410575633147508310537651713291289362891<244>] · C557

C557 = P34 · C523

P34 = 5953395590224596670581957589121611<34>

C523 = [2004998801509816834528353258112094373105529161478551283683705464440700442984709214710195875363759710481731526743624317554533712190365917140323245459612168736799912101299519392426066712075092932531520557875236443696387407579531930581235067950866698744918032256986617935009109949405241428228768640408192661482239626787198518652265480559638316410906287531592065772701689250814432033269924896413227127820439562911129321577880582441778297527405930723705963499683331617178413325297388589135242867960612562900048832019334801463851<523>]

101490+1 = 1(0)14891<1491> = 101 · 3541 · 8941 · 10729 · 27961 · 62581 · 607921 · 14118155281<11> · 4672884738461<13> · 72286688991301<14> · 171815892427926701<18> · 136916416686052955621<21> · 2336398996447692315465181<25> · 43449727365272099794386367962241<32> · [110870679844269144354635709949582391774770890704083103791132633566371413253392265378550591815806580691669808595307539634355488864836833845471616794677024940025967620229919340559408262151273358247434378152195260280636870443948931086228877135378433246056449430881437009<267>] · [1605214440709619357797351581919800889833597416421394148739815672950024771161380823847360755208273655227157019000219766490046550207325155036864476602837123952047383195091299758360303040822482624716944164463773873136231905729534814986307576307291846151794615420341552185181793289760376366513402259834628028778708825939521820938434639815230158850634413284564675945198522078882483236008364966125191436705573836033815481341830782769681163394145324260216840198126909976526595416165428782222227927578041059481<502>] · C565

C565 = P33 · C532

P33 = 288402714464678603661515072629901<33>

C532 = [4687503701333508851256425417962904885375200005043201496848030933628747825778284688210275818169480640608168077056902317515395120792907032865219785785076968504013049506348485769792263508395503545914909970684711332090901533468360290476533363489724126165274721454889372181951580540850435434732716298746125463875071075773117230503169402354871600441390151925280448418028302390337639009056554495130407551605694121397154681442893998340626858000137971953882007629207560203701156525511475684644675528789377433417628326649954345383225734414041<532>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 6, 2006

Larry Soule found the new record of near-repdigit prime. Congratulations!

The Top Twenty: Near-repdigit (Chris Caldwell)

The Prime Database: 99*10^139670-1 (Chris Caldwell)

Sep 5, 2006 (2nd)

By JMB / GGNFS-0.77.1 gnfs

(25·10165-1)/3 = 8(3)165<166> = 13 · 83 · 4639 · 32467 · 51827 · 4107116293025635448404972857043840170431<40> · C111

C111 = P49 · P62

P49 = 5999449387037714495954196079889132518450585874639<49>

P62 = 40153768547251570734358449133185923567697636094197901682467253<62>

Number: Job
N=240900502098062695718454982659129074938309425445966501601113646284209039650805899058746429435186090844480696667
  ( 111 digits)
Divisors found:
 r1=5999449387037714495954196079889132518450585874639 (pp49)
 r2=40153768547251570734358449133185923567697636094197901682467253 (pp62)
Version: GGNFS-0.77.1
Total time: 20.41 hours.
Scaled time: 37.59 units (timescale=1.842).
Factorization parameters were as follows:
name: (25*10^165-1)/3
n: 240900502098062695718454982659129074938309425445966501601113646284209039650805899058746429435186090844480696667
skew: 25466.730469
# norm 3.39E+015
c5: 27120
c4: -5390987914
c3: 8497381520849
c2: 1595269104010676103
c1: 24596920797753575326655
c0: 132349367513539707807132675
#alpha -6.330000
Y1: 314787248407
Y0: -1547793846076789196966
# Murphy_E 9.05E-010
# M 14119416429294653906379593036307881965427918338110091922459921111477241917334756269198169367046346216231247206
type: gnfs
rlim: 1500000
alim: 1500000
lpbr: 27
lpba: 27
mfbr: 48
mfba: 48
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 1500000/1500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [750000, 1750001)
Relations: rels:5560796, finalFF:280603
Initial matrix: 228357 x 280603 with sparse part having weight 33124374.
Pruned matrix : 219090 x 220295 with weight 21292064.
Total sieving time: 19.29 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.84 hours.
Time per square root: 0.12 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,27,27,48,48,2.4,2.4,50000
total time: 20.41 hours.
 --------- CPU info (if available) ----------

Sep 5, 2006

By Wataru Sakai / GMP-ECM 6.1

(4·10157-31)/9 = (4)1561<157> = 29 · 412 · 229 · 1029337 · C144

C144 = P41 · P104

P41 = 11185420019696678677811865661633748545271<41>

P104 = 34578520511371229487723717650783373547939991261364004863630803290628246801392406565091826983685186774023<104>

Sep 4, 2006

By JMB / GGNFS-0.77.1 gnfs

(5·10170-41)/9 = (5)1691<170> = 37 · 313 · 908057 · 3670254134669<13> · 24536274467882790513965408261<29> · C117

C117 = P45 · P73

P45 = 153844545425862687340722165776442412015106329<45>

P73 = 6451109343674756752111870167141420157744082464822706132191420041611257973<73>

Number: Job
N=992467984470178341940502766726206764199893272446874595614385542559268311663027354996771104251058134036124229044011117
  ( 117 digits)
Divisors found:
 r1=153844545425862687340722165776442412015106329 (pp45)
 r2=6451109343674756752111870167141420157744082464822706132191420041611257973 (pp73)
Version: GGNFS-0.77.1
Total time: 39.49 hours.
Scaled time: 71.48 units (timescale=1.810).
Factorization parameters were as follows:
name: (5*10^170-41)/9
n: 992467984470178341940502766726206764199893272446874595614385542559268311663027354996771104251058134036124229044011117
skew: 21869.570313
# norm 7.97E+015
c5: 279420
c4: 24104791726
c3: -411335644337987
c2: -11129444714046459234
c1: 94497930495376867528312
c0: 473069290404730440743411628
#alpha -6.040000
Y1: 2040608782597
Y0: -20421660632318944258709
# Murphy_E 4.31E-010
# M 600250544765919998160706580103596564837744526025385686492718238874592079176948007294093484952357404053668839267024766
type: gnfs
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1500000, 3200001)
Relations: rels:6636270, finalFF:511212
Initial matrix: 434513 x 511212 with sparse part having weight 51974095.
Pruned matrix : 411595 x 413831 with weight 34111046.
Total sieving time: 36.03 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 3.02 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,49,49,2.4,2.4,100000
total time: 39.49 hours.
 --------- CPU info (if available) ----------

Sep 3, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(4·10177-1)/3 = 1(3)177<178> = 4409 · 22961 · 43665368763292497076610163467<29> · C141

C141 = P36 · P105

P36 = 629137278840301384011004218471056683<36>

P105 = 479430089604487894618926344059780662233800055303705449563176659285817775888589892056977346367120055373397<105>

(25·10165-1)/3 = 8(3)165<166> = 13 · 83 · 4639 · 32467 · 51827 · C150

C150 = P40 · C111

P40 = 4107116293025635448404972857043840170431<40>

C111 = [240900502098062695718454982659129074938309425445966501601113646284209039650805899058746429435186090844480696667<111>]

Sep 3, 2006

By JMB / GGNFS-0.77.1 gnfs

(29·10157+7)/9 = 3(2)1563<158> = 3 · 11 · 10067 · 854403763 · 975070907 · 1066205252151981181<19> · C117

C117 = P58 · P59

P58 = 9862368846537342478020282947582970294867350950735042705057<58>

P59 = 11071846866820804070085218362918235577295451087767095667769<59>

Number: Job
N=109194637612965582757157054678170405369236672431925016095884673701161331105134448751110568439919685652183431528207833
  ( 117 digits)
Divisors found:
 r1=9862368846537342478020282947582970294867350950735042705057 (pp58)
 r2=11071846866820804070085218362918235577295451087767095667769 (pp59)
Version: GGNFS-0.77.1
Total time: 39.11 hours.
Scaled time: 70.76 units (timescale=1.809).
Factorization parameters were as follows:
name: (29*10^157+7)/9
n: 109194637612965582757157054678170405369236672431925016095884673701161331105134448751110568439919685652183431528207833
skew: 68782.632813
# norm 1.60E+016
c5: 37440
c4: -7349052604
c3: -559191156216077
c2: 28413876272894978735
c1: 1584022261071821381770041
c0: 4521208474751966537468523345
#alpha -6.460000
Y1: 1266860677159
Y0: -19632436184550177958918
# Murphy_E 4.58E-010
# M 38032488552444801230624772198371492566513504629713595090916085391814893942557929506764709525238802175151229697766689
type: gnfs
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1500000, 3200001)
Relations: rels:6627335, finalFF:516251
Initial matrix: 433511 x 516251 with sparse part having weight 51455107.
Pruned matrix : 408909 x 411140 with weight 32653240.
Total sieving time: 35.77 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 2.90 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,49,49,2.4,2.4,100000
total time: 39.11 hours.
 --------- CPU info (if available) ----------

Sep 1, 2006 (3rd)

By Yousuke Koide / GMP-ECM

10749+1 = 1(0)7481<750> = 11 · 1499 · 28463 · 32957 · 74687 · 392263 · 795653 · 909091 · 280267614929<12> · 194749234429526109677<21> · 75477148962003664034473049<26> · 628293465283949443537007319053023<33> · 9140689231828972552925524522037823147045937571379494322686226282352288670801988451<82> · C542

C542 = P35 · C507

P35 = 56551536406585191369576818265496921<35>

C507 = [228020479574439748034731153191840116996782247349077540725301759571900604992195906919299727529964169457434823051161598425307013757847295654890840215377471075792693206151779377142860486225077961374792309623921202576927179385859455798305838359439471140797559276496307070424120514928275979572460313570875861453835674283860562132374210839334869812450578929519584579066252591802632127979694097389410891779196128461569361161421596684619548820343893072038813674553976083993845844401013665766500188220965881996874493<507>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Sep 1, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(8·10163+1)/9 = (8)1629<163> = 32 · 23 · 47 · 16210981 · 14927571306573495683<20> · C133

C133 = P36 · P98

P36 = 371170022616402508958072914658993689<36>

P98 = 10172036962400690910532121592646379027538365586549967767020563977473616469588683434425556511531503<98>

(25·10183-1)/3 = 8(3)183<184> = 13 · 264283155301751969<18> · C166

C166 = P34 · C132

P34 = 3549264066261561396021839666828027<34>

C132 = [683388405517072877233927862242245555525777832139299820368098214942685744600601296640806157169483609696082817414193194488909381546507<132>]

Sep 1, 2006

By JMB / GGNFS-0.77.1 gnfs

(28·10168+17)/9 = 3(1)1673<169> = 666228053 · 12470878883<11> · 33138415031<11> · 32490475068028908608957<23> · C117

C117 = P53 · P65

P53 = 16385707085601640431344222972305731862833563422720619<53>

P65 = 21224749018633649910137929505034946199285667288473150875648596319<65>

Number: Job
N=347782520384741861506700307174557396694002746074477872300429362821720689080996955971489594953074389906021259448801461
  ( 117 digits)
Divisors found:
 r1=16385707085601640431344222972305731862833563422720619 (pp53)
 r2=21224749018633649910137929505034946199285667288473150875648596319 (pp65)
Version: GGNFS-0.77.1
Total time: 40.43 hours.
Scaled time: 73.50 units (timescale=1.818).
Factorization parameters were as follows:
name: (28*10^168+17)/9
n: 347782520384741861506700307174557396694002746074477872300429362821720689080996955971489594953074389906021259448801461
skew: 26425.080078
# norm 8.62E+015
c5: 182280
c4: -2058113582
c3: 164545497386647
c2: 5984825622362747370
c1: -183822693896929580967684
c0: -46177562120726179069454520
#alpha -6.580000
Y1: 322427535091
Y0: -18034901040942785950027
# Murphy_E 4.68E-010
# M 75060498289421360939860192635877806438078360018099897025350154299777835814830611224896812915499159086862264755479752
type: gnfs
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1500000, 3200001)
Relations: rels:6864582, finalFF:591946
Initial matrix: 433812 x 591946 with sparse part having weight 63602478.
Pruned matrix : 388948 x 391181 with weight 31094194.
Total sieving time: 37.23 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 2.78 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,49,49,2.4,2.4,100000
total time: 40.43 hours.
 --------- CPU info (if available) ----------

August 2006

Aug 31, 2006

By Wataru Sakai / GMP-ECM 6.1, GGNFS-0.77.1-20060513-pentium4 gnfs

(22·10184-1)/3 = 7(3)184<185> = 13 · 613 · 2281 · 14868970103047296245613937657<29> · C150

C150 = P40 · P44 · P67

P40 = 2031080946385714878679659203604090401921<40>

P44 = 21945234169387169334196823964344482962911429<44>

P67 = 6087289750244991176881048532900144215876009240110234950082092759569<67>

--------------------------------------------------------------------------------
Input number is
271326008406630128238872515463149625877354734768189047779930524749980293347074947943662398980732616918692654155507590620036804998472605855111160688021
(150 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1650881922
Step 1 took 349291ms
Step 2 took 112389ms
********** Factor found in step 2: 21945234169387169334196823964344482962911429
Found probable prime factor of 44 digits:
21945234169387169334196823964344482962911429
Composite cofactor
12363778226851658638804893129335340162753617078451260421665895618168765300291081742463569950579841228732049
has 107 digits
--------------------------------------------------------------------------------

Number: template
N=12363778226851658638804893129335340162753617078451260421665895618168765300291081742463569950579841228732049
  ( 107 digits)
Divisors found:
 r1=2031080946385714878679659203604090401921 (pp40)
 r2=6087289750244991176881048532900144215876009240110234950082092759569 (pp67)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 18.29 hours.
Scaled time: 22.99 units (timescale=1.257).
Factorization parameters were as follows:
name: template
n: 12363778226851658638804893129335340162753617078451260421665895618168765300291081742463569950579841228732049
skew: 22789.77
# norm 3.10e+014
c5: 2340
c4: -398302965
c3: -10216058861434
c2: -13884546662538244
c1: 2027046464299948407818
c0: -2007001082567218081705635
# alpha -5.19
Y1: 154384318913
Y0: -350423791053635097226
# Murphy_E 1.50e-009
# M 10817716021220227761602447619130818932091000933110480399993043144783173863818229918415548312281906103274965
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2450001)
Primes: RFBsize:183072, AFBsize:183087, largePrimes:4569109 encountered
Relations: rels:4788587, finalFF:554889
Max relations in full relation-set: 28
Initial matrix: 366236 x 554889 with sparse part having weight 43558978.
Pruned matrix : 242243 x 244138 with weight 23035380.
Polynomial selection time: 1.08 hours.
Total sieving time: 15.61 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.16 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
gnfs,106,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 18.29 hours.
 --------- CPU info (if available) ----------
--------------------------------------------------------------------------------

Aug 30, 2006

By JMB / GGNFS-0.77.1 gnfs

(2·10180+43)/9 = (2)1797<180> = 17 · 239 · 113177 · 15272032201952205157<20> · 136224300968205436467179879754395287<36> · C117

C117 = P40 · P77

P40 = 5558661540664315482839927301493931936647<40>

P77 = 41788890014541574244523074808400148246998304107338687225849783582778228178449<77>

Number: Job
N=232290295750883296131439774105626527875056675632797772800763276168416357472031357205659940208252291417037581678720503
  ( 117 digits)
Divisors found:
 r1=5558661540664315482839927301493931936647 (pp40)
 r2=41788890014541574244523074808400148246998304107338687225849783582778228178449 (pp77)
Version: GGNFS-0.77.1
Total time: 39.38 hours.
Scaled time: 59.14 units (timescale=1.502).
Factorization parameters were as follows:
name: (2*10^180+43)/9
n: 232290295750883296131439774105626527875056675632797772800763276168416357472031357205659940208252291417037581678720503
skew: 9349.429688
# norm 1.71E+015
c5: 264720
c4: -9523916494
c3: -61337468606242
c2: 22676187366698402
c1: -269265682539014474973
c0: 5121980116927843701921948
#alpha -4.640000
Y1: 318706942937
Y0: -15440057987372811183991
# Murphy_E 4.66E-010
# M 69253233117561781989395062316267320386824023092863487817179644402226643072076701551648395600868986918207942320169534
type: gnfs
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1500000, 3200001)
Relations: rels:6790880, finalFF:559535
Initial matrix: 433737 x 559535 with sparse part having weight 57653840.
Pruned matrix : 397949 x 400181 with weight 31074701.
Total sieving time: 35.94 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.00 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,49,49,2.4,2.4,100000
total time: 39.38 hours.
 --------- CPU info (if available) ----------

Aug 29, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(88·10169-7)/9 = 9(7)169<170> = 379 · 1277 · 4273 · 475167601 · C152

C152 = P35 · P46 · P72

P35 = 37350460755027633587644875964382999<35>

P46 = 4409353470751458981059214537553493540306417779<46>

P72 = 604170426485645551645435173395485943426251747190098266896590237901019043<72>

Number: 97777_169
N=99501663567416802757943949514997808834996790510533353884050335532583489142338088177622578683020941966164588894667452416472305275977351140857946300585503
  ( 152 digits)
SNFS difficulty: 171 digits.
Divisors found:
 r1=37350460755027633587644875964382999 (pp35)
 r2=4409353470751458981059214537553493540306417779 (pp46)
 r3=604170426485645551645435173395485943426251747190098266896590237901019043 (pp72)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 320.06 hours.
Scaled time: 215.08 units (timescale=0.672).
Factorization parameters were as follows:
name: 97777_169
n: 99501663567416802757943949514997808834996790510533353884050335532583489142338088177622578683020941966164588894667452416472305275977351140857946300585503
m: 10000000000000000000000000000000000
c5: 44
c0: -35
skew: 4
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 9800001)
Primes: RFBsize:412849, AFBsize:412837, largePrimes:6333893 encountered
Relations: rels:6634339, finalFF:947650
Max relations in full relation-set: 28
Initial matrix: 825752 x 947650 with sparse part having weight 76425953.
Pruned matrix : 730966 x 735158 with weight 59238469.
Total sieving time: 278.68 hours.
Total relation processing time: 1.49 hours.
Matrix solve time: 39.52 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
snfs,171,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 320.06 hours.
 --------- CPU info (if available) ----------

Aug 28, 2006

By Wataru Sakai / GMP-ECM 6.1, GGNFS-0.77.1-20060513-pentium4 gnfs

(4·10165-1)/3 = 1(3)165<166> = 157 · 83297702222519<14> · 31498475790963799<17> · C133

C133 = P38 · P39 · P56

P38 = 73734584147276662658901916882345178111<38>

P39 = 763162496562153777788361534760296511667<39>

P56 = 57521243829208317483878443841979756256108901163271675277<56>

Input number is 3236804907430004528606917948362126891424658553679801203805105246107656670221796513073490090353393840110682144058628658834319679302249 (133 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=93173744
Step 1 took 279290ms
Step 2 took 96017ms
********** Factor found in step 2: 73734584147276662658901916882345178111
Found probable prime factor of 38 digits: 73734584147276662658901916882345178111
Composite cofactor 43898056046059001796632047622934408387778458962541754944675353574964831022429528052130265956759 has 95 digits

---------------------------------------------------------------

Number: template
N=43898056046059001796632047622934408387778458962541754944675353574964831022429528052130265956759
  ( 95 digits)
Divisors found:
 r1=763162496562153777788361534760296511667 (pp39)
 r2=57521243829208317483878443841979756256108901163271675277 (pp56)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.83 hours.
Scaled time: 11.17 units (timescale=1.265).
Factorization parameters were as follows:
name: template
n:  43898056046059001796632047622934408387778458962541754944675353574964831022429528052130265956759
m:  5555252496116222501049
deg: 4
c4: 46092480
c3: -97993599572
c2: 595858358302098957
c1: -165953902866421130
c0: -851764011351318078373880
skew: 1635.250
type: gnfs
# adj. I(F,S) = 55.637
# E(F1,F2) = 3.551640e-005
# GGNFS version 0.77.1-20060513-pentium4 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=60.00000000, seed=1156655070.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 1200000
alim: 1200000
lpbr: 25
lpba: 25
mfbr: 45
mfba: 45
rlambda: 2.4
alambda: 2.4
qintsize: 60000

type: gnfs
Factor base limits: 1200000/1200000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 45/45
Sieved algebraic special-q in [600000, 1440001)
Primes: RFBsize:92938, AFBsize:93056, largePrimes:1920708 encountered
Relations: rels:2025755, finalFF:251251
Max relations in full relation-set: 28
Initial matrix: 186075 x 251251 with sparse part having weight 22285816.
Pruned matrix : 159264 x 160258 with weight 11995849.
Total sieving time: 8.34 hours.
Total relation processing time: 0.12 hours.
Matrix solve time: 0.32 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
gnfs,94,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1200000,1200000,25,25,45,45,2.4,2.4,60000
total time: 8.83 hours.
 --------- CPU info (if available) ----------

Aug 27, 2006

By JMB / GGNFS-0.77.1 gnfs, GGNFS-0.77.1-20050930-prescott gnfs

(19·10152-1)/9 = 2(1)152<153> = 59 · 67 · 179 · 211 · 209919090707<12> · 23255047412505613<17> · C117

C117 = P45 · P73

P45 = 103466483476477569371883659837304092315490593<45>

P73 = 2799496547093994558129967204266584630456496784372432258039009023750741721<73>

Number: N
N=289654063232356797575174326723012494182204658797247957617870812204664068855517973508513921321914344063894921748130553
  ( 117 digits)
Divisors found:
 r1=103466483476477569371883659837304092315490593 (pp45)
 r2=2799496547093994558129967204266584630456496784372432258039009023750741721 (pp73)
Version: GGNFS-0.77.1
Total time: 39.11 hours.
Scaled time: 71.29 units (timescale=1.823).
Factorization parameters were as follows:
name: (19*10^152-1)/9
n: 289654063232356797575174326723012494182204658797247957617870812204664068855517973508513921321914344063894921748130553
skew: 33281.148438
# norm 1.31E+016
c5: 146760
c4: 8776090268
c3: -378888624324306
c2: 2008532010338895485
c1: 181500397538308165856108
c0: -9512360289270801960444615
#alpha -6.180000
Y1: 1353449699413
Y0: -18157414057605125091206
# Murphy_E 4.39E-010
# M 57804010562778641285000682977123609322272133912438546446115654711394932009165525472078479225981090915205914161475441
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2000000, 3600001)
Relations: rels:6482955, finalFF:650007
Initial matrix: 566651 x 650007 with sparse part having weight 48490135.
Pruned matrix : 527816 x 530713 with weight 30728326.
Total sieving time: 35.03 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.65 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000
total time: 39.11 hours.
 --------- CPU info (if available) ----------

(16·10167-7)/9 = 1(7)167<168> = 32 · 401 · 1129 · 731121689659444742569<21> · 288186292597430549439121<24> · C117

C117 = P54 · P63

P54 = 466603873318081534951944598024969453319073680131135729<54>

P63 = 443797980480291249951903306203053836868259406908879789548246217<63>

Number: N
N=207077856662846240235313334079932768382063026764942737221802202305784699021628764915860564562697346780044408337787193
  ( 117 digits)
Divisors found:
 r1=466603873318081534951944598024969453319073680131135729 (pp54)
 r2=443797980480291249951903306203053836868259406908879789548246217 (pp63)
Version: GGNFS-0.77.1-20050930-prescott
Total time: 61.26 hours.
Scaled time: 34.73 units (timescale=0.567).
Factorization parameters were as follows:
name: (16*10^167-7)/9
n: 207077856662846240235313334079932768382063026764942737221802202305784699021628764915860564562697346780044408337787193
skew: 15523.200195
# norm 3.87E+015
c5: 95760
c4: -22188300468
c3: -68028203400212
c2: 5340600972906269443
c1: 8989035250724614085172
c0: -50635669207311551042279145
#alpha -5.510000
Y1: 660506461483
Y0: -18492286938618375162754
# Murphy_E 4.50E-010
# M 181309531116944392876346575739884961409984050243104986523315894074131008584101572192481570234445987008852354289724910
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [2000000, 3450001)
Primes: RFBsize:283146, AFBsize:283160, largePrimes:6597661 encountered
Relations: rels:6649891, finalFF:727592
Max relations in full relation-set: 40
Initial matrix: 566388 x 727592 with sparse part having weight 60993166.
Pruned matrix : 431545 x 434440 with weight 33848319.
Total sieving time: 55.21 hours.
Total relation processing time: 0.47 hours.
Matrix solve time: 4.84 hours.
Time per square root: 0.74 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000
total time: 61.26 hours.
 --------- CPU info (if available) ----------

Aug 24, 2006

By Bruce Dodson / GMP-ECM

10381+1 = 1(0)3801<382> = 7 · 11 · 13 · 2287 · 3557 · 857772733 · 1094479651<10> · 1125629957<10> · 451897625287<12> · 616896149073719728613<21> · 10860110813777339731289<23> · 1053449334720579590200819<25> · 36099531273603138218699301565567581705151216702113889<53> · C214

C214 = P67 · P147

P67 = 4444349792156709907895752551798631908946180608768737946280238078881<67>

P147 = 227106988265159616528571981140572415396122551755756282296008613353922816015404819504625289055134338407924996143023758066472872886277706507970899321<147>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 22, 2006

By JMB / GGNFS-0.77.1-20050930-prescott gnfs

(85·10152+41)/9 = 9(4)1519<153> = 13 · 197 · 647467307 · 47985896085289799139356507<26> · C116

C116 = P45 · P71

P45 = 170725642594225454451474174348792505239958339<45>

P71 = 69524300558461150094284117980194046531241851609895069471577519549231219<71>

Number: N
N=11869580888757347476677473220519036107142951936630492926951713697053493324085561964441889112990282999987147038185241
  ( 116 digits)
Divisors found:
 r1=170725642594225454451474174348792505239958339 (pp45)
 r2=69524300558461150094284117980194046531241851609895069471577519549231219 (pp71)
Version: GGNFS-0.77.1-20050930-prescott
Total time: 57.90 hours.
Scaled time: 37.86 units (timescale=0.654).
Factorization parameters were as follows:
name: N
n: 11869580888757347476677473220519036107142951936630492926951713697053493324085561964441889112990282999987147038185241
skew: 77179.72
# norm 1.06e+16
c5: 28500
c4: -1605905960
c3: -548908396432052
c2: 7781721018062958274
c1: 1362966716976629355637771
c0: 710581451553397893524894505
# alpha -6.08
Y1: 652928892803
Y0: -13302042930398130801026
# Murphy_E 4.80e-10
# M 8449198108053675294351358438215934681689131985295566294009697841106082365994216984520945583606473255174825235480823
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [2000000, 3500001)
Primes: RFBsize:283146, AFBsize:283339, largePrimes:6781742 encountered
Relations: rels:7035319, finalFF:894776
Max relations in full relation-set: 40
Initial matrix: 566568 x 894776 with sparse part having weight 74170174.
Pruned matrix : 326506 x 329402 with weight 45123261.
Total sieving time: 53.51 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 3.47 hours.
Time per square root: 0.50 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000
total time: 57.90 hours.
 --------- CPU info (if available) ----------

Aug 20, 2006

By JMB / GGNFS-0.77.1-20050930-prescott gnfs

(82·10173-1)/9 = 9(1)173<174> = 17 · 31 · 19429 · 19681 · 446657 · 2013294557<10> · 78950206397<11> · 1126772355818365857299<22> · C116

C116 = P49 · P68

P49 = 1571702898001461970102304550267406109116965542297<49>

P68 = 35960170890831727400644102888162433825269692846803398137464594472023<68>

Number: N
N=56518704801748040280654501946968595175553050255691308769059931493973136174743292493725036143767525833564358589656831
  ( 116 digits)
Divisors found:
 r1=1571702898001461970102304550267406109116965542297 (pp49)
 r2=35960170890831727400644102888162433825269692846803398137464594472023 (pp68)
Version: GGNFS-0.77.1-20050930-prescott
Total time: 62.22 hours.
Scaled time: 40.32 units (timescale=0.648).
Factorization parameters were as follows:
name: N
n: 56518704801748040280654501946968595175553050255691308769059931493973136174743292493725036143767525833564358589656831
skew: 50027.61
# norm 2.07e+16
c5: 31200
c4: -147363988
c3: -781844286702183
c2: 2754728581108013796
c1: 352679167912523767114844
c0: -2293971195865843122762610752
# alpha -5.89
Y1: 1067130078613
Y0: -17848739285818037536723
# Murphy_E 4.47e-10
# M 48101014183249661044274227258519366403604948342237387695100379056370372856318552282656444115075891531416884556421210
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [2000000, 3450001)
Primes: RFBsize:283146, AFBsize:282427, largePrimes:6542520 encountered
Relations: rels:6563316, finalFF:702600
Max relations in full relation-set: 40
Initial matrix: 565654 x 702600 with sparse part having weight 57603385.
Pruned matrix : 450451 x 453343 with weight 32528559.
Total sieving time: 56.51 hours.
Total relation processing time: 0.52 hours.
Matrix solve time: 4.62 hours.
Time per square root: 0.57 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000
total time: 62.22 hours.
 --------- CPU info (if available) ----------

Aug 19, 2006

By JMB / GGNFS-0.77.1-20050930-prescott gnfs

(64·10164+53)/9 = 7(1)1637<165> = 3 · 53503 · 940054483999<12> · 48314243429010383503977289365067<32> · C116

C116 = P43 · P74

P43 = 1236425327944059453891143340199750359794291<43>

P74 = 78893636386011202413634291580709861715696520613238084327309376292733676671<74>

Number: N
N=97546090241273282452005139478114991165570138671605243661933236313861034028750412443788439979037553951353899665685261
  ( 116 digits)
Divisors found:
 r1=1236425327944059453891143340199750359794291 (pp43)
 r2=78893636386011202413634291580709861715696520613238084327309376292733676671 (pp74)
Version: GGNFS-0.77.1-20050930-prescott
Total time: 70.33 hours.
Scaled time: 45.79 units (timescale=0.651).
Factorization parameters were as follows:
name: N
n: 97546090241273282452005139478114991165570138671605243661933236313861034028750412443788439979037553951353899665685261
skew: 80764.59
# norm 5.65e+15
c5: 8340
c4: -2213261435
c3: -160091135790358
c2: 12519422774154137710
c1: 589488626580099139001148
c0: -2075649157121883264460470960
# alpha -5.35
Y1: 329529074237
Y0: -25918451818514317799591
# Murphy_E 4.36e-10
# M 27211831738470055975133877654146693096996886542471751876593738751162646426142430179529429567875903904370129517859170
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [2000000, 3750001)
Primes: RFBsize:283146, AFBsize:284148, largePrimes:6627799 encountered
Relations: rels:6697658, finalFF:733495
Max relations in full relation-set: 40
Initial matrix: 567373 x 733495 with sparse part having weight 64372911.
Pruned matrix : 434499 x 437399 with weight 36901761.
Total sieving time: 64.04 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 4.65 hours.
Time per square root: 1.22 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000
total time: 70.33 hours.
 --------- CPU info (if available) ----------

Aug 18, 2006

By Yousuke Koide / GMP-ECM

10749+1 = 1(0)7481<750> = 11 · 1499 · 28463 · 32957 · 74687 · 392263 · 795653 · 909091 · 280267614929<12> · 194749234429526109677<21> · 75477148962003664034473049<26> · 9140689231828972552925524522037823147045937571379494322686226282352288670801988451<82> · C574

C574 = P33 · C542

P33 = 628293465283949443537007319053023<33>

C542 = [12894908452100944414773295073237073300097153241069055774583676737987242414978167908170745727915227967124884330106729412910004744110688873186180052252315852704258881528632513902371451144536293287065361925405261134609289404751378279953125297836822595137476253746855502501879820915343255108864259910503445366286746174398958106605930707640542374737365384945958881525381230321897275240619255078705928789062325522127169718285243629639148526956551496372360311580957215245892505084246451683751602241720569665488251213588481612988433384522783514936053<542>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 17, 2006

By JMB / GGNFS-0.77.1 gnfs

(68·10176+13)/9 = 7(5)1757<177> = 16223 · 17119019860271735061587461<26> · 619193651836871434301224119229241<33> · C115

C115 = P57 · P58

P57 = 548948053972127355988942710985004349672426023173799306821<57>

P58 = 8003843611567193197494230112384504996406675622815584431179<58>

Number: N
N=4393694374867054312301107826304771911374972036279600016021736599645847049491465120275629018011759197571909779771959
  ( 115 digits)
Divisors found:
 r1=548948053972127355988942710985004349672426023173799306821 (pp57)
 r2=8003843611567193197494230112384504996406675622815584431179 (pp58)
Version: GGNFS-0.77.1
Total time: 32.28 hours.
Scaled time: 58.21 units (timescale=1.803).
Factorization parameters were as follows:
name: N
n: 4393694374867054312301107826304771911374972036279600016021736599645847049491465120275629018011759197571909779771959
skew: 53771.14
# norm 3.67e+15
c5: 14820
c4: 2364063772
c3: -125507969059803
c2: -6212088143643651894
c1: 142181987154929592317020
c0: 4332116672479151476518939000
# alpha -6.03
Y1: 1352439577637
Y0: -12427816160811681721229
# Murphy_E 6.10e-10
# M 1802485709720975932650912060256348315066217203872719209037178881701464471070355288236397841569812479480893529323810
type: gnfs
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 48
mfba: 48
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1500000, 2800001)
Relations: rels:5518218, finalFF:548008
Initial matrix: 434577 x 548008 with sparse part having weight 43296502.
Pruned matrix : 392771 x 395007 with weight 22476050.
Total sieving time: 30.00 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 1.94 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,48,48,2.6,2.6,100000
total time: 32.28 hours.
 --------- CPU info (if available) ----------

Aug 15, 2006 (4th)

By JMB / GGNFS-0.77.1-20050930-prescott gnfs, GGNFS-0.77.1 gnfs

(5·10175-41)/9 = (5)1741<175> = 489133 · 1403517697<10> · 2435964161<10> · 64249247182044594022865768916254657<35> · C116

C116 = P53 · P64

P53 = 11432280413830847705222617918639919503658191618454389<53>

P64 = 4522835909054636966935411318813189352741986783000127616479400367<64>

Number: N
N=51706328378056163380057929616176601960754010322432217032605771561958673172388892161904595921026362579749982059360763
  ( 116 digits)
Divisors found:
 r1=11432280413830847705222617918639919503658191618454389 (pp53)
 r2=4522835909054636966935411318813189352741986783000127616479400367 (pp64)
Version: GGNFS-0.77.1-20050930-prescott
Total time: 67.22 hours.
Scaled time: 43.82 units (timescale=0.652).
Factorization parameters were as follows:
name: N
n: 51706328378056163380057929616176601960754010322432217032605771561958673172388892161904595921026362579749982059360763
skew: 48471.32
# norm 3.13e+16
c5: 62640
c4: -25535682078
c3: -506576515487491
c2: 39285307741783792721
c1: 883264678769304412824603
c0: -5539902059876483682909070875
# alpha -7.01
Y1: 1235812731637
Y0: -15252507920133843820594
# Murphy_E 4.57e-10
# M 29043992165356704836730301334734947366103788037605666308576012135096877153525389509722854916494244119203075603669450
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [2000000, 3450001)
Primes: RFBsize:283146, AFBsize:284128, largePrimes:6820518 encountered
Relations: rels:7099104, finalFF:911668
Max relations in full relation-set: 40
Initial matrix: 567353 x 911668 with sparse part having weight 77857218.
Pruned matrix : 328657 x 331557 with weight 50217778.
Total sieving time: 62.74 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 3.46 hours.
Time per square root: 0.54 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000
total time: 67.22 hours.
 --------- CPU info (if available) ----------

(5·10171-41)/9 = (5)1701<171> = 29 · 31 · 720497 · 1160893 · 1389257819416175659<19> · 30759678135525993098827<23> · C116

C116 = P49 · P68

P49 = 1136655398395752973921842937526529232079565032873<49>

P68 = 15210727229336895157226227619434966245190813056156538561963023879721<68>

Number: N
N=17289355218751056377545280878875714628143017402531836624568896246743444355039258118995609342080638646672485363068433
  ( 116 digits)
Divisors found:
 r1=1136655398395752973921842937526529232079565032873 (pp49)
 r2=15210727229336895157226227619434966245190813056156538561963023879721 (pp68)
Version: GGNFS-0.77.1
Total time: 34.84 hours.
Scaled time: 63.17 units (timescale=1.813).
Factorization parameters were as follows:
name: N
n: 17289355218751056377545280878875714628143017402531836624568896246743444355039258118995609342080638646672485363068433
skew: 41329.98
# norm 1.43e+16
c5: 45360
c4: 17199219306
c3: -361286661039353
c2: -30330523569186455797
c1: 147135491563252297346847
c0: 2812009785225248206216779777
# alpha -6.81
Y1: 3459577597769
Y0: -13068099480518898224536
# Murphy_E 5.16e-10
# M 2825033727445633616920687394495604557664583264776442097248695246583418859121758722048738749391100367416691389534089
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 100000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2000000, 3400001)
Relations: rels:6519610, finalFF:684370
Initial matrix: 566316 x 684370 with sparse part having weight 52581928.
Pruned matrix : 512474 x 515369 with weight 28888924.
Total sieving time: 31.34 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 3.08 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000
total time: 34.84 hours.
 --------- CPU info (if available) ----------

Aug 15, 2006 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(88·10168-7)/9 = 9(7)168<169> = 3 · 3047423 · 16256750647861<14> · C149

C149 = P55 · P95

P55 = 1161650092196977606911825290197250998288654336989039493<55>

P95 = 56633981075298388052167979569831042502150003956481301205335843212489749948759816365886195227421<95>

Number: 97777_168
N=65788869337602257470354512709932976498964658419801366922367938905952098946499946563937605731014460005019249788707206813716626708384762770883485537553
  ( 149 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=1161650092196977606911825290197250998288654336989039493 (pp55)
 r2=56633981075298388052167979569831042502150003956481301205335843212489749948759816365886195227421 (pp95)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 307.87 hours.
Scaled time: 207.19 units (timescale=0.673).
Factorization parameters were as follows:
name: 97777_168
n: 65788869337602257470354512709932976498964658419801366922367938905952098946499946563937605731014460005019249788707206813716626708384762770883485537553
m: 2000000000000000000000000000000000
c5: 2750
c0: -7
skew: 3
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 9400001)
Primes: RFBsize:412849, AFBsize:412242, largePrimes:6265476 encountered
Relations: rels:6545172, finalFF:932138
Max relations in full relation-set: 28
Initial matrix: 825158 x 932138 with sparse part having weight 72124302.
Pruned matrix : 741740 x 745929 with weight 55940787.
Total sieving time: 267.84 hours.
Total relation processing time: 1.59 hours.
Matrix solve time: 38.06 hours.
Time per square root: 0.38 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 307.87 hours.
 --------- CPU info (if available) ----------

Aug 15, 2006 (2nd)

By Wataru Sakai / GGNFS-0.77.1-20060513-pentium4

(2·10158+7)/9 = (2)1573<158> = 191 · C156

C156 = P36 · P120

P36 = 131762990689564553924901894505812253<36>

P120 = 882999942521541802647808796269686171357208978670046129416456874646530567606892048042407142275493669636303904492109195301<120>

Number: test
N=116346713205351948807446189645142524723676556137289121582315299592786503781268179173938336242001163467132053519488074461896451425247236765561372891215823153
  ( 156 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=131762990689564553924901894505812253 (pp36)
 r2=882999942521541802647808796269686171357208978670046129416456874646530567606892048042407142275493669636303904492109195301 (pp120)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 60.11 hours.
Scaled time: 76.03 units (timescale=1.265).
Factorization parameters were as follows:
n: 116346713205351948807446189645142524723676556137289121582315299592786503781268179173938336242001163467132053519488074461896451425247236765561372891215823153
m: 20000000000000000000000000000000
c5: 125
c0: 14
skew: 1
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3800001)
Primes: RFBsize:283146, AFBsize:283727, largePrimes:5772505 encountered
Relations: rels:5857015, finalFF:699322
Max relations in full relation-set: 28
Initial matrix: 566938 x 699322 with sparse part having weight 46601840.
Pruned matrix : 465701 x 468599 with weight 31108907.
Total sieving time: 54.10 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 5.54 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 60.11 hours.
 --------- CPU info (if available) ----------

Aug 15, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(4·10163-1)/3 = 1(3)163<164> = 13 · 1617029653<10> · C153

C153 = P28 · C126

P28 = 4089127132463729329999260241<28>

C126 = [155112496265691502702356326760306526844120861180050281869646762856380657373483770708019727853353298989247112858037210723680117<126>]

Aug 14, 2006 (2nd)

By Bruce Dodson / GMP-ECM

10328+1 = 1(0)3271<329> = 17 · 5882353 · 6051298241<10> · 48656086054529<14> · 669995415570582921859463287135169<33> · C264

C264 = P56 · C209

P56 = 18798124481332409484502894235050519095834690259132073729<56>

C209 = [26966706888061228309314861584452783093449979584971248841728716375604431259788120714089993744450304753814274573818260830964443146927438209553380971499989034253234857050497492661619432197590261828134053458180609<209>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 14, 2006

By JMB / GGNFS-0.77.1-20050930-prescott gnfs

(10172+71)/9 = (1)1719<172> = 32 · 4391 · 4919 · 6337 · 503573969713352179<18> · 4894102405193232341523799<25> · C117

C117 = P50 · P68

P50 = 15441280903831977725272445863464931495519706268391<50>

P68 = 23701256234827907885716605563878213283252164799721868829312661738797<68>

Number: N
N=365977755295676774775510425752865543407563187811110276370278426136480960683749215044820881215418051861192830419465627
  ( 117 digits)
Divisors found:
 r1=15441280903831977725272445863464931495519706268391 (pp50)
 r2=23701256234827907885716605563878213283252164799721868829312661738797 (pp68)
Version: GGNFS-0.77.1-20050930-prescott
Total time: 63.00 hours.
Scaled time: 40.44 units (timescale=0.642).
Factorization parameters were as follows:
name: N
n: 365977755295676774775510425752865543407563187811110276370278426136480960683749215044820881215418051861192830419465627
skew: 46221.68
# norm 2.11e+15
c5: 8880
c4: 800381912
c3: 48637968167417
c2: -2591345113024835856
c1: -66628290509630989647114
c0: 676846138220199379674969111
# alpha -4.77
Y1: 3658631464037
Y0: -33343215984948588542900
# Murphy_E 4.21e-10
# M 132425972767365485666788243273465066850953504834744825058251254902605105935877722859492830520304156857092881157938327
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 50000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 49/49
Sieved algebraic special-q in [2000000, 3550001)
Primes: RFBsize:283146, AFBsize:282237, largePrimes:6531912 encountered
Relations: rels:6522365, finalFF:676176
Max relations in full relation-set: 40
Initial matrix: 565464 x 676176 with sparse part having weight 55755486.
Pruned matrix : 474048 x 476939 with weight 33468131.
Total sieving time: 57.16 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 4.88 hours.
Time per square root: 0.55 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,100000
total time: 63.00 hours.
 --------- CPU info (if available) ----------

Aug 13, 2006 (2nd)

By JMB / GGNFS-0.77.1 gnfs

(5·10158-17)/3 = 1(6)1571<159> = 72 · 227 · 587117 · 28302487 · 4405758911640887447737379<25> · C117

C117 = P50 · P67

P50 = 67621902109110330371869937121494348175237496572533<50>

P67 = 3026700483864348901223166729369813676797114347757361309491810095819<67>

Number: N
N=204671243833471872423458363170935132549848443077825215001952886645519860774092659259664652641538107318116138813539527
  ( 117 digits)
Divisors found:
 r1=67621902109110330371869937121494348175237496572533 (pp50)
 r2=3026700483864348901223166729369813676797114347757361309491810095819 (pp67)
Version: GGNFS-0.77.1
Total time: 41.48 hours.
Scaled time: 75.41 units (timescale=1.818).
Factorization parameters were as follows:
name: N
n: 204671243833471872423458363170935132549848443077825215001952886645519860774092659259664652641538107318116138813539527
skew: 40873.77
# norm 5.27e+15
c5: 29340
c4: 1476685827
c3: -284808719427086
c2: -1625016887507574014
c1: 139298769983634584929104
c0: -300252010840174442528395056
# alpha -5.13
Y1: 456887006213
Y0: -23373258294493079571857
# Murphy_E 4.33e-10
# M 69218691873820054618000039397568631155747605271065307352011942265970179923676763177576565812296351208189263969084310
type: gnfs
rlim: 4000000
alim: 4000000
lpbr: 27
lpba: 27
mfbr: 49
mfba: 49
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2000000, 3680001)
Relations: rels:6458002, finalFF:634911
Initial matrix: 565919 x 634911 with sparse part having weight 48642764.
Pruned matrix : 533302 x 536195 with weight 32985209.
Total sieving time: 37.05 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 3.99 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4000000,4000000,27,27,49,49,2.4,2.4,60000
total time: 41.48 hours.
 --------- CPU info (if available) ----------

Aug 13, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(4·10177-1)/3 = 1(3)177<178> = 4409 · 22961 · C170

C170 = P29 · C141

P29 = 43665368763292497076610163467<29>

C141 = [301627341967929378435673111291397900932534777570343251996445617288863617272291852009571123885313428683074596057961228788786605535514717262151<141>]

Aug 12, 2006

By JMB / Msieve v. 2.04

(34·10155-43)/9 = 3(7)1543<156> = 11 · 520702915570613<15> · 5555018987718121828955407<25> · 4441619662273433601989908731614767<34> · C82

C82 = P35 · P47

P35 = 35949300598985833824141852183554201<35>

P47 = 74359481489915926639112034917743709079659453219<47>

Msieve v. 2.04
Fri Aug 11 07:21:22 2006
random seeds: 16034e40 0065c729
factoring 2673171352465710644495563497271882852656939209210070623777550975107357
875710423019 (82 digits)
using multiplier of 1
using sieve block of 65536
using a sieve bound of 1508867 (57131 primes)
using large prime bound of 15088670 (23 bits)

prp35 factor: 35949300598985833824141852183554201
prp47 factor: 74359481489915926639112034917743709079659453219
elapsed time 01:12:29

Aug 11, 2006 (2nd)

By JMB / GMP-ECM 6.0.1 B1=11000000

(34·10155-43)/9 = 3(7)1543<156> = 11 · 520702915570613<15> · 5555018987718121828955407<25> · C116

C116 = P34 · C82

P34 = 4441619662273433601989908731614767<34>

C82 = [2673171352465710644495563497271882852656939209210070623777550975107357875710423019<82>]

Aug 11, 2006

By JMB / GMP-ECM 6.0.1 B1=11000000

10171+9 = 1(0)1709<172> = 114870713498291<15> · 152103797335211<15> · 1077903296318851813591058561693<31> · C113

C113 = P39 · P75

P39 = 119386461467535400538961423925754434819<39>

P75 = 444749782753570053864318452769186104647351235367140088183461389738755377327<75>

Aug 10, 2006

By JMB / GMP-ECM 6.0.1 B1=11000000

(28·10162+17)/9 = 3(1)1613<163> = 196961 · 76407693552855061<17> · 615007859440361597069371583<27> · C114

C114 = P35 · P80

P35 = 14985999353401319166603348866934571<35>

P80 = 22430131294455821462057713883010980947736349572806097941827659523032229508329521<80>

Aug 9, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000, GGNFS-0.77.1-20060513-pentium4 gnfs

10162+9 = 1(0)1619<163> = 5573 · 735595652772776933<18> · C141

C141 = P32 · P47 · P63

P32 = 44574910306875039119713293503029<32>

P47 = 15796214831501458885442791692067196909108663273<47>

P63 = 346440210180306140299079585071546545979928246632083029744358053<63>

Number: template
N=5472443986278634559182270530295372853227297441893538310967286061401558754596631170156064966170636476322887469
  ( 109 digits)
Divisors found:
 r1=15796214831501458885442791692067196909108663273 (pp47)
 r2=346440210180306140299079585071546545979928246632083029744358053 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 23.20 hours.
Scaled time: 29.24 units (timescale=1.260).
Factorization parameters were as follows:
name: template
n: 5472443986278634559182270530295372853227297441893538310967286061401558754596631170156064966170636476322887469
skew: 11018.09
# norm 3.20e+014
c5: 15000
c4: 2049539905
c3: -16085797091712
c2: -213274340734910712
c1: 131380839582017791300
c0: -170902177794463511226600
# alpha -4.86
Y1: 62487254993
Y0: -817367011602365383949
# Murphy_E 1.12e-009
# M 5004784583434845831078841956713121671236324974689500294609609848605805097246009678817654938417451410693748427
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2900001)
Primes: RFBsize:230209, AFBsize:230832, largePrimes:7319197 encountered
Relations: rels:7139177, finalFF:579821
Max relations in full relation-set: 28
Initial matrix: 461116 x 579821 with sparse part having weight 43420824.
Pruned matrix : 363223 x 365592 with weight 24332046.
Polynomial selection time: 1.35 hours.
Total sieving time: 18.27 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 2.90 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 23.20 hours.
 --------- CPU info (if available) ----------

Aug 9, 2006

By JMB / GGNFS-0.77.1-20050930-prescott gnfs

(4·10166-31)/9 = (4)1651<166> = 43 · 421 · 11489 · 13063 · 219281 · 2114323 · 1401498638512800602338683574933<31> · C112

C112 = P44 · P68

P44 = 73852723653066632145630012304772718105985831<44>

P68 = 34088684369438135938395966419974474187769342866960086047456527452129<68>

Number: (4ツキ10166-31)/9  C112
N=2517542186432726614519045066152878943434736864305600228130570201750511709672675584135765717546155715010204784199
  ( 112 digits)
Divisors found:
 r1=73852723653066632145630012304772718105985831 (pp44)
r2=34088684369438135938395966419974474187769342866960086047456527452129 (pp68)
Version: GGNFS-0.77.1-20050930-prescott
Total time: 32.53 hours.
Scaled time: 19.81 units (timescale=0.609).
Factorization parameters were as follows:
name: (4ツキ10166-31)/9  C112
n: 2517542186432726614519045066152878943434736864305600228130570201750511709672675584135765717546155715010204784199
skew: 20807.37
# norm 5.54e+15
c5: 38400
c4: -5696422944
c3: -270524084185390
c2: 2834749926957496277
c1: 13883696403005631212110
c0: -33266943953232428779977728
# alpha -6.34
Y1: 673389653299
Y0: -2308515873579294509673
# Murphy_E 8.40e-10
# M 1689938327551674534910204802217113629727040156762154475652360671688288051808192850060885510573294732167029196891
type: gnfs
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 48
mfba: 48
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2450001)
Primes: RFBsize:216816, AFBsize:216527, largePrimes:5456723 encountered
Relations: rels:5350941, finalFF:537741
Max relations in full relation-set: 40
Initial matrix: 433419 x 537741 with sparse part having weight 40511458.
Pruned matrix : 345227 x 347458 with weight 21610858.
Total sieving time: 28.65 hours.
Total relation processing time: 0.48 hours.
Matrix solve time: 3.03 hours.
Time per square root: 0.38 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,48,48,2.6,2.6,100000
total time: 32.53 hours.
 --------- CPU info (if available) ----------
3.2ghz P4, 2gb DDR, 7200 RPM IDE

Aug 7, 2006

Daniel Heuer found the largest known near-repdigit prime number 3·10119292-1 = 2(9)119292<119293>. Congratulations!

References:

Aug 6, 2006 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4

(19·10167-1)/9 = 2(1)167<168> = 48761 · 7783163 · C156

C156 = P52 · P104

P52 = 9213779069369765001437791549262278092034656923926957<52>

P104 = 60373251713664375579895563454106435402505689903757733131520095501842512209171123875885660397963312420961<104>

Number: 21111_167
N=556265802989153120515703738711098287930938971259492519112654427574545887025752040989524841887031236074654193034645440519108902890194259867325067154799745677
  ( 156 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=9213779069369765001437791549262278092034656923926957 (pp52)
 r2=60373251713664375579895563454106435402505689903757733131520095501842512209171123875885660397963312420961 (pp104)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 247.08 hours.
Scaled time: 150.72 units (timescale=0.610).
Factorization parameters were as follows:
n: 556265802989153120515703738711098287930938971259492519112654427574545887025752040989524841887031236074654193034645440519108902890194259867325067154799745677
m: 1000000000000000000000000000000000
c5: 1900
c0: -1
skew: 1
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7850001)
Primes: RFBsize:380800, AFBsize:380927, largePrimes:6183340 encountered
Relations: rels:6431532, finalFF:886589
Max relations in full relation-set: 28
Initial matrix: 761794 x 886589 with sparse part having weight 68124049.
Pruned matrix : 666101 x 669973 with weight 51560289.
Total sieving time: 209.69 hours.
Total relation processing time: 3.21 hours.
Matrix solve time: 33.74 hours.
Time per square root: 0.44 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 247.08 hours.
 --------- CPU info (if available) ----------

Aug 6, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(22·10163-1)/3 = 7(3)163<164> = 197 · 84948082135073744830961689889<29> · C133

C133 = P31 · P102

P31 = 5766978834890632029154858016207<31>

P102 = 759859441556857392031887053491686419668387447209216643623736091892709102130571496823704046528074412543<102>

Aug 5, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000, Msieve v. 1.07, GGNFS-0.77.1-20060513-pentium4 gnfs

(8·10181+1)/9 = (8)1809<181> = 32 · 162703 · 436529 · 198685966079416987465648073668331204609<39> · C131

C131 = P33 · P39 · P60

P33 = 542441679016241624644644490188229<33>

P39 = 496477762884048622818601277837137881409<39>

P60 = 259882036616767224751131892084058161800893633111811279277667<60>

Wed Aug 02 23:25:50 2006  Msieve v. 1.07
Wed Aug 02 23:25:50 2006  random seeds: e7b26820 9874fbc3
Wed Aug 02 23:25:50 2006  factoring
129025652153242999985739343146124661528545137305441516429669637230365891830754470129895176228192803
(99 digits)
Wed Aug 02 23:25:51 2006  using multiplier of 35
Wed Aug 02 23:25:51 2006  sieve interval: 9 blocks of size 65536
Wed Aug 02 23:25:51 2006  processing polynomials in batches of 6
Wed Aug 02 23:25:51 2006  using a sieve bound of 2542933 (92576 primes)
Wed Aug 02 23:25:51 2006  using large prime bound of 381439950 (28 bits)
Wed Aug 02 23:25:51 2006  using double large prime bound of
2796192470588850 (43-52 bits)
Wed Aug 02 23:25:51 2006  using trial factoring cutoff of 57 bits
Wed Aug 02 23:25:51 2006  polynomial 'A' values have 13 factors
Thu Aug 03 10:52:49 2006  93021 relations (22595 full + 70426 combined
from 1375827 partial), need 92672
Thu Aug 03 10:52:51 2006  begin with 1375827 relations
Thu Aug 03 10:52:52 2006  reduce to 219529 relations in 11 passes
Thu Aug 03 10:52:52 2006  attempting to read 22595 full and 219529
partial relations
Thu Aug 03 10:52:57 2006  recovered 22595 full and 219529 partial relations
Thu Aug 03 10:52:57 2006  recovered 231943 polynomials
Thu Aug 03 10:52:57 2006  attempting to build 70426 cycles
Thu Aug 03 10:52:57 2006  found 70426 cycles in 5 passes
Thu Aug 03 10:52:58 2006  distribution of cycle lengths:
Thu Aug 03 10:52:58 2006     length 2 : 16312
Thu Aug 03 10:52:58 2006     length 3 : 15721
Thu Aug 03 10:52:58 2006     length 4 : 12700
Thu Aug 03 10:52:58 2006     length 5 : 9570
Thu Aug 03 10:52:58 2006     length 6 : 6390
Thu Aug 03 10:52:58 2006     length 7 : 3981
Thu Aug 03 10:52:58 2006     length 8 : 2563
Thu Aug 03 10:52:58 2006     length 9+: 3189
Thu Aug 03 10:52:58 2006  largest cycle: 21 relations
Thu Aug 03 10:52:58 2006  92576 x 92640 system, weight 5982638 (avg 64.58/col)
Thu Aug 03 10:52:58 2006  reduce to 91077 x 91141 in 3 passes
Thu Aug 03 10:55:46 2006  lanczos halted after 1442 iterations
Thu Aug 03 10:55:46 2006  recovered 63 nontrivial dependencies
Thu Aug 03 10:56:18 2006  prp39 factor: 496477762884048622818601277837137881409
Thu Aug 03 10:56:18 2006  prp60 factor:
259882036616767224751131892084058161800893633111811279277667
Thu Aug 03 10:56:18 2006  elapsed time 11:30:28
Number: template
N=129025652153242999985739343146124661528545137305441516429669637230365891830754470129895176228192803
  ( 99 digits)
Divisors found:
 r1=496477762884048622818601277837137881409 (pp39)
 r2=259882036616767224751131892084058161800893633111811279277667 (pp60)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 6.16 hours.
Scaled time: 7.73 units (timescale=1.254).
Factorization parameters were as follows:
name: template
n: 129025652153242999985739343146124661528545137305441516429669637230365891830754470129895176228192803
skew: 9546.64
# norm 5.82e+013
c5: 25440
c4: 327356204
c3: -2756380090446
c2: -26695770066661670
c1: 13726476804124437779
c0: 730114543638448319289596
# alpha -6.09
Y1: 10835548823
Y0: -5508452295331048625
# Murphy_E 4.07e-009
# M 43647947722120531491045537206099770873096300206510332994071869368876871426009741108841708977697337
type: gnfs
rlim: 1800000
alim: 1800000
lpbr: 26
lpba: 26
mfbr: 48
mfba: 48
rlambda: 2.5
alambda: 2.5
qintsize: 100000
Factor base limits: 1800000/1800000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 48/48
Sieved algebraic special-q in [900000, 1300001)
Primes: RFBsize:135072, AFBsize:135627, largePrimes:3897401 encountered
Relations: rels:3987587, finalFF:468705
Max relations in full relation-set: 28
Initial matrix: 270777 x 468705 with sparse part having weight 31420460.
Pruned matrix : 135986 x 137403 with weight 11779890.
Polynomial selection time: 0.45 hours.
Total sieving time: 5.17 hours.
Total relation processing time: 0.16 hours.
Matrix solve time: 0.27 hours.
Time per square root: 0.11 hours.
Prototype def-par.txt line would be:
gnfs,98,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1800000,1800000,26,26,48,48,2.5,2.5,100000
total time: 6.16 hours.
 --------- CPU info (if available) ----------

Aug 5, 2006

By Yousuke Koide / GMP-ECM

10631+1 = 1(0)6301<632> = 11 · 111478771 · 7144726022423651<16> · 25275592878679576093<20> · 324340568278356513982411<24> · C564

C564 = P33 · C531

P33 = 215007779702918011813855565694983<33>

C531 = [647549189090766885539933216048953381766282962756191273299208190433157850091993991879210354251404437260181512652894093774881642980661569572938361554582904065808145062221178935594264088903446558313933923951452627617040506754385034509397492029650065938555770272362685341300381208344171606718543565358130740121026865773917747329408645838090080628394617515583502194446165611330220785781361533250749575952629581355453371379965611509754045286244674853219793092966102089424772461223062153805403748147135382956547785370167119053568537747219<531>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Aug 4, 2006

By JMB / GGNFS-0.77.1-20050930-prescott gnfs, GMP-ECM 6.0.1

(61·10170-7)/9 = 6(7)170<171> = 89 · 59149 · 73106034559740600637<20> · 455443373077175325700179430733987<33> · C112

C112 = P54 · P59

P54 = 259634246889555898861112235610888816344185272851756101<54>

P59 = 14893621763832231129772178482053300115800386287663092493903<59>

Number: N
N=3866894270110480495299331929349939555976910470220605286134629327779460046947883016645268141896942460825185552203
  ( 112 digits)
Divisors found:
 r1=259634246889555898861112235610888816344185272851756101 (pp54)
 r2=14893621763832231129772178482053300115800386287663092493903 (pp59)
Version: GGNFS-0.77.1-20050930-prescott
Total time: 38.99 hours.
Scaled time: 25.62 units (timescale=0.657).
Factorization parameters were as follows:
name: N
n: 3866894270110480495299331929349939555976910470220605286134629327779460046947883016645268141896942460825185552203
skew: 40962.73
# norm 5.21e+15
c5: 17400
c4: -239661230
c3: -193594578520121
c2: 459645264047848230
c1: 12630770380130446786544
c0: -185397841779260423540488128
# alpha -6.15
Y1: 526615703819
Y0: -2946882526904680098125
# Murphy_E 7.99e-10
# M 906621222046150642737111880646727832873613351095034764872743174328229588823611973950586077300151454670273150662
type: gnfs
rlim: 3000000
alim: 3000000
lpbr: 27
lpba: 27
mfbr: 48
mfba: 48
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2400001)
Primes: RFBsize:216816, AFBsize:216754, largePrimes:5420312 encountered
Relations: rels:5291749, finalFF:520517
Max relations in full relation-set: 40
Initial matrix: 433648 x 520517 with sparse part having weight 36906463.
Pruned matrix : 359939 x 362171 with weight 20487459.
Total sieving time: 36.43 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 1.93 hours.
Time per square root: 0.36 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3000000,3000000,27,27,48,48,2.6,2.6,100000
total time: 38.99 hours.
 --------- CPU info (if available) ----------

(86·10192+31)/9 = 9(5)1919<193> = 13 · 79801 · 113754799183<12> · 1840989671002883<16> · 64478288440428854599<20> · 477664605616311721510870585903<30> · C112

C112 = P48 · P64

P48 = 544743413352596587064461975415669241172263459607<48>

P64 = 2621528754462436339398526557224274787788408344875291572559019753<64>

Aug 2, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(88·10167-7)/9 = 9(7)167<168> = 547 · 255917 · 62987719 · 168095479 · C144

C144 = P36 · P109

P36 = 173057865665730828088779240795479581<36>

P109 = 3811978501475933954155211857611104093457904408402378553499026213538586627283954077584331779888287710077425683<109>

Number: 97777_167
N=659692863429076083431306133363648261064622208616886952777689858266262337273979785875087842161434570070362767114570543284589051713060979871478823
  ( 144 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=173057865665730828088779240795479581 (pp36)
 r2=3811978501475933954155211857611104093457904408402378553499026213538586627283954077584331779888287710077425683 (pp109)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 237.31 hours.
Scaled time: 144.52 units (timescale=0.609).
Factorization parameters were as follows:
name: 97777_167
n: 659692863429076083431306133363648261064622208616886952777689858266262337273979785875087842161434570070362767114570543284589051713060979871478823
m: 2000000000000000000000000000000000
c5: 275
c0: -7
skew: 3
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7750001)
Primes: RFBsize:380800, AFBsize:381318, largePrimes:6147199 encountered
Relations: rels:6384742, finalFF:880495
Max relations in full relation-set: 28
Initial matrix: 762184 x 880495 with sparse part having weight 65754152.
Pruned matrix : 670303 x 674177 with weight 49760472.
Total sieving time: 206.57 hours.
Total relation processing time: 1.11 hours.
Matrix solve time: 29.28 hours.
Time per square root: 0.34 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 237.31 hours.
 --------- CPU info (if available) ----------

July 2006

Jul 31, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(4·10181-31)/9 = (4)1801<181> = 691 · C178

C178 = P35 · C144

P35 = 18341311570927686739221204596281603<35>

C144 = [350678423961842493729246583229724423685615232184993031214145040572519155068819591779849294477911743031232439012498194912517275810305005552598017<144>]

Jul 30, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(8·10194+1)/9 = (8)1939<194> = 7129 · 7193 · 490057 · 13676537335459<14> · 59621355333702961<17> · C151

C151 = P35 · P117

P35 = 12622486933254640856936731027878923<35>

P117 = 343668142793819369342868699647116068318546166592509493762943274316967670246952436452566986782105405574673788064694033<117>

Jul 26, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000, GGNFS-0.77.1-20060513-pentium4 gnfs

(8·10184+1)/9 = (8)1839<184> = 3 · 19603 · 172173708801163613627<21> · C159

C159 = P29 · C131

P29 = 27179099398845119796776615939<29>

C131 = [32299945255435921563264500910223759473383544543244622969530356135443820563047187110300569176110925997216606362828072402522777701457<131>]

(8·10181+1)/9 = (8)1809<181> = 32 · 162703 · 436529 · C170

C170 = P39 · C131

P39 = 198685966079416987465648073668331204609<39>

C131 = [69988891390170684419064864292472492567266787296607386124102937093503944074615798168449992226257202972265875496995584237861973115887<131>]

(8·10175+1)/9 = (8)1749<175> = 3 · 103 · 270950423 · 24229424690721201848947<23> · C142

C142 = P37 · P43 · P64

P37 = 1187459593948663942345533369324773863<37>

P43 = 1621372469742717880365943926655152482024861<43>

P64 = 2275906557941688510267400481774821829901703819890554273677954787<64>

Number: template
N=3690092236753563552546589205826588094126097050469521337750003386324822725505644653827392179184738967959607
  ( 106 digits)
Divisors found:
 r1=1621372469742717880365943926655152482024861 (pp43)
 r2=2275906557941688510267400481774821829901703819890554273677954787 (pp64)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 13.34 hours.
Scaled time: 16.68 units (timescale=1.250).
Factorization parameters were as follows:
name: template
n: 3690092236753563552546589205826588094126097050469521337750003386324822725505644653827392179184738967959607
skew: 17540.76
# norm 2.22e+014
c5: 18540
c4: 445661492
c3: -20154034773225
c2: -117243062043128466
c1: 2055231393406905905146
c0: 6780112294565646891804960
# alpha -5.98
Y1: 90312434587
Y0: -181879797367810544261
# Murphy_E 1.89e-009
# M 559630045337832813518883705861953988295828468353446159222632565406767852774425818137205583461403479764802
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2150001)
Primes: RFBsize:183072, AFBsize:182547, largePrimes:4443465 encountered
Relations: rels:4565926, finalFF:502025
Max relations in full relation-set: 28
Initial matrix: 365702 x 502025 with sparse part having weight 36650530.
Pruned matrix : 257832 x 259724 with weight 17722141.
Total sieving time: 11.85 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 1.12 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
gnfs,105,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 13.34 hours.
 --------- CPU info (if available) ----------

(8·10187+1)/9 = (8)1869<187> = 3 · 263 · 26821 · 88883 · 1119746363<10> · 918134378332008821<18> · C148

C148 = P33 · P36 · P80

P33 = 165805694449843257500642766390827<33>

P36 = 934070656153121251699814499393013861<36>

P80 = 29680534863754695395148746244944140636632693438105910924697912984920615447644347<80>

Jul 23, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(88·10166-7)/9 = 9(7)166<167> = 107 · 22585789 · 644297617169<12> · 4056411030394169<16> · C131

C131 = P60 · P71

P60 = 795997355428448940999990564851890555756567795185419778731011<60>

P71 = 19448271711557563851095010492190619092216476162100540985170829304296669<71>

Number: 97777_166
N=15480772850053735174812154400698448628670785732665450293762375478799791273005124409888204255075924043017964918964150912682694302359
  ( 131 digits)
SNFS difficulty: 168 digits.
Divisors found:
 r1=795997355428448940999990564851890555756567795185419778731011 (pp60)
 r2=19448271711557563851095010492190619092216476162100540985170829304296669 (pp71)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 211.66 hours.
Scaled time: 142.23 units (timescale=0.672).
Factorization parameters were as follows:
name: 97777_166
n: 15480772850053735174812154400698448628670785732665450293762375478799791273005124409888204255075924043017964918964150912682694302359
m: 2000000000000000000000000000000000
c5: 55
c0: -14
skew: 2
type: snfs
Factor base limits: 5500000/5500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2750000, 7150001)
Primes: RFBsize:380800, AFBsize:380438, largePrimes:6071781 encountered
Relations: rels:6279833, finalFF:858677
Max relations in full relation-set: 28
Initial matrix: 761304 x 858677 with sparse part having weight 61581012.
Pruned matrix : 685817 x 689687 with weight 47025780.
Total sieving time: 181.11 hours.
Total relation processing time: 0.93 hours.
Matrix solve time: 29.30 hours.
Time per square root: 0.31 hours.
Prototype def-par.txt line would be:
snfs,168,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.6,2.6,100000
total time: 211.66 hours.
 --------- CPU info (if available) ----------

Jul 23, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

10190+9 = 1(0)1899<191> = 17 · 661 · 3617 · 9255737 · C176

C176 = P38 · C138

P38 = 58578835214747005278058475891560020601<38>

C138 = [453784202451725518980480133089420040136273460591104916659256777047754295589507064687162836139574199000297912034696834143699088261379945733<138>]

10171+9 = 1(0)1709<172> = 114870713498291<15> · 152103797335211<15> · C176

C143 = P31 · C113

P31 = 1077903296318851813591058561693<31>

C113 = [53097102801403831665746807018118510756849451124526459253855124796660194850247112567565191453771626718853971948813<113>]

Jul 17, 2006

By Alfred Reich / Msieve V 1.06

(10161+71)/9 = (1)1609<161> = 23327 · 321131832988051<15> · 1191317231086892298689<22> · C121

C121 = P39 · P82

P39 = 157827640943815926474954927538137344371<39>

P82 = 7888687536686028472531832671390978588451330433797341725738861291549234482598071113<82>

Jul 15, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(22·10161-1)/3 = 7(3)161<162> = 73 · 34653533 · C153

C153 = P32 · C122

P32 = 22935196665910109914667553700279<32>

C122 = [12639461723608598020994817140915197006312553495483248231488432539680347420405192366902367090348663282604229103442194528503<122>]

(25·10197-1)/3 = 8(3)197<198> = 656603 · 170454115654360806479399<24> · C169

C169 = P33 · P137

P33 = 165593497569484456997057320046729<33>

P137 = 44964018754490646891491038249988341848259629720873308924575013742259137181650315743036690343984815431548345392057804704806670264403772241<137>

(22·10152-1)/3 = 7(3)152<153> = 417587987 · 10350831019<11> · C135

C135 = P35 · P100

P35 = 17497935690527231337957237637215421<35>

P100 = 9695972941720835118569525522840796078591641123474745316988805837411044124787063482971552015328045641<100>

Jul 14, 2006 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(88·10165-7)/9 = 9(7)165<166> = 3 · C166

C166 = P77 · P89

P77 = 45346200595934146934131296942427106498745059419385026179154277004358396423331<77>

P89 = 71875024068752797477559446177335736254751869797365522711198282153882911150417196506178889<89>

Number: 97777_165
N=3259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259
  ( 166 digits)
SNFS difficulty: 166 digits.
Divisors found:
 r1=45346200595934146934131296942427106498745059419385026179154277004358396423331 (pp77)
 r2=71875024068752797477559446177335736254751869797365522711198282153882911150417196506178889 (pp89)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 178.89 hours.
Scaled time: 120.39 units (timescale=0.673).
Factorization parameters were as follows:
name: 97777_165
n: 3259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259259
m: 1000000000000000000000000000000000
c5: 88
c0: -7
skew: 2
type: snfs
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2500000, 
)
Primes: RFBsize:348513, AFBsize:348862, largePrimes:6048552 encountered
Relations: rels:6244545, finalFF:823730
Max relations in full relation-set: 28
Initial matrix: 697441 x 823730 with sparse part having weight 63288732.
Pruned matrix : 602166 x 605717 with weight 47023567.
Total sieving time: 158.14 hours.
Total relation processing time: 0.93 hours.
Matrix solve time: 19.53 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,166,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000
total time: 178.89 hours.
 --------- CPU info (if available) ----------

Jul 14, 2006 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4

(7·10154-61)/9 = (7)1531<154> = 59040511 · 30846605261<11> · C136

C136 = P36 · P41 · P60

P36 = 169750613328204889527307493147334971<36>

P41 = 70847408418392222124674327036637004102729<41>

P60 = 355109856140986847622896672372910163920648639023544483933139<60>

Number: 77771_154
N=4270689989174991981377200663819930402301374317453540384390776208047194568640332560832240274686466139739702588331996549083657274648231401
  ( 136 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=169750613328204889527307493147334971 (pp36)
 r2=70847408418392222124674327036637004102729 (pp41)
 r3=355109856140986847622896672372910163920648639023544483933139 (pp60)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 55.96 hours.
Scaled time: 35.92 units (timescale=0.642).
Factorization parameters were as follows:
n: 4270689989174991981377200663819930402301374317453540384390776208047194568640332560832240274686466139739702588331996549083657274648231401
m: 10000000000000000000000000000000
c5: 7
c0: -610
skew: 2.44
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3000001)
Primes: RFBsize:216816, AFBsize:217162, largePrimes:5654054 encountered
Relations: rels:5570235, finalFF:503190
Max relations in full relation-set: 28
Initial matrix: 434043 x 503190 with sparse part having weight 42264052.
Pruned matrix : 404056 x 406290 with weight 30433715.
Total sieving time: 46.92 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 8.44 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 55.96 hours.
 --------- CPU info (if available) ----------

Jul 14, 2006

By Wataru Sakai / GGNFS-0.77.1-20060513-pentium4

10139+9 = 1(0)1389<140> = 23 · 881 · 2143 · C132

C132 = P41 · P43 · P49

P41 = 24164159986601181377625015589587447765463<41>

P43 = 2160786218367515171952203262064220489890903<43>

P49 = 4410527972854632022342616725553254342960601726209<49>

Number: 132
N=230289472254597723556326237185858964417259744578116480369008481077655245099503360027030457095355662400147348415927381807440279779601
  ( 132 digits)
SNFS difficulty: 140 digits.
Divisors found:
 r1=24164159986601181377625015589587447765463 (pp41)
 r2=2160786218367515171952203262064220489890903 (pp43)
 r3=4410527972854632022342616725553254342960601726209 (pp49)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 11.71 hours.
Scaled time: 14.75 units (timescale=1.260).
Factorization parameters were as follows:
n: 230289472254597723556326237185858964417259744578116480369008481077655245099503360027030457095355662400147348415927381807440279779601
m: 10000000000000000000000000000
c5: 1
c0: 90
skew: 2.46
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1900001)
Primes: RFBsize:78498, AFBsize:64158, largePrimes:1620854 encountered
Relations: rels:1636099, finalFF:171123
Max relations in full relation-set: 28
Initial matrix: 142720 x 171123 with sparse part having weight 17573423.
Pruned matrix : 135646 x 136423 with weight 12496049.
Total sieving time: 11.31 hours.
Total relation processing time: 0.09 hours.
Matrix solve time: 0.25 hours.
Time per square root: 0.05 hours.
Prototype def-par.txt line would be:
snfs,140,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 11.71 hours.
 --------- CPU info (if available) ----------

Jul 11, 2006

By Wataru Sakai / GGNFS-0.77.1-20060513-pentium4, GMP-ECM 6.1 B1=11000000

10132+9 = 1(0)1319<133> = 17401 · C128

C128 = P51 · P78

P51 = 411766421379824555923211974201163701971862160573257<51>

P78 = 139564468173065601765541228336856563574840263361218702800225268893329303849737<78>

Number: 132
N=57467961611401643583702086087006493879662088385724958335727831733808401815987586920291937244985920349405206597321992988908683409
  ( 128 digits)
SNFS difficulty: 132 digits.
Divisors found:
 r1=411766421379824555923211974201163701971862160573257 (pp51)
 r2=139564468173065601765541228336856563574840263361218702800225268893329303849737 (pp78)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 6.31 hours.
Scaled time: 7.55 units (timescale=1.196).
Factorization parameters were as follows:
n: 57467961611401643583702086087006493879662088385724958335727831733808401815987586920291937244985920349405206597321992988908683409
m: 100000000000000000000000000
c5: 100
c0: 9
skew: 1
type: snfs
Factor base limits: 800000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [400000, 1100001)
Primes: RFBsize:63951, AFBsize:63918, largePrimes:1507019 encountered
Relations: rels:1497774, finalFF:158693
Max relations in full relation-set: 28
Initial matrix: 127933 x 158693 with sparse part having weight 12991852.
Pruned matrix : 119793 x 120496 with weight 8138677.
Total sieving time: 6.03 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.16 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,132,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000
total time: 6.31 hours.
 --------- CPU info (if available) ----------

10200+9 = 1(0)1999<201> = 27793 · 1619861 · 67747437129266000269703021<26> · C164

C164 = P39 · P125

P39 = 400259908045666561971192213216134042261<39>

P125 = 81912816932939583803515921686223425749837243002793830987141671128762200181930502382006509105387526239568992549021452850921893<125>

Jul 9, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000, GGNFS-0.77.1-20060513-pentium4 gnfs

10160+9 = 1(0)1599<161> = 14215681 · 3834622668996503113<19> · C135

C135 = P32 · P37 · P67

P32 = 49511107570580443175710053727301<32>

P37 = 1308389305580216069241507311202182597<37>

P67 = 2831848842389382643911352301752663424041355458316158491328312822249<67>

Number: template
N=3705160740401983100863517084343862366824251826484260212973356231617143408125614337889537228469702200653
  ( 103 digits)
Divisors found:
 r1=1308389305580216069241507311202182597 (pp37)
 r2=2831848842389382643911352301752663424041355458316158491328312822249 (pp67)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 12.29 hours.
Scaled time: 15.45 units (timescale=1.257).
Factorization parameters were as follows:
name: template
n: 3705160740401983100863517084343862366824251826484260212973356231617143408125614337889537228469702200653
skew: 4201.71
# norm 7.68e+013
c5: 90300
c4: -2164338660
c3: -1124179346981
c2: 42838024495449134
c1: 61102231652332890264
c0: -405169698669360292416
# alpha -5.23
Y1: 24804153473
Y0: -33313894859610357733
# Murphy_E 2.50e-009
# M 409331033215913408196436280112604987913307780173380076602933295804435792192031068107187579200174582780
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1950001)
Primes: RFBsize:169511, AFBsize:168711, largePrimes:4431119 encountered
Relations: rels:4528620, finalFF:477444
Max relations in full relation-set: 28
Initial matrix: 338303 x 477444 with sparse part having weight 35664560.

Pruned matrix : 232265 x 234020 with weight 17071067.

Polynomial selection time: 0.70 hours.
Total sieving time: 10.32 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.90 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 12.29 hours.
 --------- CPU info (if available) ----------

10187+9 = 1(0)1869<188> = 131 · 889796277314453<15> · 257182844103564007<18> · C153

C153 = P33 · C120

P33 = 534221796617984999646462038876207<33>

C120 = [624416717075815956418387439219885297129632171625703612920258713290457714163614874975484756782174120692018842001812960287<120>]

(22·10182-1)/3 = 7(3)182<183> = 89 · 30881 · 50951 · C172

C172 = P30 · P143

P30 = 211784225570152472986757190977<30>

P143 = 24727131741565022058499972481875489125584547784555429383313765026067944643006887924236480665366530944658610666404211729996682943925108626752731<143>

(4·10168-31)/9 = (4)1671<168> = 3 · 31583582440048607<17> · 1950453510567170479421<22> · C130

C130 = P26 · P51 · P53

P26 = 40723997197061580454452377<26>

P51 = 619122012365504891624162034727407775467907313977069<51>

P53 = 95383354177663653668796178560357826807941934754091677<53>

Number: template
N=59053934184646809250152288479730635440029899839203450505619529839464005477473756144806045588979501754713
  ( 104 digits)
Divisors found:
 r1=619122012365504891624162034727407775467907313977069 (pp51)
 r2=95383354177663653668796178560357826807941934754091677 (pp53)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 12.42 hours.
Scaled time: 15.68 units (timescale=1.262).
Factorization parameters were as follows:
name: template
n: 59053934184646809250152288479730635440029899839203450505619529839464005477473756144806045588979501754713
skew: 1584.29
# norm 7.76e+013
c5: 71820
c4: -1805456645
c3: 11521704364278
c2: 6361480388015250
c1: -933919547984490022
c0: -275396482201632940785
# alpha -4.41
Y1: 35687964367
Y0: -60673908364196146748
# Murphy_E 2.20e-009
# M 49808284345992182295493254281137799247143107035608798248782164222227195480358896851882845839564880622878
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1950001)
Primes: RFBsize:169511, AFBsize:170363, largePrimes:4462254 encountered
Relations: rels:4584204, finalFF:495463
Max relations in full relation-set: 28
Initial matrix: 339955 x 495463 with sparse part having weight 37585090.

Pruned matrix : 225047 x 226810 with weight 17772037.

Polynomial selection time: 0.79 hours.
Total sieving time: 10.47 hours.
Total relation processing time: 0.19 hours.
Matrix solve time: 0.80 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 12.42 hours.
 --------- CPU info (if available) ----------

Jul 9, 2006

By Yousuke Koide / GMP-ECM

(10909-1)/9 = (1)909<909> = 32 · 37 · 3637 · 139987 · 333667 · 2096761 · 85556852551<11> · 272295362253883<15> · 4531530181816613234555190841<28> · 759144383635787638836170905729<30> · 129063282232848961951985354966759<33> · 18998088572819375252842078421374368604969<41> · 157793041231623437279937408119546555586267712054762280488959320521697937521092276297325262649574267470228259745983773969571127099146658127611270714291518805884658999061123143366757<180> · C551

C551 = P34 · C518

P34 = 1612816483312672025726565521114761<34>

C518 = [18731404609543283232112940354795529905218765028242063904196821320680480327243060323107781513864932349843045574631527371074296472799300221176307921568568002896760698073729122374916147359104494785465229670909538835427313759161196304769503931083522392265590989266657153680618595864394113036876314100827462251460591513613066058256339288827531526049865833183556781227354644105909808435821244299021369213150268134537877336607415598924249317297200399350701289053180044523558985734207417941440449142445239590201068779937245641<518>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 6, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(88·10161-7)/9 = 9(7)161<162> = 6445832807<10> · 876136231807637<15> · C138

C138 = P42 · P96

P42 = 326386964613543818430660282822859481650049<42>

P96 = 530464933735084358644926407333310225908640242061529220050842604319203486402399066374016158839947<96>

Number: 97777_161
N=173136839555718845089395520437996758583369835563867385590113997400708115694647626459437368550520023989996609780014966931069180525255707403
  ( 138 digits)
SNFS difficulty: 163 digits.
Divisors found:
 r1=326386964613543818430660282822859481650049 (pp42)
 r2=530464933735084358644926407333310225908640242061529220050842604319203486402399066374016158839947 (pp96)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 120.62 hours.
Scaled time: 81.06 units (timescale=0.672).
Factorization parameters were as follows:
name: 97777_161
n: 173136839555718845089395520437996758583369835563867385590113997400708115694647626459437368550520023989996609780014966931069180525255707403
m: 200000000000000000000000000000000
c5: 55
c0: -14
skew: 2
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4950001)
Primes: RFBsize:315948, AFBsize:315472, largePrimes:5815005 encountered
Relations: rels:5892056, finalFF:708237
Max relations in full relation-set: 28
Initial matrix: 631486 x 708237 with sparse part having weight 49942408.
Pruned matrix : 576793 x 580014 with weight 37827629.
Total sieving time: 102.75 hours.
Total relation processing time: 0.72 hours.
Matrix solve time: 16.87 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,163,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 120.62 hours.
 --------- CPU info (if available) ----------

Jul 5, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4

8·10151-3 = 7(9)1507<152> = 7 · 11 · 547 · 773187643 · C139

C139 = P35 · P36 · P69

P35 = 14629262442055574950399532444482723<35>

P36 = 196829145630461974806359025749407327<36>

P69 = 853129957804341508281677086652220527996609373987586466237769116989621<69>

Number: 79997_151
N=2456558048184250863322473394420778738862152389300191605362777223146582956017106437011501898864484201066970818565473010790375814652861561441
  ( 139 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=14629262442055574950399532444482723 (pp35)
 r2=196829145630461974806359025749407327 (pp36)
 r3=853129957804341508281677086652220527996609373987586466237769116989621 (pp69)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 27.22 hours.
Scaled time: 16.96 units (timescale=0.623).
Factorization parameters were as follows:
n: 2456558048184250863322473394420778738862152389300191605362777223146582956017106437011501898864484201066970818565473010790375814652861561441
m: 2000000000000000000000000000000
c5: 5
c0: -6
skew: 1.04
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1200000
)
Primes: RFBsize:176302, AFBsize:176493, largePrimes:5630517 encountered
Relations: rels:5727860, finalFF:651263
Max relations in full relation-set: 28
Initial matrix: 352860 x 651263 with sparse part having weight 54729852.
Pruned matrix : 233396 x 235224 with weight 23367511.
Total sieving time: 24.99 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 1.83 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 27.22 hours.
 --------- CPU info (if available) ----------

Jul 4, 2006 (3rd)

By Yousuke Koide / GMP-ECM

10910+1 = 1(0)9091<911> = 29 · 101 · 281 · 421 · 521 · 3541 · 27961 · 2311921 · 3471301 · 13489841 · 121499449 · 13159402621<11> · 60368344121<11> · 173827038841<12> · 654721485601<12> · 8886004303541<13> · 19721126575796101<17> · 131454539198398781<18> · 527145878168855401<18> · 1031498834064949381<19> · 12763852652999774041<20> · 643852143556794829021<21> · 848654483879497562821<21> · 1900381976777332243781<22> · 12119730504567977254081<23> · 2737820036624672031089487008281<31> · 3571618567996393297210217238290456648947344377957590363519828421<64> · 431916413820617754546053476804635449461410533962843828981966782964481<69> · 4767139238062537528030092551972140250033930916026378932262992171010636949541765875548467191896982395151649733315765032710728474425304027277684227427428124448895116793267389997296790711552867188304460393677245196360641469741<223> · C248

C248 = P48 · P200

P48 = 191616955559592384669436097618582851538253404221<48>

P200 = 60604177158952949654034234379162779182404932436722562911710488710546750366134190897463822800510718962616059662401246546056631138751315004311007246335189571430318613812710829402180309391025505571625641<200>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 4, 2006 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4

(28·10168-1)/9 = 3(1)168<169> = 32 · 12377 · 41984093 · C156

C156 = P39 · P118

P39 = 149519217696375701284876859610392404589<39>

P118 = 4449137523398654304792825589316222412507885968946755039869777257202378161648912566744773192577933233445826406381882751<118>

Number: 31111_168
N=665231561922157233475900748929464114477514261952773705464562504266252579976754133622808054623764706488624353353542718704652248879655622068869216787952344339
  ( 156 digits)
SNFS difficulty: 169 digits.
Divisors found:
 r1=149519217696375701284876859610392404589 (pp39)
 r2=4449137523398654304792825589316222412507885968946755039869777257202378161648912566744773192577933233445826406381882751 (pp118)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 197.02 hours.
Scaled time: 119.59 units (timescale=0.607).
Factorization parameters were as follows:
n: 665231561922157233475900748929464114477514261952773705464562504266252579976754133622808054623764706488624353353542718704652248879655622068869216787952344339
m: 2000000000000000000000000000000000
c5: 875
c0: -1
skew: 1
type: snfs
Factor base limits: 6000000/6000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [3000000, 6800001)
Primes: RFBsize:412849, AFBsize:412326, largePrimes:5990289 encountered
Relations: rels:6246818, finalFF:925072
Max relations in full relation-set: 28
Initial matrix: 825241 x 925072 with sparse part having weight 51654832.
Pruned matrix : 740939 x 745129 with weight 38208626.
Total sieving time: 163.63 hours.
Total relation processing time: 2.39 hours.
Matrix solve time: 30.57 hours.
Time per square root: 0.42 hours.
Prototype def-par.txt line would be:
snfs,169,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000
total time: 197.02 hours.
 --------- CPU info (if available) ----------

Jul 4, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(4·10154-31)/9 = (4)1531<154> = 193 · C152

C152 = P33 · P120

P33 = 226956410701884405296554862880163<33>

P120 = 101465340791608510434494867505301603408393063217871447504733527448696165828183418411522030373903962435273708671186630099<120>

(4·10189-31)/9 = (4)1881<189> = 3 · 7 · 59 · 11766674917381365427<20> · 899820802396378955324797<24> · C143

C143 = P33 · P111

P33 = 151931647080061133943087045931571<33>

P111 = 222991415928408701409099236295630310191601638543825165330887266241674230685086304307031418000582086049995350531<111>

Jul 2, 2006

By Yousuke Koide / GMP-ECM

(10831-1)/9 = (1)831<831> = 3 · 37 · 1016157022810759<16> · 102092644289739525085919338335107091799<39> · [10710314284791727138118967000605618050187771277688525854207599641117948350932588043961150274118997769379253719854788136101522618592904749621229242261158372761237323432155862577154173589241914856373487807099618367356448232871<224>] · C552

C552 = P32 · C521

P32 = 14583704002876908994687648285921<32>

C521 = [61774491632796531682229129873134854879188889606538991865332732378489613917642712894011233667125452960677817718645793548343784265838763017108563978280693473570714461360003441670259367095714791812784790366631151371036353906505354116538073913505900343716004543484940400938476020223329814783335017162164415847386994139858278658122209555752018698663655721317115426995955226660305071601616168697847105681145122778246346351136132821871465226031104186177624186006825691556823580704133107006746051978806489360025005083661153378671<521>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jul 2, 2006

By Wataru Sakai / GMP-ECM 6.1, Msieve v. 1.06, GGNFS-0.77.1-20060513-pentium4 gnfs

(4·10161-31)/9 = (4)1601<161> = 131 · 883 · 2208991 · 797310706397702315094462679<27> · C123

C123 = P30 · P36 · P58

P30 = 153277297944560404960341396997<30>

P36 = 193655081371246644974840248683617429<36>

P58 = 7349490069689279731072870885529978893158946134836342940881<58>

(4·10166-31)/9 = (4)1651<166> = 43 · 421 · 11489 · 13063 · 219281 · 2114323 · C142

C142 = P31 · C112

P31 = 1401498638512800602338683574933<31>

C112 = [2517542186432726614519045066152878943434736864305600228130570201750511709672675584135765717546155715010204784199<112>]

(4·10171-31)/9 = (4)1701<171> = 3 · 72 · 8461 · C165

C165 = P35 · P130

P35 = 75940027078135399879289466595503179<35>

P130 = 4705520875214939206494061499478771720307848518422079127300817212971538067413967160505918436922055101273111247866701496915002960237<130>

(4·10174-31)/9 = (4)1731<174> = 32 · 1511 · C170

C170 = P33 · C137

P33 = 598391798346729415087360619163761<33>

C137 = [54616627017681544743986838092415411816852954873128335763888764844274262889698533737577934396314791125895856004100260211391989572520846519<137>]

(4·10176-31)/9 = (4)1751<176> = C176

C176 = P35 · C142

P35 = 11555355372315498456034551118161869<35>

C142 = [3846220476345118832108998656213957231199997566866995772725881777424686109863785283056075100863623068462636649438105703704881296092597727524989<142>]

(4·10183-31)/9 = (4)1821<183> = 33 · 7 · 101450189547527<15> · 5144414891929831963<19> · C148

C148 = P31 · C118

P31 = 1494159724423093628331262781519<31>

C118 = [3015572696584852809456973175599019254442494069685606449037092916837733527003570743285631033556963439554618401900680351<118>]

(4·10191-31)/9 = (4)1901<191> = 17 · 79 · 12641819 · C181

C181 = P29 · P37 · P55 · P61

P29 = 46245390417253053507069198277<29>

P37 = 3288698610155369685906033017650636339<37>

P55 = 6012569771633282473568788226836503805781988591612498859<55>

P61 = 2862722471577172119621072059567891400550774220987060325119249<61>

Number: template
N=17212318597180223748039000448764292888344649921197914387046064123268426383453754767791117982035636735387868051436891
 ( 116 digits)
Divisors found:
 r1=6012569771633282473568788226836503805781988591612498859 (pp55)
 r2=2862722471577172119621072059567891400550774220987060325119249 (pp61)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 58.42 hours.
Scaled time: 74.02 units (timescale=1.267).
Factorization parameters were as follows:
name: template
n: 17212318597180223748039000448764292888344649921197914387046064123268426383453754767791117982035636735387868051436891
skew: 91533.13
# norm 1.54e+016
c5: 7980
c4: 4784704672
c3: -222715949872387
c2: -28504304548550969888
c1: 807182662022460227434248
c0: 37026508934687569946500720770
# alpha -6.60
Y1: 284642025107
Y0: -18482745986698681165733
# Murphy_E 5.10e-010
# M 796204495222869985094069394924151158413871914738322193795127044010427633415413290021916171230526019932611113948771
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 3570001)
Primes: RFBsize:315948, AFBsize:316377, largePrimes:7496042 encountered
Relations: rels:7514280, finalFF:746705
Max relations in full relation-set: 28
Initial matrix: 632408 x 746705 with sparse part having weight 56823289.
Pruned matrix : 530076 x 533302 with weight 34084002.
Polynomial selection time: 3.19 hours.
Total sieving time: 46.55 hours.
Total relation processing time: 0.52 hours.
Matrix solve time: 7.77 hours.
Time per square root: 0.38 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 58.42 hours.
 --------- CPU info (if available) ----------

(4·10194-31)/9 = (4)1931<194> = 157 · 983 · 107612863 · 18342123221<11> · 6108145067228494618057<22> · 12278415751815556076259294677<29> · C121

C121 = P39 · P41 · P42

P39 = 101989504789797446295973287236116553803<39>

P41 = 41521142648191624706188680775787708523349<41>

P42 = 459382092743332026030965233512572367869779<42>

(4·10196-31)/9 = (4)1951<196> = 173 · 8951 · 406573 · C184

C184 = P29 · C156

P29 = 18872789591510503930184653933<29>

C156 = [374046150228173323380807595022805382554654053940337044029074580835216463679660422954179214722659465000076502672706389982552032900972277554928993940469580563<156>]

Jul 1, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(88·10159-7)/9 = 9(7)159<160> = 3 · 103 · 5775893 · C151

C151 = P34 · P117

P34 = 5975646174723226470913875531969593<34>

P117 = 916806470240261764242266409467665050319996173440276451312922130501690767888779961598648122293529899763384835078305697<117>

Number: 97777_159
N=5478511076852723780235660847157060648052640735371009236667389281655145464018197502578354313971024281791862019220095682055259107438013227824279762671321
  ( 151 digits)
SNFS difficulty: 161 digits.
Divisors found:
 r1=5975646174723226470913875531969593 (pp34)
 r2=916806470240261764242266409467665050319996173440276451312922130501690767888779961598648122293529899763384835078305697 (pp117)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 102.43 hours.
Scaled time: 68.83 units (timescale=0.672).
Factorization parameters were as follows:
name: 97777_159
n: 5478511076852723780235660847157060648052640735371009236667389281655145464018197502578354313971024281791862019220095682055259107438013227824279762671321
m: 100000000000000000000000000000000
c5: 44
c0: -35
skew: 2
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4550001)
Primes: RFBsize:315948, AFBsize:316147, largePrimes:5850617 encountered
Relations: rels:5997354, finalFF:772910
Max relations in full relation-set: 28
Initial matrix: 632161 x 772910 with sparse part having weight 47864839.
Pruned matrix : 522860 x 526084 with weight 32637755.
Total sieving time: 88.02 hours.
Total relation processing time: 0.71 hours.
Matrix solve time: 13.48 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,161,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 102.43 hours.
 --------- CPU info (if available) ----------

June 2006

Jun 30, 2006 (2nd)

By Wojciech Florek / GMP-ECM 6.1

10200+3 = 1(0)1993<201> = C201

C201 = P29 · C172

P29 = 16892897616604738393032473779<29>

C172 = [5919647550678682918318585392550030687321219331802429980672060525048639901448866420111089641083403610030206379807979210510870824800479444820240779860283084327969945191577457<172>]

Jun 30, 2006

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

(22·10172-1)/3 = 7(3)172<173> = 13 · 84201814666201<14> · C158

C158 = P28 · C131

P28 = 1272085084357714677202671397<28>

C131 = [52664802777632128483139943807112499915228136328357345310586727772346381267412255744083863646372276716206868216067462224684412144253<131>]

10189+9 = 1(0)1889<190> = 14929 · 269221423 · C177

C177 = P35 · P143

P35 = 12192227834085072186320734367252819<35>

P143 = 20406879351220085024953499773532182396131297871099978867280706469418636599119483854979393271010719938699602587208502179786539720548754102460333<143>

Jun 29, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4

(2·10157+1)/3 = (6)1567<157> = 7 · 23 · 541 · C152

C152 = P27 · P125

P27 = 890782728330524191869166267<27>

P125 = 85923866571843740803540965749926517381370019113790480690155834870443120275131486394405562940747729082323857462899385910744101<125>

Number: 66667_157
N=76539496293574891983635855692433688093898654052957677485524467763477648553594868792168478739241417052234379245550185034232289717301370439681136458440967
  ( 152 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=890782728330524191869166267 (pp27)
 r2=85923866571843740803540965749926517381370019113790480690155834870443120275131486394405562940747729082323857462899385910744101 (pp125)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 48.81 hours.
Scaled time: 31.29 units (timescale=0.641).
Factorization parameters were as follows:
n: 76539496293574891983635855692433688093898654052957677485524467763477648553594868792168478739241417052234379245550185034232289717301370439681136458440967
m: 10000000000000000000000000000000
c5: 200
c0: 1
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216391, largePrimes:5587411 encountered
Relations: rels:5531851, finalFF:540104
Max relations in full relation-set: 28
Initial matrix: 433272 x 540104 with sparse part having weight 41840958.
Pruned matrix : 367301 x 369531 with weight 26704226.
Total sieving time: 41.91 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 6.39 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 48.81 hours.
 --------- CPU info (if available) ----------

(2·10162-11)/9 = (2)1611<162> = 2999 · 13291 · 737369127871<12> · C142

C142 = P58 · P85

P58 = 3477161523419951142339720131731396316406999807975085010917<58>

P85 = 2174420563538039342235832474859054013840635530546636646389334682567283354466126851267<85>

Number: 22221_162
N=7560811519267597547267443095951233885561978836680096060752707770152009100385863396144664462142405057459157349147876168151822386943389530281839
  ( 142 digits)
SNFS difficulty: 162 digits.
Divisors found:
 r1=3477161523419951142339720131731396316406999807975085010917 (pp58)
 r2=2174420563538039342235832474859054013840635530546636646389334682567283354466126851267 (pp85)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 80.13 hours.
Scaled time: 50.56 units (timescale=0.631).
Factorization parameters were as follows:
n: 7560811519267597547267443095951233885561978836680096060752707770152009100385863396144664462142405057459157349147876168151822386943389530281839
m: 100000000000000000000000000000000
c5: 200
c0: -11
skew: 1
type: snfs
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2250000, 4549000
)
Primes: RFBsize:315948, AFBsize:316992, largePrimes:5799465 encountered
Relations: rels:5908229, finalFF:740494
Max relations in full relation-set: 28
Initial matrix: 633005 x 740494 with sparse part having weight 45607314.
Pruned matrix : 551212 x 554441 with weight 32109977.
Total sieving time: 66.12 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 13.41 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000
total time: 80.13 hours.
 --------- CPU info (if available) ----------

Jun 28, 2006

By Yousuke Koide / GMP-ECM / Jun 13, 2006

(10629-1)/9 = (1)629<629> = 52837 · 2028119 · 2071723 · 247629013 · 654756293 · 5363222357<10> · 2212394296770203368013<22> · C563

C563 = P37 · C527

P37 = 1789869609522556717733652117803369849<37>

C527 = [14534606650760746267274530737012122249588886991871533480924248527831473439337496631299129179522033276819164732384678553894131236188994972432041295892899181561322393208614711702308252990527266567131722050002675497142409690259209102269418390421674637868575482378208912819748484996888540615006146463031999507378641474887080601161024829052876998932648990033604585060950024365773053544964048384392311758635258298416485361871913055731243696761053009538099247807223175971678734515859190036820748543634426650689638017502134520137543399<527>]

By Brude Dodson / GMP-ECM / Jun 25, 2006

(10369-1)/9 = (1)369<369> = 32 · 37 · 83 · 1231 · 333667 · 538987 · 1811791 · 626920594693<12> · 9425856976319889649<19> · 1900016393894413508477719<25> · 201763709900322803748657942361<30> · 3151445759294008336434146467746716852125711<43> · 8414640003465161203119978906558054839526493<43> · C174

C174 = P52 · P122

P52 = 4624740815741021164555032450406356165555243059597323<52>

P122 = 36075379229129405137442680972370788324414060277012433191198831287911648192680373281921936535843435181632954359677168188643<122>

By Yousuke Koide / GMP-ECM / Jun 28, 2006

(10791-1)/9 = (1)791<791> = 227 · 239 · 4649 · 123397 · 1177009 · 142101569 · 908191467191<12> · 1793584572599<13> · 5325832146769<13> · 827436967363609<15> · 609308862837834547266089<24> · 53895712312217719065267103426685397298498705173449226555003346881878523705781079015749721646701723<98> · C589

C589 = P38 · C552

P38 = 17268952016347267202474461693447627333<38>

C552 = [524338276467821469306866110640693273267456771354911491249811039886750737206459012463989313027609454624719205006551535049494191144723719815372375176302554242015920402149910500053458715224907875055739914800002691751396537788564528624249078377798631613710343087407520477946788491848531530083964817956899222619192798538490548065449464266022982267809530617447686365811014092939620045876935557367216873409267163582736418854782229284649982294276357936431663242770726403360599987506648872509414316421874236089815724432810048030031264456545314684078313249739241<552>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jun 27, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(88·10154-7)/9 = 9(7)154<155> = 739 · 1409 · 89561 · 9944520990408625844894246647<28> · C117

C117 = P40 · P77

P40 = 5837116682833462849392995823393826958467<40>

P77 = 18062736791772976438494600135843067934866747134653325808014080402535275160343<77>

Number: 97777_154
N=105434302264887821200236582241715413873905252645232754612561173722931173696896607522883110803817912699363819426474181
  ( 117 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=5837116682833462849392995823393826958467 (pp40)
 r2=18062736791772976438494600135843067934866747134653325808014080402535275160343 (pp77)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 61.01 hours.
Scaled time: 37.15 units (timescale=0.609).
Factorization parameters were as follows:
name: 97777_154
n: 105434302264887821200236582241715413873905252645232754612561173722931173696896607522883110803817912699363819426474181
m: 10000000000000000000000000000000
c5: 44
c0: -35
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3000001)
Primes: RFBsize:216816, AFBsize:216382, largePrimes:5730781 encountered
Relations: rels:5731090, finalFF:574418
Max relations in full relation-set: 28
Initial matrix: 433264 x 574418 with sparse part having weight 48987164.
Pruned matrix : 363853 x 366083 with weight 31040164.
Total sieving time: 53.51 hours.
Total relation processing time: 0.53 hours.
Matrix solve time: 6.76 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 61.01 hours.
 --------- CPU info (if available) ----------

Jun 24, 2006 (3rd)

By suberi / GGNFS-0.77.1-20060513-pentium4

(2·10156+7)/9 = (2)1553<156> = 23 · 3499 · 23646641 · C144

C144 = P61 · P83

P61 = 6926356052576897781946985964283783248377448772933915690211713<61>

P83 = 16859373684167425982860874223536195143299267692900426968939447864947450149457709003<83>

Number: 22223_156
N=116774024959988722821062037579716837704602479668438645177019103488857401948400666554562683576727032687209786010840712519018713258848097016152139
  ( 144 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=6926356052576897781946985964283783248377448772933915690211713 (pp61)
 r2=16859373684167425982860874223536195143299267692900426968939447864947450149457709003 (pp83)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 44.21 hours.
Scaled time: 26.92 units (timescale=0.609).
Factorization parameters were as follows:
n: 116774024959988722821062037579716837704602479668438645177019103488857401948400666554562683576727032687209786010840712519018713258848097016152139
m: 10000000000000000000000000000000
c5: 20
c0: 7
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2500001)
Primes: RFBsize:216816, AFBsize:215976, largePrimes:5576703 encountered
Relations: rels:5572542, finalFF:588575
Max relations in full relation-set: 28
Initial matrix: 432858 x 588575 with sparse part having weight 43819791.
Pruned matrix : 321876 x 324104 with weight 27043784.
Total sieving time: 37.95 hours.
Total relation processing time: 0.73 hours.
Matrix solve time: 5.26 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 44.21 hours.
 --------- CPU info (if available) ----------

10154-3 = (9)1537<154> = 13 · 11243 · 6067869097<10> · C140

C140 = P37 · P48 · P56

P37 = 1640121535660974334937516641312705897<37>

P48 = 632474589733957453044658343116704489644784209341<48>

P56 = 10869739116142629212501414649177235931983515829671794207<56>

Number: 99997_154
N=11275562949784345252112605626469572573490020234580540167103938207368024209876467537743006522462110907256030913689041774978331494305994400539
  ( 140 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=1640121535660974334937516641312705897 (pp37)
 r2=632474589733957453044658343116704489644784209341 (pp48)
 r3=10869739116142629212501414649177235931983515829671794207 (pp56)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 37.22 hours.
Scaled time: 23.49 units (timescale=0.631).
Factorization parameters were as follows:
n: 11275562949784345252112605626469572573490020234580540167103938207368024209876467537743006522462110907256030913689041774978331494305994400539
m: 10000000000000000000000000000000
c5: 1
c0: -30
skew: 1.97
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2400001)
Primes: RFBsize:216816, AFBsize:215581, largePrimes:5481373 encountered
Relations: rels:5403721, finalFF:528307
Max relations in full relation-set: 28
Initial matrix: 432461 x 528307 with sparse part having weight 37745359.
Pruned matrix : 360063 x 362289 with weight 23851643.
Total sieving time: 30.84 hours.
Total relation processing time: 0.27 hours.
Matrix solve time: 5.94 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 37.22 hours.
 --------- CPU info (if available) ----------

Jun 24, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.1 B1=11000000

10152+9 = 1(0)1519<153> = 29 · 293 · 1640081714429881<16> · C133

C133 = P33 · P101

P33 = 269884379947565697172496988236741<33>

P101 = 26588335208574136942682656526949478340363566869268859697120096025992721634714319195150472641068851757<101>

10157+9 = 1(0)1569<158> = 103 · 379 · 11025855177473150881<20> · C134

C134 = P30 · P104

P30 = 489153471136315018633879719917<30>

P104 = 47496995862766072526492146025536044546152041717277054294283602053960385357153879208150508927116593915441<104>

10194+9 = 1(0)1939<195> = 601 · 1669 · 4157 · 102873857153<12> · C174

C174 = P30 · P144

P30 = 779377879409212880284613409841<30>

P144 = 299113536682015207303470362477684416309447351856104432130038973632908830947016400385722023444292682919977688505297634840607839940972350056603601<144>

Jun 24, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(88·10153-7)/9 = 9(7)153<154> = 33 · 19 · 71 · 3260123 · C143

C143 = P38 · P43 · P63

P38 = 99116919537660717344019019386864967843<38>

P43 = 1546063793752448861604594357599366716472771<43>

P63 = 537347530384367705748566479582863469498681675372594701184956221<63>

Number: 97777_153
N=82343716238265332733845578767001197316759534003740090541991240208597861404143350691125394255272175363383252368085479900141859271017232097820613
  ( 143 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=99116919537660717344019019386864967843 (pp38)
 r2=1546063793752448861604594357599366716472771 (pp43)
 r3=537347530384367705748566479582863469498681675372594701184956221 (pp63)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 50.96 hours.
Scaled time: 34.24 units (timescale=0.672).
Factorization parameters were as follows:
name: 97777_153
n: 82343716238265332733845578767001197316759534003740090541991240208597861404143350691125394255272175363383252368085479900141859271017232097820613
m: 2000000000000000000000000000000
c5: 2750
c0: -7
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2700001)
Primes: RFBsize:216816, AFBsize:216172, largePrimes:5588683 encountered
Relations: rels:5518212, finalFF:527248
Max relations in full relation-set: 28
Initial matrix: 433055 x 527248 with sparse part having weight 41503672.
Pruned matrix : 374357 x 376586 with weight 27113464.
Total sieving time: 44.17 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 6.18 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 50.96 hours.
 --------- CPU info (if available) ----------

Jun 22, 2006 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4

(37·10153-1)/9 = 4(1)153<154> = 19 · 52673 · 6828739 · 53203810549582657<17> · C125

C125 = P58 · P67

P58 = 1449115186608669999968721909978577884920205127608130753117<58>

P67 = 7802457274112608923698648032270060088171243614756391036896564625483<67>

Number: 41111_153
N=11306659328781867934200901863811224235021793204640218687383945073613523898676275009234833635994753050785147831466037839880511
  ( 125 digits)
SNFS difficulty: 154 digits.
Divisors found:
 r1=1449115186608669999968721909978577884920205127608130753117 (pp58)
 r2=7802457274112608923698648032270060088171243614756391036896564625483 (pp67)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 53.40 hours.
Scaled time: 34.28 units (timescale=0.642).
Factorization parameters were as follows:
n: 11306659328781867934200901863811224235021793204640218687383945073613523898676275009234833635994753050785147831466037839880511
m: 1000000000000000000000000000000
c5: 37000
c0: -1
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3000001)
Primes: RFBsize:216816, AFBsize:217626, largePrimes:5592626 encountered
Relations: rels:5485878, finalFF:487203
Max relations in full relation-set: 28
Initial matrix: 434509 x 487203 with sparse part having weight 39884456.
Pruned matrix : 411756 x 413992 with weight 30091644.
Total sieving time: 44.27 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 8.51 hours.
Time per square root: 0.22 hours.
Prototype def-par.txt line would be:
snfs,154,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 53.40 hours.
 --------- CPU info (if available) ----------

8·10152-1 = 7(9)152<153> = 23 · C152

C152 = P40 · P112

P40 = 7901339528982736247439245218030751681423<40>

P112 = 4402115434739492378122395747854232895486096498939727009935645870272775578543880889791663422087920251843606452631<112>

Number: 79999_152
N=34782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913
  ( 152 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=7901339528982736247439245218030751681423 (pp40)
 r2=4402115434739492378122395747854232895486096498939727009935645870272775578543880889791663422087920251843606452631 (pp112)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 33.81 hours.
Scaled time: 20.62 units (timescale=0.610).
Factorization parameters were as follows:
n: 34782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913
m: 2000000000000000000000000000000
c5: 25
c0: -1
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176093, largePrimes:5463800 encountered
Relations: rels:5400866, finalFF:508492
Max relations in full relation-set: 28
Initial matrix: 352459 x 508492 with sparse part having weight 43119422.
Pruned matrix : 279663 x 281489 with weight 22308678.
Total sieving time: 29.53 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 3.46 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 33.81 hours.
 --------- CPU info (if available) ----------

Jun 22, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(88·10152-7)/9 = 9(7)152<153> = 432 · 1699 · 9787 · 26731 · C139

C139 = P36 · P52(1123...) · P52(7199...)

P36 = 147069431940540632633622231942675241<36>

P52(1123...) = 1123545359101834709721738804452009746749923728439347<52>

P52(7199...) = 7199992653826193042600639583180770081495925912971633<52>

Number: 97777_152
N=1189720865726551197046584113282700046958525888139439104529939391718176978625271748994829022891657295537737626613238339384672302925168944891
  ( 139 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=147069431940540632633622231942675241 (pp36)
 r2=1123545359101834709721738804452009746749923728439347 (pp52)
 r3=7199992653826193042600639583180770081495925912971633 (pp52)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 44.45 hours.
Scaled time: 27.07 units (timescale=0.609).
Factorization parameters were as follows:
name: 97777_152
n: 1189720865726551197046584113282700046958525888139439104529939391718176978625271748994829022891657295537737626613238339384672302925168944891
m: 2000000000000000000000000000000
c5: 275
c0: -7
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:176544, largePrimes:5634915 encountered
Relations: rels:5575605, finalFF:493838
Max relations in full relation-set: 28
Initial matrix: 352912 x 493838 with sparse part having weight 45407063.
Pruned matrix : 299744 x 301572 with weight 25519786.
Total sieving time: 39.81 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 4.14 hours.
Time per square root: 0.18 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 44.45 hours.
 --------- CPU info (if available) ----------

Jun 20, 2006 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4

2·10153-9 = 1(9)1521<154> = 11 · C153

C153 = P41 · P45 · P68

P41 = 14143455769740740001759009960126743688349<41>

P45 = 453912657024767148614711372141519336680287959<45>

P68 = 28321058492200039254937740121739341593546053812714710601460743639391<68>

Number: 19991_153
N=181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181
  ( 153 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=14143455769740740001759009960126743688349 (pp41)
 r2=453912657024767148614711372141519336680287959 (pp45)
 r3=28321058492200039254937740121739341593546053812714710601460743639391 (pp68)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 37.97 hours.
Scaled time: 23.05 units (timescale=0.607).
Factorization parameters were as follows:
n: 181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181818181
m: 2000000000000000000000000000000
c5: 125
c0: -18
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176188, largePrimes:5665430 encountered
Relations: rels:5691661, finalFF:578636
Max relations in full relation-set: 28
Initial matrix: 352556 x 578636 with sparse part having weight 51231586.
Pruned matrix : 262318 x 264144 with weight 24854504.
Total sieving time: 33.49 hours.
Total relation processing time: 0.69 hours.
Matrix solve time: 3.55 hours.
Time per square root: 0.24 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 37.97 hours.
 --------- CPU info (if available) ----------

Jun 20, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

6·10151-1 = 5(9)151<152> = 61 · 129113 · C145

C145 = P33 · P47 · P66

P33 = 836660367018273797355323968615817<33>

P47 = 17524625066162102246330727763070206160904572767<47>

P66 = 519581298814572713681606589033971690588245769057952345724971828437<66>

Number: 59999_151
N=7618183741196077701919007787434389979650561529975077111890677031798171966023408393181573187954686535228449650090472280413154419441706483315606243
  ( 145 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=836660367018273797355323968615817 (pp33)
 r2=17524625066162102246330727763070206160904572767 (pp47)
 r3=519581298814572713681606589033971690588245769057952345724971828437 (pp66)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 32.65 hours.
Scaled time: 19.88 units (timescale=0.609).
Factorization parameters were as follows:
name: 59999_151
n: 7618183741196077701919007787434389979650561529975077111890677031798171966023408393181573187954686535228449650090472280413154419441706483315606243
m: 1000000000000000000000000000000
c5: 60
c0: -1
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:175738, largePrimes:5548666 encountered
Relations: rels:5544388, finalFF:557581
Max relations in full relation-set: 28
Initial matrix: 352107 x 557581 with sparse part having weight 49093900.
Pruned matrix : 263359 x 265183 with weight 23631186.
Total sieving time: 29.11 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 3.06 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 32.65 hours.
 --------- CPU info (if available) ----------

Jun 19, 2006

By Wojciech Florek / GMP-ECM 6.0.1 B1=250000

10182+3 = 1(0)1813<183> = C183

C183 = P27 · P156

P27 = 406739627350936953562388377<27>

P156 = 245857529671480737053230473791951684664784508684537281437794354233101717382061812791982857492060102011506560855529194447399887136377222705239997696635282939<156>

Jun 18, 2006 (4th)

By Alfred Reich / Msieve v. 1.06

(2·10157+43)/9 = (2)1567<157> = 7 · 6011267 · 11340661 · 26297446143827679370836289<26> · C117

C117 = P54 · P63

P54 = 297907083346305195502362629714985396531415470201105233<54>

P63 = 594416225273485143935306604924356739743242652295164459113417819<63>

prp54 factor: 297907083346305195502362629714985396531415470201105233
prp63 factor: 594416225273485143935306604924356739743242652295164459113417819

Fri Jun 16 15:30:27 2006  
Fri Jun 16 15:30:27 2006  
Fri Jun 16 15:30:27 2006  Msieve v. 1.06
Fri Jun 16 15:30:27 2006  random seeds: 6e3be7d0 af211ff4
Fri Jun 16 15:30:27 2006  factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits)
Fri Jun 16 15:30:28 2006  using multiplier of 17
Fri Jun 16 15:30:28 2006  sieve interval: 19 blocks of size 65536
Fri Jun 16 15:30:28 2006  processing polynomials in batches of 3
Fri Jun 16 15:30:28 2006  using a sieve bound of 10566139 (350000 primes)
Fri Jun 16 15:30:28 2006  using large prime bound of 1584920850 (30 bits)
Fri Jun 16 15:30:28 2006  using double large prime bound of 36308945412966600 (47-56 bits)
Fri Jun 16 15:30:28 2006  using trial factoring cutoff of 68 bits
Fri Jun 16 15:30:28 2006  polynomial 'A' values have 16 factors
Sat Jun 17 14:47:39 2006  5839 relations (5561 full + 278 combined from 322304 partial), need 350096
Sat Jun 17 14:47:39 2006  elapsed time 23:17:12
Sat Jun 17 14:48:21 2006  
Sat Jun 17 14:48:21 2006  
Sat Jun 17 14:48:21 2006  Msieve v. 1.06
Sat Jun 17 14:48:21 2006  random seeds: a6d38e10 66593cf6
Sat Jun 17 14:48:21 2006  factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits)
Sat Jun 17 14:48:23 2006  using multiplier of 17
Sat Jun 17 14:48:23 2006  sieve interval: 19 blocks of size 65536
Sat Jun 17 14:48:23 2006  processing polynomials in batches of 3
Sat Jun 17 14:48:23 2006  using a sieve bound of 10566139 (350000 primes)
Sat Jun 17 14:48:23 2006  using large prime bound of 1584920850 (30 bits)
Sat Jun 17 14:48:23 2006  using double large prime bound of 36308945412966600 (47-56 bits)
Sat Jun 17 14:48:23 2006  using trial factoring cutoff of 68 bits
Sat Jun 17 14:48:23 2006  polynomial 'A' values have 16 factors
Sat Jun 17 15:05:03 2006  67 relations (67 full + 0 combined from 3929 partial), need 350096
Sat Jun 17 15:05:03 2006  elapsed time 00:16:42
Sat Jun 17 15:08:44 2006  
Sat Jun 17 15:08:44 2006  
Sat Jun 17 15:08:44 2006  Msieve v. 1.06
Sat Jun 17 15:08:44 2006  random seeds: 2edef0b0 ff574550
Sat Jun 17 15:08:44 2006  factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits)
Sat Jun 17 15:08:46 2006  using multiplier of 17
Sat Jun 17 15:08:46 2006  sieve interval: 19 blocks of size 65536
Sat Jun 17 15:08:46 2006  processing polynomials in batches of 3
Sat Jun 17 15:08:46 2006  using a sieve bound of 10566139 (350000 primes)
Sat Jun 17 15:08:46 2006  using large prime bound of 1584920850 (30 bits)
Sat Jun 17 15:08:46 2006  using double large prime bound of 36308945412966600 (47-56 bits)
Sat Jun 17 15:08:46 2006  using trial factoring cutoff of 68 bits
Sat Jun 17 15:08:46 2006  polynomial 'A' values have 16 factors
Sat Jun 17 15:08:52 2006  restarting with 45113 full and 2586148 partial relations
Sat Jun 17 15:10:15 2006  79829 relations (45115 full + 34714 combined from 2586446 partial), need 350096
Sat Jun 17 15:10:15 2006  elapsed time 00:01:31
Sat Jun 17 15:11:28 2006  
Sat Jun 17 15:11:28 2006  
Sat Jun 17 15:11:28 2006  Msieve v. 1.06
Sat Jun 17 15:11:28 2006  random seeds: f0c64d78 a1063e8e
Sat Jun 17 15:11:28 2006  factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits)
Sat Jun 17 15:11:29 2006  using multiplier of 17
Sat Jun 17 15:11:29 2006  sieve interval: 19 blocks of size 65536
Sat Jun 17 15:11:29 2006  processing polynomials in batches of 3
Sat Jun 17 15:11:29 2006  using a sieve bound of 10566139 (350000 primes)
Sat Jun 17 15:11:29 2006  using large prime bound of 1584920850 (30 bits)
Sat Jun 17 15:11:29 2006  using double large prime bound of 36308945412966600 (47-56 bits)
Sat Jun 17 15:11:29 2006  using trial factoring cutoff of 68 bits
Sat Jun 17 15:11:29 2006  polynomial 'A' values have 16 factors
Sun Jun 18 14:02:17 2006  5722 relations (5458 full + 264 combined from 315736 partial), need 350096
Sun Jun 18 14:02:17 2006  elapsed time 22:50:49
Sun Jun 18 14:53:41 2006  
Sun Jun 18 14:53:41 2006  
Sun Jun 18 14:53:41 2006  Msieve v. 1.06
Sun Jun 18 14:53:41 2006  random seeds: a7040c00 6bf83931
Sun Jun 18 14:53:41 2006  factoring 177080803964944263576713030557411134623070902269225184654689439234506372676272442327285572763581070913582793916346827 (117 digits)
Sun Jun 18 14:53:43 2006  using multiplier of 17
Sun Jun 18 14:53:43 2006  sieve interval: 19 blocks of size 65536
Sun Jun 18 14:53:43 2006  processing polynomials in batches of 3
Sun Jun 18 14:53:43 2006  using a sieve bound of 10566139 (350000 primes)
Sun Jun 18 14:53:43 2006  using large prime bound of 1584920850 (30 bits)
Sun Jun 18 14:53:43 2006  using double large prime bound of 36308945412966600 (47-56 bits)
Sun Jun 18 14:53:43 2006  using trial factoring cutoff of 68 bits
Sun Jun 18 14:53:43 2006  polynomial 'A' values have 16 factors
Sun Jun 18 14:53:58 2006  restarting with 98809 full and 5685171 partial relations
Sun Jun 18 14:53:58 2006  489590 relations (98809 full + 390781 combined from 5685171 partial), need 350096
Sun Jun 18 14:54:19 2006  begin with 5685171 relations
Sun Jun 18 14:54:35 2006  reduce to 1179398 relations in 14 passes
Sun Jun 18 14:54:35 2006  attempting to read 98809 full and 1179398 partial relations
Sun Jun 18 14:55:21 2006  recovered 98809 full and 1179398 partial relations
Sun Jun 18 14:55:21 2006  recovered 1255866 polynomials
Sun Jun 18 14:55:27 2006  attempting to build 390781 cycles
Sun Jun 18 14:55:28 2006  found 390781 cycles in 6 passes
Sun Jun 18 14:55:30 2006  distribution of cycle lengths:
Sun Jun 18 14:55:30 2006     length 2 : 76003
Sun Jun 18 14:55:30 2006     length 3 : 82423
Sun Jun 18 14:55:30 2006     length 4 : 72166
Sun Jun 18 14:55:30 2006     length 5 : 57921
Sun Jun 18 14:55:30 2006     length 6 : 40330
Sun Jun 18 14:55:30 2006     length 7 : 26146
Sun Jun 18 14:55:30 2006     length 8 : 16036
Sun Jun 18 14:55:30 2006     length 9+: 19756
Sun Jun 18 14:55:30 2006  largest cycle: 21 relations
Sun Jun 18 14:55:31 2006  350000 x 350064 system, weight 22152847 (avg 63.28/col)
Sun Jun 18 14:55:34 2006  reduce to 338708 x 338772 in 4 passes
Sun Jun 18 16:11:11 2006  lanczos halted after 5357 iterations
Sun Jun 18 16:11:15 2006  recovered 56 nontrivial dependencies
Sun Jun 18 16:13:09 2006  prp54 factor: 297907083346305195502362629714985396531415470201105233
Sun Jun 18 16:13:09 2006  prp63 factor: 594416225273485143935306604924356739743242652295164459113417819
Sun Jun 18 16:13:12 2006  elapsed time 01:19:31

Jun 18, 2006 (3rd)

By Wataru Sakai / GMP-ECM 6.1

(25·10161-1)/3 = 8(3)161<162> = 71 · 627632323902741384517983871<27> · C134

C134 = P33 · P101

P33 = 402923263960731990459276252411929<33>

P101 = 46412264609376042963875982573595320846726898199501545598399929674110110204265192309020927313561073797<101>

(25·10189-1)/3 = 8(3)189<190> = 13 · 69481 · 14970782913227<14> · 86676545786512496411372249<26> · C145

C145 = P29 · P33 · P85

P29 = 22947665214016491792948713879<29>

P33 = 263220054799792924810769047222031<33>

P85 = 1177079381440907821047749257131763892168650187727161937621530953691546230966643693843<85>

(25·10193-1)/3 = 8(3)193<194> = 2729 · 9431 · 113622631267<12> · C176

C176 = P37 · P140

P37 = 1234673054650272416503200054655444603<37>

P140 = 23080258080801038899595047931573006063528336563000814220369471250323182879121823026175822141456825879452373941615318614152585303505844325067<140>

Jun 18, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(73·10151-1)/9 = 8(1)151<152> = 3 · 29 · 47 · 193 · 457697 · C141

C141 = P33 · P34 · P75

P33 = 528012984669708627919758887087231<33>

P34 = 2640623962369281969675262349483603<34>

P75 = 161055923586852517269688910385341375145213411153442717701673814626750164283<75>

Number: 81111_151
N=224557655449331640744698222153463653716415037742054456753768335971442934095442031868984712643312221148993545757459799412236334041135414093919
  ( 141 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=528012984669708627919758887087231 (pp33)
 r2=2640623962369281969675262349483603 (pp34)
 r3=161055923586852517269688910385341375145213411153442717701673814626750164283 (pp75)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 44.55 hours.
Scaled time: 29.98 units (timescale=0.673).
Factorization parameters were as follows:
name: 81111_151
n: 224557655449331640744698222153463653716415037742054456753768335971442934095442031868984712643312221148993545757459799412236334041135414093919
m: 1000000000000000000000000000000
c5: 730
c0: -1
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:176503, largePrimes:5534398 encountered
Relations: rels:5399634, finalFF:435070
Max relations in full relation-set: 28
Initial matrix: 352872 x 435070 with sparse part having weight 39896073.
Pruned matrix : 320448 x 322276 with weight 25707123.
Total sieving time: 39.82 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 4.20 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 44.55 hours.
 --------- CPU info (if available) ----------

Jun 18, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4

(8·10153-71)/9 = (8)1521<153> = 8825839534511526662522911<25> · C129

C129 = P46 · P83

P46 = 1296444514871243498998765398449712354381717833<46>

P83 = 77685061845475214425509536216756309596984840086525079446336201532416456388867813687<83>

Number: 88881_153
N=100714372316999662567112812918965620315388389942591227612416816485546219492067911197547793034221068381867775300311816362049380271
  ( 129 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=1296444514871243498998765398449712354381717833 (pp46)
 r2=77685061845475214425509536216756309596984840086525079446336201532416456388867813687 (pp83)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 60.66 hours.
Scaled time: 37.13 units (timescale=0.612).
Factorization parameters were as follows:
n: 100714372316999662567112812918965620315388389942591227612416816485546219492067911197547793034221068381867775300311816362049380271
m: 2000000000000000000000000000000
c5: 250
c0: -71
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2700001)
Primes: RFBsize:176302, AFBsize:175124, largePrimes:5822215 encountered
Relations: rels:5825108, finalFF:487746
Max relations in full relation-set: 28
Initial matrix: 351492 x 487746 with sparse part having weight 52251534.
Pruned matrix : 305361 x 307182 with weight 32152741.
Total sieving time: 53.71 hours.
Total relation processing time: 1.08 hours.
Matrix solve time: 5.58 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 60.66 hours.
 --------- CPU info (if available) ----------

Jun 17, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4

(4·10153+41)/9 = (4)1529<153> = 23 · 29 · 7877 · 873567461478995351<18> · C128

C128 = P53 · P76

P53 = 10278202000310109853026337644927666384593872391970911<53>

P76 = 9421438220178605267247787803414490154127967731184104140712790580208553504351<76>

Number: 44449_153
N=96835445160437861836793054504352665974763358359367105494199949648027977115227878216143159883536675005810147600085224164703933761
  ( 128 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=10278202000310109853026337644927666384593872391970911 (pp53)
 r2=9421438220178605267247787803414490154127967731184104140712790580208553504351 (pp76)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 36.61 hours.
Scaled time: 23.54 units (timescale=0.643).
Factorization parameters were as follows:
n: 96835445160437861836793054504352665974763358359367105494199949648027977115227878216143159883536675005810147600085224164703933761
m: 2000000000000000000000000000000
c5: 125
c0: 41
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2300001)
Primes: RFBsize:176302, AFBsize:176674, largePrimes:5475359 encountered
Relations: rels:5331530, finalFF:432026
Max relations in full relation-set: 28
Initial matrix: 353041 x 432026 with sparse part having weight 38289105.
Pruned matrix : 319991 x 321820 with weight 24785869.
Total sieving time: 31.58 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 4.55 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 36.61 hours.
 --------- CPU info (if available) ----------

(5·10157-41)/9 = (5)1561<157> = 31638006853<11> · 127308301733038781811409<24> · C124

C124 = P47 · P77

P47 = 62177795589380677359547676171051471759978319277<47>

P77 = 22183309247072798284455041381076813661365827752047238245813949734174421655119<77>

Number: 55551_157
N=1379309267860510631923280660454483985542807005995371878444954987504570972707580675762406732618983047945197528669850163428963
  ( 124 digits)
SNFS difficulty: 157 digits.
Divisors found:
 r1=62177795589380677359547676171051471759978319277 (pp47)
 r2=22183309247072798284455041381076813661365827752047238245813949734174421655119 (pp77)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 53.50 hours.
Scaled time: 36.75 units (timescale=0.687).
Factorization parameters were as follows:
n: 1379309267860510631923280660454483985542807005995371878444954987504570972707580675762406732618983047945197528669850163428963
m: 10000000000000000000000000000000
c5: 500
c0: -41
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 3300001)
Primes: RFBsize:216816, AFBsize:216877, largePrimes:5686463 encountered
Relations: rels:5613572, finalFF:490335
Max relations in full relation-set: 28
Initial matrix: 433759 x 490335 with sparse part having weight 45003353.
Pruned matrix : 410960 x 413192 with weight 34410874.
Total sieving time: 43.92 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 9.07 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 53.50 hours.
 --------- CPU info (if available) ----------

Jun 16, 2006 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(28·10151-1)/9 = 3(1)151<152> = 31 · 19843 · 434831 · C141

C141 = P60 · P81

P60 = 974853410034804062561219744184438708636042947181325656020147<60>

P81 = 119312702335017997752212094830142486881715593155366467314651908260291633099814831<81>

Number: 31111_151
N=116312394731759824276532451135704508184575224005721352126402868892503361415954444774635572442848479083945663759064809382402290241666105400157
  ( 141 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=974853410034804062561219744184438708636042947181325656020147 (pp60)
 r2=119312702335017997752212094830142486881715593155366467314651908260291633099814831 (pp81)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 36.44 hours.
Scaled time: 24.31 units (timescale=0.667).
Factorization parameters were as follows:
name:  31111_151
n: 116312394731759824276532451135704508184575224005721352126402868892503361415954444774635572442848479083945663759064809382402290241666105400157
m: 1000000000000000000000000000000
c5: 280
c0: -1
skew: 2
type: snfs
 Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176603, largePrimes:5432957 encountered
Relations: rels:5288454, finalFF:437164
Max relations in full relation-set: 28
Initial matrix: 352972 x 437164 with sparse part having weight 38153671.
Pruned matrix : 312776 x 314604 with weight 23827219.
Total sieving time: 32.14 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 3.80 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 36.44 hours.
 --------- CPU info (if available) ----------

Jun 16, 2006 (2nd)

By Alexander Mkrtychyan / ggnfs-0.77.1-20060513-win32

(10186+71)/9 = (1)1859<186> = C186

C186 = P53 · P133

P53 = 21956285956390994430963419957738743694747827961903819<53>

P133 = 5060560394039188481932328242445842739178885005851611298737492037561232350261294769209243502470606386060971130677592702162720129986701<133>

From dependence 1, sqrt obtained:
r1=21956285956390994430963419957738743694747827961903819 (p53)
r2=5060560394039188481932328242445842739178885005851611298737492037561232350261294769209243502470606386060971130677592702162720129986701 (p133)

sieving params:

n: 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111119
m: 10000000000000000000000000000000000000
c5: 10
c0: 71
skew: 1.48
type: snfs
rlim: 11000000
alim: 11000000
lbpr: 28
lbpa: 28
mfbr: 48
mfba: 48
rlambda: 2.2
alambda: 2.2

CPU RAM
Process:          (GHz days) (Max RSS)
----------------- ---------- ---------
gnfs-lasieve4I14e     562        58MB
procrels	     0.06	 ??MB
matbuild	     0.06	672MB
matsolve	     5.17	348MB
sqrt                 0.08        ??MB
----------
total 567.37

Special-q: ~[6M;51M)

Processing with different factor bases (with additional(+1M) special-q sieving):
--------
13M/13M
unique relations: 3134973
full relation sets: 1730732
Pruning matrix with wt=0.700
Initial matrix is 1696502 x 1730732 with sparse part having weight 39373085.
(total weight is 106462937)
Matrix pruned to 1670902 x 1679448 with weight 39534812.

matsolve found only trivial dependencies.

6M/6M
unique relations: 3362796
full relation sets: 949650
Pruning matrix with wt=0.700
Initial matrix is 825087 x 949650 with sparse part having weight 107831245.
(total weight is 172292685)
Matrix pruned to 780833 x 785022 with weight 77805320.

(4·10189-7)/3 = 1(3)1881<190> = 11 · C189

C189 = P77 · P112

P77 = 22727342670242448304921294300019680181558260484479909955238866999770020899617<77>

P112 = 5333316920100283702649243746356914291163645388535270424514041824457524502483749417048804695185211155141229296313<112>

From dependence 0, sqrt obtained:
r1=5333316920100283702649243746356914291163645388535270424514041824457524502483749417048804695185211155141229296313 (p112)
r2=22727342670242448304921294300019680181558260484479909955238866999770020899617 (p77)

sieving params:

m: 100000000000000000000000000000000000000
c5: 2
c0: -35
skew: 1.77
type: snfs
rlim: 14000000
alim: 14000000
lbpr: 29
lbpa: 29
mfbr: 54
mfba: 54
rlambda: 2.3
alambda: 2.3

Special-q: ~[6M;60M)

Processing with different factor bases (with additional(+0.3M) special-q sieving):
--------

8M/8M
unique relations: 3691813
full relation sets: 1245850
Pruning matrix with wt=0.700
Initial matrix is 1079262 x 1245850 with sparse part having weight 81530763.
(total weight is 145966109)
Matrix pruned to 1004047 x 1009507 with weight 56671324.

7M/7M
unique relations: 3837154
full relation sets: 1169049
Pruning matrix with wt=0.700
Initial matrix is 952777 x 1169049 with sparse part having weight 105082045.
(total weight is 174741652)
Matrix pruned to 868214 x 873041 with weight 67229090.

!Solved successfully

CPU RAM
Process:          (GHz days) (Max RSS)
----------------- ---------- ---------
gnfs-lasieve4I14e      675       62MB
procrels	      0.06       ??MB
matbuild	      0.08      765MB
matsolve	      5.38	300MB
sqrt                  0.04      132MB
----------
total 680.56

These are the largest number and the second largest number factored by GGNFS in our tables so far. Congratulations!

Jun 16, 2006

By Alfred Reich / Msieve v. 1.06

10161+9 = 1(0)1609<162> = 7 · 13 · 23 · 157 · 8059 · 13415957160051517<17> · 33227221889480924019367<23> · C113

C113 = P47 · P67

P47 = 37811313891994346064305264570354822948081755411<47>

P67 = 2240332608851730481538608681856319442213805555106852747449191086419<67>

number: 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)

prp47 factor: 37811313891994346064305264570354822948081755411
prp67 factor: 2240332608851730481538608681856319442213805555106852747449191086419

Tue Jun 06 14:10:29 2006  
Tue Jun 06 14:10:29 2006  
Tue Jun 06 14:10:29 2006  Msieve v. 1.06
Tue Jun 06 14:10:29 2006  random seeds: 82bb10e0 ef1ee166
Tue Jun 06 14:10:29 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Tue Jun 06 14:10:30 2006  using multiplier of 1
Tue Jun 06 14:10:30 2006  sieve interval: 17 blocks of size 65536
Tue Jun 06 14:10:31 2006  processing polynomials in batches of 3
Tue Jun 06 14:10:31 2006  using a sieve bound of 8423407 (282760 primes)
Tue Jun 06 14:10:31 2006  using large prime bound of 1263511050 (30 bits)
Tue Jun 06 14:10:31 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Tue Jun 06 14:10:31 2006  using trial factoring cutoff of 65 bits
Tue Jun 06 14:10:31 2006  polynomial 'A' values have 15 factors
Tue Jun 06 14:10:31 2006  restarting with 563 full and 34999 partial relations
Tue Jun 06 14:26:35 2006  579 relations (576 full + 3 combined from 36265 partial), need 282856
Tue Jun 06 14:26:35 2006  elapsed time 00:16:06
Tue Jun 06 14:27:05 2006  
Tue Jun 06 14:27:05 2006  
Tue Jun 06 14:27:05 2006  Msieve v. 1.06
Tue Jun 06 14:27:05 2006  random seeds: 14acdaf0 f2db2c6e
Tue Jun 06 14:27:05 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Tue Jun 06 14:27:06 2006  using multiplier of 1
Tue Jun 06 14:27:06 2006  sieve interval: 17 blocks of size 65536
Tue Jun 06 14:27:06 2006  processing polynomials in batches of 3
Tue Jun 06 14:27:06 2006  using a sieve bound of 8423407 (282760 primes)
Tue Jun 06 14:27:06 2006  using large prime bound of 1263511050 (30 bits)
Tue Jun 06 14:27:06 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Tue Jun 06 14:27:06 2006  using trial factoring cutoff of 65 bits
Tue Jun 06 14:27:06 2006  polynomial 'A' values have 15 factors
Wed Jun 07 10:19:26 2006  1110 relations (1097 full + 13 combined from 66807 partial), need 282856
Wed Jun 07 10:19:26 2006  elapsed time 19:52:21
Wed Jun 07 10:23:45 2006  
Wed Jun 07 10:23:45 2006  
Wed Jun 07 10:23:45 2006  Msieve v. 1.06
Wed Jun 07 10:23:45 2006  random seeds: b353bbc0 876a3e65
Wed Jun 07 10:23:45 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Wed Jun 07 10:23:46 2006  using multiplier of 1
Wed Jun 07 10:23:46 2006  sieve interval: 17 blocks of size 65536
Wed Jun 07 10:23:46 2006  processing polynomials in batches of 3
Wed Jun 07 10:23:46 2006  using a sieve bound of 8423407 (282760 primes)
Wed Jun 07 10:23:46 2006  using large prime bound of 1263511050 (30 bits)
Wed Jun 07 10:23:46 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Wed Jun 07 10:23:46 2006  using trial factoring cutoff of 65 bits
Wed Jun 07 10:23:46 2006  polynomial 'A' values have 15 factors
Wed Jun 07 12:03:49 2006  5 relations (5 full + 0 combined from 375 partial), need 282856
Wed Jun 07 12:03:49 2006  elapsed time 01:40:04
Wed Jun 07 12:05:32 2006  
Wed Jun 07 12:05:32 2006  
Wed Jun 07 12:05:32 2006  Msieve v. 1.06
Wed Jun 07 12:05:32 2006  random seeds: d4971db8 71711aba
Wed Jun 07 12:05:32 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Wed Jun 07 12:05:34 2006  using multiplier of 1
Wed Jun 07 12:05:34 2006  sieve interval: 17 blocks of size 65536
Wed Jun 07 12:05:34 2006  processing polynomials in batches of 3
Wed Jun 07 12:05:34 2006  using a sieve bound of 8423407 (282760 primes)
Wed Jun 07 12:05:34 2006  using large prime bound of 1263511050 (30 bits)
Wed Jun 07 12:05:34 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Wed Jun 07 12:05:34 2006  using trial factoring cutoff of 65 bits
Wed Jun 07 12:05:34 2006  polynomial 'A' values have 15 factors
Wed Jun 07 12:05:34 2006  restarting with 251 full and 16479 partial relations
Sun Jun 11 18:34:58 2006  2339 relations (2267 full + 72 combined from 140829 partial), need 282856
Sun Jun 11 18:34:58 2006  elapsed time 102:29:26
Sun Jun 11 18:35:59 2006  
Sun Jun 11 18:35:59 2006  
Sun Jun 11 18:35:59 2006  Msieve v. 1.06
Sun Jun 11 18:35:59 2006  random seeds: cefb7950 3127a798
Sun Jun 11 18:35:59 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Sun Jun 11 18:36:00 2006  using multiplier of 1
Sun Jun 11 18:36:00 2006  sieve interval: 17 blocks of size 65536
Sun Jun 11 18:36:00 2006  processing polynomials in batches of 3
Sun Jun 11 18:36:00 2006  using a sieve bound of 8423407 (282760 primes)
Sun Jun 11 18:36:00 2006  using large prime bound of 1263511050 (30 bits)
Sun Jun 11 18:36:00 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Sun Jun 11 18:36:00 2006  using trial factoring cutoff of 65 bits
Sun Jun 11 18:36:00 2006  polynomial 'A' values have 15 factors
Mon Jun 12 08:41:31 2006  1024 relations (1015 full + 9 combined from 63554 partial), need 282856
Mon Jun 12 08:41:31 2006  elapsed time 14:05:32
Mon Jun 12 08:42:14 2006  
Mon Jun 12 08:42:14 2006  
Mon Jun 12 08:42:14 2006  Msieve v. 1.06
Mon Jun 12 08:42:14 2006  random seeds: 79f08e3c 332b9a51
Mon Jun 12 08:42:14 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Mon Jun 12 08:42:16 2006  using multiplier of 1
Mon Jun 12 08:42:16 2006  sieve interval: 17 blocks of size 65536
Mon Jun 12 08:42:16 2006  processing polynomials in batches of 3
Mon Jun 12 08:42:16 2006  using a sieve bound of 8423407 (282760 primes)
Mon Jun 12 08:42:16 2006  using large prime bound of 1263511050 (30 bits)
Mon Jun 12 08:42:16 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Mon Jun 12 08:42:16 2006  using trial factoring cutoff of 65 bits
Mon Jun 12 08:42:16 2006  polynomial 'A' values have 15 factors
Mon Jun 12 17:08:38 2006  647 relations (645 full + 2 combined from 38538 partial), need 282856
Mon Jun 12 17:08:38 2006  elapsed time 08:26:24
Mon Jun 12 17:09:29 2006  
Mon Jun 12 17:09:29 2006  
Mon Jun 12 17:09:29 2006  Msieve v. 1.06
Mon Jun 12 17:09:29 2006  random seeds: f3d65b18 0b843bac
Mon Jun 12 17:09:29 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Mon Jun 12 17:09:31 2006  using multiplier of 1
Mon Jun 12 17:09:31 2006  sieve interval: 17 blocks of size 65536
Mon Jun 12 17:09:31 2006  processing polynomials in batches of 3
Mon Jun 12 17:09:31 2006  using a sieve bound of 8423407 (282760 primes)
Mon Jun 12 17:09:31 2006  using large prime bound of 1263511050 (30 bits)
Mon Jun 12 17:09:31 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Mon Jun 12 17:09:31 2006  using trial factoring cutoff of 65 bits
Mon Jun 12 17:09:31 2006  polynomial 'A' values have 15 factors
Mon Jun 12 19:20:38 2006  3 relations (3 full + 0 combined from 307 partial), need 282856
Mon Jun 12 19:20:38 2006  elapsed time 02:11:09
Tue Jun 13 20:38:45 2006  
Tue Jun 13 20:38:45 2006  
Tue Jun 13 20:38:45 2006  Msieve v. 1.06
Tue Jun 13 20:38:45 2006  random seeds: a273f300 21eb8982
Tue Jun 13 20:38:45 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Tue Jun 13 20:38:46 2006  using multiplier of 1
Tue Jun 13 20:38:46 2006  sieve interval: 17 blocks of size 65536
Tue Jun 13 20:38:46 2006  processing polynomials in batches of 3
Tue Jun 13 20:38:46 2006  using a sieve bound of 8423407 (282760 primes)
Tue Jun 13 20:38:46 2006  using large prime bound of 1263511050 (30 bits)
Tue Jun 13 20:38:46 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Tue Jun 13 20:38:46 2006  using trial factoring cutoff of 65 bits
Tue Jun 13 20:38:46 2006  polynomial 'A' values have 15 factors
Tue Jun 13 20:39:13 2006  restarting with 65188 full and 4084882 partial relations
Tue Jun 13 20:39:13 2006  283482 relations (65188 full + 218294 combined from 4084882 partial), need 282856
Tue Jun 13 20:39:35 2006  begin with 4084882 relations
Tue Jun 13 20:41:14 2006  reduce to 682551 relations in 11 passes
Tue Jun 13 20:41:14 2006  attempting to read 65188 full and 682551 partial relations
Tue Jun 13 20:42:40 2006  
Tue Jun 13 20:42:40 2006  
Tue Jun 13 20:42:40 2006  Msieve v. 1.06
Tue Jun 13 20:42:40 2006  random seeds: d70a9350 476c372a
Tue Jun 13 20:42:40 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Tue Jun 13 20:42:42 2006  using multiplier of 1
Tue Jun 13 20:42:42 2006  sieve interval: 17 blocks of size 65536
Tue Jun 13 20:42:42 2006  processing polynomials in batches of 3
Tue Jun 13 20:42:42 2006  using a sieve bound of 8423407 (282760 primes)
Tue Jun 13 20:42:42 2006  using large prime bound of 1263511050 (30 bits)
Tue Jun 13 20:42:42 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Tue Jun 13 20:42:42 2006  using trial factoring cutoff of 65 bits
Tue Jun 13 20:42:42 2006  polynomial 'A' values have 15 factors
Tue Jun 13 20:42:42 2006  restarting with 40 full and 2846 partial relations
Wed Jun 14 08:18:35 2006  869 relations (861 full + 8 combined from 55706 partial), need 282856
Wed Jun 14 08:18:36 2006  elapsed time 11:35:56
Wed Jun 14 08:35:10 2006  
Wed Jun 14 08:35:10 2006  
Wed Jun 14 08:35:10 2006  Msieve v. 1.06
Wed Jun 14 08:35:10 2006  random seeds: e8029fd8 a91fd695
Wed Jun 14 08:35:10 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Wed Jun 14 08:35:12 2006  using multiplier of 1
Wed Jun 14 08:35:12 2006  sieve interval: 17 blocks of size 65536
Wed Jun 14 08:35:12 2006  processing polynomials in batches of 3
Wed Jun 14 08:35:12 2006  using a sieve bound of 8423407 (282760 primes)
Wed Jun 14 08:35:12 2006  using large prime bound of 1263511050 (30 bits)
Wed Jun 14 08:35:12 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Wed Jun 14 08:35:12 2006  using trial factoring cutoff of 65 bits
Wed Jun 14 08:35:12 2006  polynomial 'A' values have 15 factors
Wed Jun 14 08:35:12 2006  restarting with 861 full and 55706 partial relations
Wed Jun 14 10:07:52 2006  982 relations (969 full + 13 combined from 62762 partial), need 282856
Wed Jun 14 10:07:52 2006  elapsed time 01:32:42
Wed Jun 14 10:20:08 2006  
Wed Jun 14 10:20:08 2006  
Wed Jun 14 10:20:08 2006  Msieve v. 1.06
Wed Jun 14 10:20:08 2006  random seeds: 5238bafc 871b85b0
Wed Jun 14 10:20:08 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Wed Jun 14 10:20:09 2006  using multiplier of 1
Wed Jun 14 10:20:10 2006  sieve interval: 17 blocks of size 65536
Wed Jun 14 10:20:10 2006  processing polynomials in batches of 3
Wed Jun 14 10:20:10 2006  using a sieve bound of 8423407 (282760 primes)
Wed Jun 14 10:20:10 2006  using large prime bound of 1263511050 (30 bits)
Wed Jun 14 10:20:10 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Wed Jun 14 10:20:10 2006  using trial factoring cutoff of 65 bits
Wed Jun 14 10:20:10 2006  polynomial 'A' values have 15 factors
Wed Jun 14 10:20:10 2006  restarting with 969 full and 62762 partial relations
Wed Jun 14 13:12:30 2006  1209 relations (1193 full + 16 combined from 75765 partial), need 282856
Wed Jun 14 13:12:30 2006  elapsed time 02:52:22
Wed Jun 14 18:50:58 2006  
Wed Jun 14 18:50:58 2006  
Wed Jun 14 18:50:58 2006  Msieve v. 1.06
Wed Jun 14 18:50:58 2006  random seeds: 8c3ee704 426cdfd2
Wed Jun 14 18:50:58 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Wed Jun 14 18:50:59 2006  using multiplier of 1
Wed Jun 14 18:50:59 2006  sieve interval: 17 blocks of size 65536
Wed Jun 14 18:50:59 2006  processing polynomials in batches of 3
Wed Jun 14 18:50:59 2006  using a sieve bound of 8423407 (282760 primes)
Wed Jun 14 18:50:59 2006  using large prime bound of 1263511050 (30 bits)
Wed Jun 14 18:50:59 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Wed Jun 14 18:50:59 2006  using trial factoring cutoff of 65 bits
Wed Jun 14 18:50:59 2006  polynomial 'A' values have 15 factors
Wed Jun 14 18:51:00 2006  restarting with 1193 full and 75765 partial relations
Wed Jun 14 19:51:59 2006  1271 relations (1255 full + 16 combined from 80189 partial), need 282856
Wed Jun 14 19:52:00 2006  elapsed time 01:01:02
Wed Jun 14 22:17:46 2006  
Wed Jun 14 22:17:46 2006  
Wed Jun 14 22:17:46 2006  Msieve v. 1.06
Wed Jun 14 22:17:46 2006  random seeds: 2dad8c00 a44d233d
Wed Jun 14 22:17:46 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Wed Jun 14 22:17:48 2006  using multiplier of 1
Wed Jun 14 22:17:48 2006  sieve interval: 17 blocks of size 65536
Wed Jun 14 22:17:48 2006  processing polynomials in batches of 3
Wed Jun 14 22:17:48 2006  using a sieve bound of 8423407 (282760 primes)
Wed Jun 14 22:17:48 2006  using large prime bound of 1263511050 (30 bits)
Wed Jun 14 22:17:48 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Wed Jun 14 22:17:48 2006  using trial factoring cutoff of 65 bits
Wed Jun 14 22:17:48 2006  polynomial 'A' values have 15 factors
Wed Jun 14 22:17:51 2006  restarting with 1255 full and 80189 partial relations
Thu Jun 15 00:50:04 2006  1436 relations (1415 full + 21 combined from 90611 partial), need 282856
Thu Jun 15 00:50:05 2006  elapsed time 02:32:19
Thu Jun 15 11:31:23 2006  
Thu Jun 15 11:31:23 2006  
Thu Jun 15 11:31:23 2006  Msieve v. 1.06
Thu Jun 15 11:31:23 2006  random seeds: 8e6443e4 c4db7961
Thu Jun 15 11:31:23 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Thu Jun 15 11:31:25 2006  using multiplier of 1
Thu Jun 15 11:31:25 2006  sieve interval: 17 blocks of size 65536
Thu Jun 15 11:31:25 2006  processing polynomials in batches of 3
Thu Jun 15 11:31:25 2006  using a sieve bound of 8423407 (282760 primes)
Thu Jun 15 11:31:25 2006  using large prime bound of 1263511050 (30 bits)
Thu Jun 15 11:31:25 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Thu Jun 15 11:31:25 2006  using trial factoring cutoff of 65 bits
Thu Jun 15 11:31:25 2006  polynomial 'A' values have 15 factors
Thu Jun 15 11:31:57 2006  restarting with 1684 full and 106708 partial relations
Thu Jun 15 11:56:42 2006  1745 relations (1712 full + 33 combined from 108446 partial), need 282856
Thu Jun 15 11:56:42 2006  elapsed time 00:25:19
Thu Jun 15 11:57:29 2006  
Thu Jun 15 11:57:29 2006  
Thu Jun 15 11:57:29 2006  Msieve v. 1.06
Thu Jun 15 11:57:29 2006  random seeds: 2b5719bc ac70f93d
Thu Jun 15 11:57:29 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Thu Jun 15 11:57:30 2006  using multiplier of 1
Thu Jun 15 11:57:30 2006  sieve interval: 17 blocks of size 65536
Thu Jun 15 11:57:30 2006  processing polynomials in batches of 3
Thu Jun 15 11:57:30 2006  using a sieve bound of 8423407 (282760 primes)
Thu Jun 15 11:57:30 2006  using large prime bound of 1263511050 (30 bits)
Thu Jun 15 11:57:30 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Thu Jun 15 11:57:30 2006  using trial factoring cutoff of 65 bits
Thu Jun 15 11:57:30 2006  polynomial 'A' values have 15 factors
Thu Jun 15 11:57:31 2006  restarting with 1415 full and 90611 partial relations
Thu Jun 15 13:24:02 2006  1536 relations (1511 full + 25 combined from 96442 partial), need 282856
Thu Jun 15 13:24:03 2006  elapsed time 01:26:34
Thu Jun 15 14:41:32 2006  
Thu Jun 15 14:41:32 2006  
Thu Jun 15 14:41:32 2006  Msieve v. 1.06
Thu Jun 15 14:41:32 2006  random seeds: 2bf13d00 55c23d38
Thu Jun 15 14:41:32 2006  factoring 84709919495763372228335377440286814318511534763916180607303055314394459823404282788543194231612700162099721863209 (113 digits)
Thu Jun 15 14:41:34 2006  using multiplier of 1
Thu Jun 15 14:41:34 2006  sieve interval: 17 blocks of size 65536
Thu Jun 15 14:41:34 2006  processing polynomials in batches of 3
Thu Jun 15 14:41:34 2006  using a sieve bound of 8423407 (282760 primes)
Thu Jun 15 14:41:34 2006  using large prime bound of 1263511050 (30 bits)
Thu Jun 15 14:41:34 2006  using double large prime bound of 24145837678737600 (47-55 bits)
Thu Jun 15 14:41:34 2006  using trial factoring cutoff of 65 bits
Thu Jun 15 14:41:34 2006  polynomial 'A' values have 15 factors
Thu Jun 15 14:42:02 2006  restarting with 66448 full and 4166452 partial relations
Thu Jun 15 14:42:02 2006  288182 relations (66448 full + 221734 combined from 4166452 partial), need 282856
Thu Jun 15 14:42:24 2006  begin with 4166452 relations
Thu Jun 15 14:43:44 2006  reduce to 700937 relations in 11 passes
Thu Jun 15 14:43:44 2006  attempting to read 66448 full and 700937 partial relations
Thu Jun 15 14:44:56 2006  recovered 66448 full and 700937 partial relations
Thu Jun 15 14:44:56 2006  recovered 756557 polynomials
Thu Jun 15 14:45:51 2006  attempting to build 221734 cycles
Thu Jun 15 14:45:54 2006  found 221734 cycles in 6 passes
Thu Jun 15 14:52:54 2006  distribution of cycle lengths:
Thu Jun 15 14:52:54 2006     length 2 : 47366
Thu Jun 15 14:52:54 2006     length 3 : 47173
Thu Jun 15 14:52:54 2006     length 4 : 39485
Thu Jun 15 14:52:54 2006     length 5 : 31205
Thu Jun 15 14:52:54 2006     length 6 : 21691
Thu Jun 15 14:52:54 2006     length 7 : 14202
Thu Jun 15 14:52:54 2006     length 8 : 8893
Thu Jun 15 14:52:54 2006     length 9+: 11719
Thu Jun 15 14:52:54 2006  largest cycle: 23 relations
Thu Jun 15 14:53:30 2006  282760 x 282824 system, weight 19624908 (avg 69.39/col)
Thu Jun 15 14:53:49 2006  reduce to 278846 x 278910 in 3 passes
Thu Jun 15 19:56:16 2006  lanczos halted after 4412 iterations
Thu Jun 15 19:56:26 2006  recovered 60 nontrivial dependencies
Thu Jun 15 20:07:51 2006  prp47 factor: 37811313891994346064305264570354822948081755411
Thu Jun 15 20:07:51 2006  prp67 factor: 2240332608851730481538608681856319442213805555106852747449191086419
Thu Jun 15 20:08:04 2006  elapsed time 05:26:32

Jun 15, 2006 (3rd)

By Wojciech Florek / GMP-ECM 6.0.1 B1=50000

10200+9 = 1(0)1999<201> = 27793 · 1619861 · C190

C190 = P26 · C164

P26 = 67747437129266000269703021<26>

C164 = [32786416573339916713456581271610480336366936402832697536081978826368233931128306550623785015488259274779087861845908056248255213200999357697362157495980354472120073<164>]

Jun 15, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

3·10151-1 = 2(9)151<152> = 103 · 15607 · 35159 · 14094323 · C134

C134 = P48 · P86

P48 = 803919452098002873794823857201688324440053056001<48>

P86 = 46845872075351073831628759072931045137614880228706167557837224075618406020863534117667<86>

Number: 29999_151
N=37660307811869368071143626717392891077148245893848443905585408084269631973112722238396669205370621661836143893933492373568490474469667
  ( 134 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=803919452098002873794823857201688324440053056001 (pp48)
 r2=46845872075351073831628759072931045137614880228706167557837224075618406020863534117667 (pp86)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 32.36 hours.
Scaled time: 19.77 units (timescale=0.611).
Factorization parameters were as follows:
name: 29999_151
n: 37660307811869368071143626717392891077148245893848443905585408084269631973112722238396669205370621661836143893933492373568490474469667
m: 1000000000000000000000000000000
c5: 30
c0: -1
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:175423, largePrimes:5562413 encountered
Relations: rels:5551679, finalFF:551257
Max relations in full relation-set: 28
Initial matrix: 351792 x 551257 with sparse part having weight 48702916.
Pruned matrix : 264444 x 266266 with weight 23590245.
Total sieving time: 28.86 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 3.04 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 32.36 hours.
 --------- CPU info (if available) ----------

Jun 15, 2006

By Wojciech Florek / GMP-ECM 6.0.1 B1=50000

10155+9 = 1(0)1549<156> = 7 · 13 · 36819899903<11> · C143

C143 = P26 · P117

P26 = 79017600284684020776597601<26>

P117 = 377704507649203485094138150729343418582135548032657891156331722185962796664870047824029441603130922378771354117137333<117>

10185+9 = 1(0)1849<186> = 7 · 13 · 229846571 · 1275374768743384691<19> · C157

C157 = P31 · C127

P31 = 2601396325020582930122538337721<31>

C127 = [1441040661382525705417821587285663316407691187456963366088056617767879156058816313976715675551433626176389802439909676048900179<127>]

Jun 14, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4

(4·10152-13)/9 = (4)1513<152> = 17 · 157 · 6476783 · C142

C142 = P68 · P74

P68 = 70051112394180511931099325798622432992902701888617624858258185590861<68>

P74 = 36702405181637427368617502969073420790220101845842707621638501963536194669<74>

Number: 44443_152
N=2571044310515636631591363642344402560399099518358547822280233718276022116764197533447168630264726143496554443438364403140703983099575283320009
  ( 142 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=70051112394180511931099325798622432992902701888617624858258185590861 (pp68)
 r2=36702405181637427368617502969073420790220101845842707621638501963536194669 (pp74)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 37.42 hours.
Scaled time: 23.50 units (timescale=0.628).
Factorization parameters were as follows:
n: 2571044310515636631591363642344402560399099518358547822280233718276022116764197533447168630264726143496554443438364403140703983099575283320009
m: 2000000000000000000000000000000
c5: 25
c0: -26
skew: 1.01
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2200001)
Primes: RFBsize:176302, AFBsize:176748, largePrimes:5547592 encountered
Relations: rels:5457284, finalFF:473655
Max relations in full relation-set: 28
Initial matrix: 353114 x 473655 with sparse part having weight 41920058.
Pruned matrix : 304103 x 305932 with weight 24002656.
Total sieving time: 32.17 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 4.80 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 37.42 hours.
 --------- CPU info (if available) ----------

Jun 13, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(25·10151-1)/3 = 8(3)151<152> = 40213 · 31173893 · 13946968278689<14> · C127

C127 = P46 · P81

P46 = 8173120943122339742908571543763108966367651147<46>

P81 = 583167752877706836532991362620680694133049760946451667127882465043575940344860839<81>

Number: 83333_151
N=4766300574398378856441697253711236415813730164095873758343781948185529731621724242828907536094532267344007114712574137013732333
  ( 127 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=8173120943122339742908571543763108966367651147 (pp46)
 r2=583167752877706836532991362620680694133049760946451667127882465043575940344860839 (pp81)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 39.49 hours.
Scaled time: 26.61 units (timescale=0.674).
Factorization parameters were as follows:
name: 83333_151
n: 4766300574398378856441697253711236415813730164095873758343781948185529731621724242828907536094532267344007114712574137013732333
m: 1000000000000000000000000000000
c5: 250
c0: -1
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2200001)
Primes: RFBsize:176302, AFBsize:175838, largePrimes:5676207 encountered
Relations: rels:5686431, finalFF:561341
Max relations in full relation-set: 28
Initial matrix: 352206 x 561341 with sparse part having weight 51177717.
Pruned matrix : 270625 x 272450 with weight 25638975.
Total sieving time: 35.78 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 3.24 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 39.49 hours.
 --------- CPU info (if available) ----------

Jun 12, 2006 (3rd)

By Wojciech Florek / GMP-ECM 6.0.1 B1=250000

10171+3 = 1(0)1703<172> = C172

C172 = P26 · C146

P26 = 11766503516695099357653883<26>

C146 = [84987014076113040368276240003085477274619465136310452297603910182168194570059311533447910927491502082842012464686661684313334515329656218133967641<146>]

Jun 12, 2006 (2nd)

By Wojciech Florek / GGNFS-0.77.1

10155+3 = 1(0)1543<156> = C156

C156 = P77 · P79

P77 = 82104127886814499369024993996312311665706556142420410416782489897012262753547<77>

P79 = 1217965558782331157844625900310263781587935921261132202891162537797114525084649<79>

Number: 10,310-M
N=100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
  ( 156 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=82104127886814499369024993996312311665706556142420410416782489897012262753547 (pp77)
 r2=1217965558782331157844625900310263781587935921261132202891162537797114525084649 (pp79)
Version: GGNFS-0.77.1
Total time: 88.84 hours.
Scaled time: 48.68 units (timescale=0.548).
Factorization parameters were as follows:
name: 10^155+3 10,310-M
n: 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
type: snfs
m: 10000000000000000000000000000000
skew: 1.2
c5: 1
c4: 0
c3: 0
c2: 0
c1: 0
c0: 3
rlim: 4000000
alim: 3700000
lpbr: 27
lpba: 27
mfbr: 48
mfba: 48
rlambda: 2.3
alambda: 2.3
qintsize: 50000
Factor base limits: 4000000/3700000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1850000, 2300001)
Relations: rels:5171311, finalFF:626344
Initial matrix: 546367 x 626344 with sparse part having weight 32686910.
Pruned matrix : 502764 x 505559 with weight 19259495.
Total sieving time: 77.41 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 10.59 hours.
Time per square root: 0.25 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,4000000,3700000,27,27,48,48,2.3,2.3,100000
total time: 88.84 hours.
 --------- CPU info (if available) ----------
CPU0: Intel Pentium III (Coppermine) stepping 06
CPU1: Intel Pentium III (Coppermine) stepping 06
Memory: 514812k/524224k available (1676k kernel code, 8652k reserved, 708k data, 180k init, 0k highmem)
Calibrating delay loop... 1851.39 BogoMIPS
Calibrating delay loop... 1867.77 BogoMIPS
Total of 2 processors activated (3719.16 BogoMIPS).
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 2 CPUs
--------------------------------------------------------------------------
CPU #1
Family: 6 Model: 8 Stepping: 6 Type: 0 Brand: 2
CPU Model: Pentium III-M (Coppermine) [cC0] Original OEM
Instruction TLB: 4KB pages, 4-way associative, 32 entries
Instruction TLB: 4MB pages, fully associative, 2 entries
Data TLB: 4KB pages, 4-way associative, 64 entries
L2 unified cache:
	Size: 256KB	8-way associative.
	line size=32 bytes.
L1 Instruction cache:
	Size: 16KB	4-way associative.
	line size=32 bytes.
Data TLB: 4MB pages, 4-way associative, 8 entries
L1 Data cache:
	Size: 16KB	4-way associative.
	line size=32 bytes.
950MHz processor (estimate).

--------------------------------------------------------------------------
CPU #2
Family: 6 Model: 8 Stepping: 6 Type: 0 Brand: 2
CPU Model: Pentium III-M (Coppermine) [cC0] Original OEM
Instruction TLB: 4KB pages, 4-way associative, 32 entries
Instruction TLB: 4MB pages, fully associative, 2 entries
Data TLB: 4KB pages, 4-way associative, 64 entries
L2 unified cache:
	Size: 256KB	8-way associative.
	line size=32 bytes.
L1 Instruction cache:
	Size: 16KB	4-way associative.
	line size=32 bytes.
Data TLB: 4MB pages, 4-way associative, 8 entries
L1 Data cache:
	Size: 16KB	4-way associative.
	line size=32 bytes.
950MHz processor (estimate).

--------------------------------------------------------------------------
WARNING: Detected SMP, but unable to access cpuid driver.
Used Uniprocessor CPU routines. Results inaccurate.

P77 is the largest factor found by GGNFS in our tables so far. Congratulations!

Jun 12, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4 gnfs

(2·10177+61)/9 = (2)1769<177> = 373 · 52452310739<11> · 122313301254781630237<21> · 698935614467460981599711<24> · C120

C120 = P39 · P82

P39 = 102274804112509011932166621876688728607<39>

P82 = 1299075864221558361306831248327523719975317527188803043876725435794660391001753143<82>

Number: 22229_177
N=132862729540548235885710325806135088341175371249479339168970742759531835213425691441068602652953432293108269044736261801
  ( 120 digits)
Divisors found:
 r1=102274804112509011932166621876688728607 (pp39)
 r2=1299075864221558361306831248327523719975317527188803043876725435794660391001753143 (pp82)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 94.67 hours.
Scaled time: 60.78 units (timescale=0.642).
Factorization parameters were as follows:
name: 22229_177
n: 132862729540548235885710325806135088341175371249479339168970742759531835213425691441068602652953432293108269044736261801
skew: 118264.19
# norm 2.48e+016
c5: 16380
c4: 2906053828
c3: -842318987455755
c2: -31805894219144108025
c1: 3829700256869416762366795
c0: 61382773760292758874608119257
# alpha -6.53
Y1: 11968793848913
Y0: -95899409147692607700800
# Murphy_E 3.46e-010
# M 97739709333115584892434197029876455362571111405703888251707455578910987395730840374213972981668836923260695644624972375
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [2250000, 4110001)
Primes: RFBsize:315948, AFBsize:315964, largePrimes:7684067 encountered
Relations: rels:7782590, finalFF:772270
Max relations in full relation-set: 28
Initial matrix: 631997 x 772270 with sparse part having weight 65670693.
Pruned matrix : 514290 x 517513 with weight 40913071.
Total sieving time: 76.06 hours.
Total relation processing time: 1.04 hours.
Matrix solve time: 17.06 hours.
Time per square root: 0.52 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 94.67 hours.
 --------- CPU info (if available) ----------

Jun 11, 2006

By Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4

(16·10151-1)/3 = 5(3)151<152> = 152311 · 715209641 · 313198861778351<15> · C124

C124 = P55 · P69

P55 = 4492114583152676075568292046791383513694243521858826159<55>

P69 = 347987062260942870395968830956400479517277155958985376021550782808187<69>

Number: 53333_151
N=1563197757130839718450150233073190481919155646304989399336964917055382221284358227647965491014654792583752170529025474963733
  ( 124 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=4492114583152676075568292046791383513694243521858826159 (pp55)
 r2=347987062260942870395968830956400479517277155958985376021550782808187 (pp69)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 33.13 hours.
Scaled time: 22.33 units (timescale=0.674).
Factorization parameters were as follows:
name: 53333_151
n: 1563197757130839718450150233073190481919155646304989399336964917055382221284358227647965491014654792583752170529025474963733
m: 1000000000000000000000000000000
c5: 160
c0: -1
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2000001)
Primes: RFBsize:176302, AFBsize:176093, largePrimes:5402411 encountered
Relations: rels:5275796, finalFF:456173
Max relations in full relation-set: 28
Initial matrix: 352462 x 456173 with sparse part having weight 38619267.
Pruned matrix : 299185 x 301011 with weight 22581981.
Total sieving time: 29.04 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 3.59 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 33.13 hours.
 --------- CPU info (if available) ----------

Jun 10, 2006

By suberi / GGNFS-0.77.1-20060513-pentium4

(2·10158-11)/9 = (2)1571<158> = 32 · 7 · 3373 · 244846033 · C144

C144 = P48 · P97

P48 = 136373220163038473408001030523801101796795796597<48>

P97 = 3131903903250503659877494912285800041740438149611919544242941413416214051230896603159433989608979<97>

Number: 22221_158
N=427107820527460481965800659937090806025710492398582629787910040201168839154848698242923514230339462348863549244998158835338352432003242848844463
  ( 144 digits)
SNFS difficulty: 158 digits.
Divisors found:
 r1=136373220163038473408001030523801101796795796597 (pp48)
 r2=3131903903250503659877494912285800041740438149611919544242941413416214051230896603159433989608979 (pp97)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 61.35 hours.
Scaled time: 42.08 units (timescale=0.686).
Factorization parameters were as follows:
n: 427107820527460481965800659937090806025710492398582629787910040201168839154848698242923514230339462348863549244998158835338352432003242848844463
m: 20000000000000000000000000000000
c5: 125
c0: -22
skew: 1
type: snfs
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3600001)
Primes: RFBsize:283146, AFBsize:282598, largePrimes:5660000 encountered
Relations: rels:5693705, finalFF:658134
Max relations in full relation-set: 28
Initial matrix: 565809 x 658134 with sparse part having weight 41765004.
Pruned matrix : 492727 x 495620 with weight 28196709.
Total sieving time: 50.11 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 10.76 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
snfs,158,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: 61.35 hours.
 --------- CPU info (if available) ----------

Jun 9, 2006 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1

(28·10154-1)/9 = 3(1)154<155> = 29 · 523 · 356947 · 1279301069<10> · 329796478307462684783<21> · C116

C116 = P51 · P65

P51 = 300621016513776590359526923103344706640342409501697<51>

P65 = 45307905222633353862121896072140996414543098670746516403110579681<65>

Number: 31111_154
N=13620508524137886095135775437549085410611631881407400493766199272054663054717943584997443021365877512209360023218657
  ( 116 digits)
SNFS difficulty: 156 digits.
Divisors found:
 r1=300621016513776590359526923103344706640342409501697 (pp51)
 r2=45307905222633353862121896072140996414543098670746516403110579681 (pp65)
Version: GGNFS-0.77.1
Total time: 48.44 hours.
Scaled time: 32.22 units (timescale=0.665).
Factorization parameters were as follows:
name: 31111_154
n: 13620508524137886095135775437549085410611631881407400493766199272054663054717943584997443021365877512209360023218657
m: 10000000000000000000000000000000
c5: 14
c0: -5
skew: 2
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1500000, 2700001)
Relations: rels:5727743, finalFF:603263
Initial matrix: 434263 x 603263 with sparse part having weight 48582766.
Pruned matrix : 391440 x 393675 with weight 21231753.
Total sieving time: 43.42 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 4.55 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 48.44 hours.
 --------- CPU info (if available) ----------

Jun 9, 2006 (2nd)

By Bryan Koen / GGNFS-0.77.1-20060513-pentium3 gnfs

10151+9 = 1(0)1509<152> = 47 · 59 · 1259 · 7127 · 2966921 · 11067807493<11> · 72688089600520497603686170777972481<35> · C90

C90 = P42 · P48

P42 = 304041896967341114744845407635505771861889<42>

P48 = 553800538862497459614953502422358377149435369453<48>

Number: 10009_151
N=168378566377289441526058266352233242122150864612576030629541165580379898372848314405476717
  ( 90 digits)
Divisors found:
 r1=304041896967341114744845407635505771861889 (pp42)
 r2=553800538862497459614953502422358377149435369453 (pp48)
Version: GGNFS-0.77.1-20060513-pentium3
Total time: 7.78 hours.
Scaled time: 4.87 units (timescale=0.626).
Factorization parameters were as follows:
name: 10009_151
n:  168378566377289441526058266352233242122150864612576030629541165580379898372848314405476717
m:  397102947624127176218
deg: 4
c4: 6771336
c3: -9421734641
c2: -17097857456607989
c1: 52700057966859489
c0: 20139528042945550388527
skew: 1635.250
type: gnfs
# adj. I(F,S) = 50.521
# E(F1,F2) = 2.015879e-04
# GGNFS version 0.77.1-20060513-pentium3 polyselect.
# Options were: 
# lcd=1, enumLCD=24, maxS1=58.00000000, seed=1149781811.
# maxskew=2000.0
# These parameters should be manually set:
rlim: 700000
alim: 700000
lpbr: 25
lpba: 25
mfbr: 44
mfba: 44
rlambda: 2.4
alambda: 2.4
qintsize: 40000

type: gnfs
Factor base limits: 700000/700000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 44/44
Sieved algebraic special-q in [350000, 750001)
Primes: RFBsize:56543, AFBsize:56325, largePrimes:1619047 encountered
Relations: rels:1627644, finalFF:155272
Max relations in full relation-set: 28
Initial matrix: 112945 x 155272 with sparse part having weight 13574909.
Pruned matrix : 100318 x 100946 with weight 6869840.
Polynomial selection time: 0.17 hours.
Total sieving time: 6.85 hours.
Total relation processing time: 0.20 hours.
Matrix solve time: 0.47 hours.
Time per square root: 0.08 hours.
Prototype def-par.txt line would be:
gnfs,89,4,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,700000,700000,25,25,44,44,2.4,2.4,40000
total time: 7.78 hours.
 --------- CPU info (if available) ----------
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 8 Stepping: 10 Type: 0 Brand: 2
CPU Model: Pentium III-M (Coppermine) [cD0] Original OEM
Instruction TLB: 4KB pages, 4-way associative, 32 entries
Instruction TLB: 4MB pages, fully associative, 2 entries
Data TLB: 4KB pages, 4-way associative, 64 entries
L2 unified cache:
	Size: 256KB	8-way associative.
	line size=32 bytes.
L1 Instruction cache:
	Size: 16KB	4-way associative.
	line size=32 bytes.
Data TLB: 4MB pages, 4-way associative, 8 entries
L1 Data cache:
	Size: 16KB	4-way associative.
	line size=32 bytes.
1.0Ghz processor (estimate).

Jun 9, 2006

By Wojciech Florek / GMP-ECM 6.0.1 B1=250000

10199+3 = 1(0)1983<200> = 13 · 4533299 · 259556761 · 111011352372742720485057131<27> · C157

C157 = P33 · C125

P33 = 505135145839533539009957298516389<33>

C125 = [11658292768317820781554389954230436794449000313821548811563233466427335134152895851328952839749423751087120161554182716468331<125>]

Jun 8, 2006 (5th)

By Yousuke Koide / GMP-ECM

(10607-1)/9 = (1)607<607> = 10857536471<11> · C597

C597 = P34 · C563

P34 = 8030222013165659643947340265695409<34>

C563 = [12743791025705280337647107449763389196590743381995489997602359492550670282914658786866644132251081530183945513634942367344940945849768823651695138554796618106799788799265038643749276286863772813091423307583327488336703425138962767003020761379082230966326019896681052112375556339576356383468466444597317090588231683659499086434219490053020977894894071243326908124169207137882751682358057098873428276903560922268298083613125322614771267815515696194827324894983730224274660295001335913828824662433094826344709281811146432335327830920101507170509517110651808908417249<563>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jun 8, 2006 (4th)

By Bryan Koen / GMP-ECM 6.1 B1=3000000

10151+9 = 1(0)1509<152> = 47 · 59 · 1259 · 7127 · 2966921 · 11067807493<11> · C125

C125 = P35 · C90

P35 = 72688089600520497603686170777972481<35>

C90 = [168378566377289441526058266352233242122150864612576030629541165580379898372848314405476717<90>]

Jun 8, 2006 (3rd)

By Bryan Koen / GMP-ECM 6.1 B1=3000000

10149+9 = 1(0)1489<150> = 7 · 13 · 1289 · 14111809 · 2038469620239917<16> · C122

C122 = P26 · P96

P26 = 80577406982383442189446811<26>

P96 = 367794702512173851463405661443194990091070675569301662648266498490154427340333411671971726316077<96>

Jun 8, 2006 (2nd)

By Wojciech Florek / Msieve v. 1.03

10140+9 = 1(0)1399<141> = 47017 · 74498093 · 6280399637<10> · 378185559992276358710822426933737<33> · C86

C86 = P36 · P50

P36 = 275290255655372346657479721190470389<36>

P50 = 43663331382360791758121439349427121020054742354629<50>

Jun 8, 2006

By Bryan Koen / GMP-ECM 6.1 B1=3000000

10140+9 = 1(0)1399<141> = 47017 · 74498093 · 6280399637<10> · C118

C118 = P33 · C86

P33 = 378185559992276358710822426933737<33>

C86 = [12020089659015344816036119415930027908760447367801456885997889765522261556089961580681<86>]

Jun 7, 2006 (2nd)

By Bryan Koen / GGNFS-0.77.1-20060513-pentium3

10138+9 = 1(0)1379<139> = 876233 · 3884165579644422661<19> · C114

C114 = P44 · P70

P44 = 78273652233899717283899884219650481533344701<44>

P70 = 3753764830682790162556690001403905303929149813189408310793058874824593<70>

Number: 10009_138
N=293820882924708172219936720052802603554401992112281932163797281493515360316752301778857178250591701547951981031693
  ( 114 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=78273652233899717283899884219650481533344701 (pp44)
 r2=3753764830682790162556690001403905303929149813189408310793058874824593 (pp70)
Version: GGNFS-0.77.1-20060513-pentium3
Total time: 17.78 hours.
Scaled time: 11.13 units (timescale=0.626).
Factorization parameters were as follows:
n: 293820882924708172219936720052802603554401992112281932163797281493515360316752301778857178250591701547951981031693
m: 1000000000000000000000000000
c5: 1000
c0: 9
skew: 1
type: snfs

Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1525001)
Primes: RFBsize:78498, AFBsize:63873, largePrimes:1570583 encountered
Relations: rels:1573135, finalFF:171984
Max relations in full relation-set: 28
Initial matrix: 142438 x 171984 with sparse part having weight 15803147.
Pruned matrix : 133995 x 134771 with weight 10765947.
Total sieving time: 16.39 hours.
Total relation processing time: 0.22 hours.
Matrix solve time: 1.04 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 17.78 hours.
 --------- CPU info (if available) ----------
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 8 Stepping: 10 Type: 0 Brand: 2
CPU Model: Pentium III-M (Coppermine) [cD0] Original OEM
Instruction TLB: 4KB pages, 4-way associative, 32 entries
Instruction TLB: 4MB pages, fully associative, 2 entries
Data TLB: 4KB pages, 4-way associative, 64 entries
L2 unified cache:
	Size: 256KB	8-way associative.
	line size=32 bytes.
L1 Instruction cache:
	Size: 16KB	4-way associative.
	line size=32 bytes.
Data TLB: 4MB pages, 4-way associative, 8 entries
L1 Data cache:
	Size: 16KB	4-way associative.
	line size=32 bytes.
1.0Ghz processor (estimate).

Jun 7, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(5·10163+13)/9 = (5)1627<163> = 7 · 491 · 1046680382986660661<19> · 26988494111082482595723749<26> · C116

C116 = P33 · P35 · P49

P33 = 217331380417265405385792427178641<33>

P35 = 55344255753515407497857400669052247<35>

P49 = 4757296669612601389627040223185439915807754519687<49>

Number: 55557_163
N=57220971289632372895013854360486568742682462018091052842231747397803851776811199836976065406658831179664130202209649
  ( 116 digits)
Divisors found:
 r1=217331380417265405385792427178641 (pp33)
 r2=55344255753515407497857400669052247 (pp35)
 r3=4757296669612601389627040223185439915807754519687 (pp49)
Version: GGNFS-0.77.1
Total time: 72.54 hours.
Scaled time: 48.24 units (timescale=0.665).
Factorization parameters were as follows:
name: 55557_163
n: 57220971289632372895013854360486568742682462018091052842231747397803851776811199836976065406658831179664130202209649
skew: 63091.21
# norm 1.03e+16
c5: 10980
c4: -567513282
c3: -288483363928883
c2: -42686857066294
c1: -10217904753094925098120
c0: 805345242548038392245007424
# alpha -6.11
Y1: 920218306469
Y0: -22049094785443788512841
# Murphy_E 5.16e-10
# M 21548108821676313080445840778074574074874607909847815919519715036737519808444584049118282893032989879028308785080208
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2250000, 3630001)
Relations: rels:7694457, finalFF:806287
Initial matrix: 631773 x 806287 with sparse part having weight 63262568.
Pruned matrix : 555050 x 558272 with weight 30385169.
Polynomial selection time: 1.52 hours.
Total sieving time: 60.64 hours.
Total relation processing time: 1.09 hours.
Matrix solve time: 8.75 hours.
Time per square root: 0.54 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 72.54 hours.
 --------- CPU info (if available) ----------

Jun 6, 2006 (3rd)

By Wojciech Florek / Msieve v. 1.03

10152+3 = 1(0)1513<153> = 43613668999<11> · 12179717710063<14> · 128492693814335713<18> · 2456091372331436862367783336363<31> · C81

C81 = P38 · P44

P38 = 15820959142195526790315426273379632223<38>

P44 = 37703736485632074700837740810673485387490687<44>

Jun 6, 2006 (2nd)

By Alfred Reich / Msieve v. 1.06

10144+3 = 1(0)1433<145> = 134060221 · 895346379774329815520794224163<30> · C106

C106 = P43 · P64

P43 = 3312794646750731247992525345573307418477327<43>

P64 = 2514863810750094284798767186768560521807692068531696374269371643<64>

Jun 6, 2006

By Bryan Koen / GMP-ECM 6.1 B1=1000000

10152+3 = 1(0)1513<153> = 43613668999<11> · 12179717710063<14> · 128492693814335713<18> · C112

C112 = P31 · C81

P31 = 2456091372331436862367783336363<31>

C81 = [596509274447291814464580040316696780259376731908870341805954675607430656897607201<81>]

10122+9 = 1(0)1219<123> = 797 · 87324709 · C112

C112 = P32 · P80

P32 = 46442319103878729137347867918441<32>

P80 = 30937885895272059997914839937905492541094892096918455339201066688438011910438513<80>

10129+9 = 1(0)1289<130> = 383 · 470957 · 925380361 · C112

C112 = P29 · P84

P29 = 26662284559638260051010569411<29>

P84 = 224699616945787993015228728987794854226294266940075097993481422453900414417478640009<84>

Jun 5, 2006 (3rd)

By Wojciech Florek / GMP-ECM 6.0.1 B1=250000

10160+3 = 1(0)1593<161> = 72 · 823 · C156

C156 = P28 · P129

P28 = 2418343914073834818913548979<28>

P129 = 102538278668961192433911894438328850160845843852041786502290291129164567462464059585048892813551072785448461295685350000183704391<129>

Jun 5, 2006 (2nd)

By Bryan Koen / GGNFS-0.77.1-20060513-pentium3

10141+3 = 1(0)1403<142> = 23 · 179 · 644783 · 1095239290136891<16> · C117

C117 = P51 · P66

P51 = 803739638634605270206280169488592754569025676064749<51>

P66 = 427938295026116307934098302562270778494869844206815199155275017447<66>

Number: 10003_141
N=343950970602199819231512078234382265236200797813972452208461451756224073663979763523341432993779852136795871276675803
  ( 117 digits)
SNFS difficulty: 141 digits.
Divisors found:
 r1=803739638634605270206280169488592754569025676064749 (pp51)
 r2=427938295026116307934098302562270778494869844206815199155275017447 (pp66)
Version: GGNFS-0.77.1-20060513-pentium3
Total time: 21.59 hours.
Scaled time: 13.51 units (timescale=0.626).
Factorization parameters were as follows:
n: 343950970602199819231512078234382265236200797813972452208461451756224073663979763523341432993779852136795871276675803
m: 10000000000000000000000000000
c5: 10
c0: 3
skew: 1
type: snfs
Factor base limits: 1300000/1300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 45/45
Sieved algebraic special-q in [650000, 1750001)
Primes: RFBsize:100021, AFBsize:99998, largePrimes:2680955 encountered
Relations: rels:2643376, finalFF:256210
Max relations in full relation-set: 28
Initial matrix: 200085 x 256210 with sparse part having weight 22916201.
Pruned matrix : 182362 x 183426 with weight 14089073.
Total sieving time: 19.25 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 1.90 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,141,5,0,0,0,0,0,0,0,0,1300000,1300000,26,26,45,45,2.3,2.3,100000
total time: 21.59 hours.
 --------- CPU info (if available) ----------
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 8 Stepping: 10 Type: 0 Brand: 2
CPU Model: Pentium III-M (Coppermine) [cD0] Original OEM
Instruction TLB: 4KB pages, 4-way associative, 32 entries
Instruction TLB: 4MB pages, fully associative, 2 entries
Data TLB: 4KB pages, 4-way associative, 64 entries
L2 unified cache:
	Size: 256KB	8-way associative.
	line size=32 bytes.
L1 Instruction cache:
	Size: 16KB	4-way associative.
	line size=32 bytes.
Data TLB: 4MB pages, 4-way associative, 8 entries
L1 Data cache:
	Size: 16KB	4-way associative.
	line size=32 bytes.
1.0Ghz processor (estimate).

Jun 5, 2006

By Tyler Cadigan / PRIMO 2.2.0 beta 6

The prime number (34·10773-7)/9 was certified by PRIMO. All prime numbers under 1000 digits in our tables have been certified.

Jun 4, 2006 (4th)

By Alexander Mkrtychyan / Msieve v. 1.06

10167+3 = 1(0)1663<168> = 613 · 3042701 · 5418606523951<13> · 210504879244969399<18> · 104420640192739457415377<24> · C105

C105 = P50 · P56

P50 = 12671007740661978399849262965676367229484426614023<50>

P56 = 35524907704428477072483751792823172988116747462504646589<56>

Thu Jun 01 07:44:48 2006  Msieve v. 1.06
Thu Jun 01 07:44:48 2006  random seeds: b14be000 1f671996
Thu Jun 01 07:44:48 2006  factoring 450136380509115586818824476925994457819859020646634121016333059079851013391762916786707134979013526517547 (105 digits)
Thu Jun 01 07:44:49 2006  using multiplier of 13
Thu Jun 01 07:44:49 2006  sieve interval: 9 blocks of size 65536
Thu Jun 01 07:44:49 2006  processing polynomials in batches of 6
Thu Jun 01 07:44:49 2006  using a sieve bound of 3943937 (140000 primes)
Thu Jun 01 07:44:49 2006  using large prime bound of 591590550 (29 bits)
Thu Jun 01 07:44:49 2006  using double large prime bound of 6160815113841750 (44-53 bits)
Thu Jun 01 07:44:49 2006  using trial factoring cutoff of 60 bits
Thu Jun 01 07:44:49 2006  polynomial 'A' values have 14 factors
Thu Jun 01 07:44:49 2006  restarting with 3042 full and 194490 partial relations
Sat Jun 03 05:48:23 2006  140203 relations (33009 full + 107194 combined from 2073320 partial), need 140096
Sat Jun 03 05:48:47 2006  begin with 2073320 relations
Sat Jun 03 05:48:50 2006  reduce to 338226 relations in 11 passes
Sat Jun 03 05:48:50 2006  attempting to read 33009 full and 338226 partial relations
Sat Jun 03 05:49:15 2006  recovered 33009 full and 338226 partial relations
Sat Jun 03 05:49:15 2006  recovered 364498 polynomials
Sat Jun 03 05:49:16 2006  attempting to build 107194 cycles
Sat Jun 03 05:49:17 2006  found 107194 cycles in 6 passes
Sat Jun 03 05:49:17 2006  distribution of cycle lengths:
Sat Jun 03 05:49:17 2006     length 2 : 23465
Sat Jun 03 05:49:17 2006     length 3 : 23358
Sat Jun 03 05:49:17 2006     length 4 : 19359
Sat Jun 03 05:49:17 2006     length 5 : 14682
Sat Jun 03 05:49:17 2006     length 6 : 10184
Sat Jun 03 05:49:17 2006     length 7 : 6633
Sat Jun 03 05:49:17 2006     length 8 : 4199
Sat Jun 03 05:49:17 2006     length 9+: 5314
Sat Jun 03 05:49:17 2006  largest cycle: 21 relations
Sat Jun 03 05:49:18 2006  140000 x 140064 system, weight 9718057 (avg 69.38/col)
Sat Jun 03 05:49:19 2006  reduce to 138118 x 138182 in 3 passes
Sat Jun 03 06:08:39 2006  lanczos halted after 2185 iterations
Sat Jun 03 06:08:41 2006  recovered 58 nontrivial dependencies
Sat Jun 03 06:10:00 2006  prp50 factor: 12671007740661978399849262965676367229484426614023
Sat Jun 03 06:10:00 2006  prp56 factor: 35524907704428477072483751792823172988116747462504646589
Sat Jun 03 06:10:01 2006  elapsed time 46:25:13

Jun 4, 2006 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(34·10176-7)/9 = 3(7)176<177> = 13 · 829 · 318683 · 11176757 · 3948411858562751<16> · 428211044560044339671392979782357<33> · C112

C112 = P38 · P75

P38 = 11694279611466984831142203943332807419<38>

P75 = 497748584082412889125755168559358506745646837820266378957660155569774344887<75>

Number: 37777_176
N=5820811118471521231475918967207027515179168849013239199862519224248461311165696923761581519214488363575258316653
  ( 112 digits)
Divisors found:
 r1=11694279611466984831142203943332807419 (pp38)
 r2=497748584082412889125755168559358506745646837820266378957660155569774344887 (pp75)
Version: GGNFS-0.77.1
Total time: 53.33 hours.
Scaled time: 35.47 units (timescale=0.665).
Factorization parameters were as follows:
name: 37777_176
n: 5820811118471521231475918967207027515179168849013239199862519224248461311165696923761581519214488363575258316653
skew: 32740.23
# norm 7.73e+14
c5: 7800
c4: 790299208
c3: -34647393104357
c2: -702585806193034208
c1: 6659086119635802079482
c0: 123094738763234464057267500
# alpha -5.03
Y1: 484020890317
Y0: -3754712135906934550109
# Murphy_E 8.03e-10
# M 4302948463608880647102223092922936267994757185578952181911465511761176268904489859460161461822645693421840905721
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2750001)
Relations: rels:7677602, finalFF:705015
Initial matrix: 499803 x 705015 with sparse part having weight 61142504.
Pruned matrix : 419449 x 422012 with weight 24554381.
Polynomial selection time: 0.52 hours.
Total sieving time: 45.83 hours.
Total relation processing time: 0.77 hours.
Matrix solve time: 5.74 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 53.33 hours.
 --------- CPU info (if available) ----------

Jun 4, 2006 (2nd)

By Tyler Cadigan / PRIMO 2.2.0 beta 6

The following 11 prime numbers under 1000 digits were certified by PRIMO.

10700+7, 10999+7, (5·10461+1)/3, (5·10840+1)/3, (5·10847+1)/3, (7·10522-1)/3, (7·10597-1)/3, (13·10727-1)/3, (53·10439+1)/9, (61·10785-7)/9, (61·10799-7)/9.

Jun 4, 2006

By Bryan Koen / GGNFS-0.77.1-20060513-pentium3

10138+3 = 1(0)1373<139> = 103 · 990513749998083607<18> · 34585142462197870945875655226509<32> · C87

C87 = P42 · P45

P42 = 515100320152004920978466573096213025512461<42>

P45 = 550200369707475541148787748643398354924032907<45>

Number: 10003_138
N=283408386584072121357621650236515295775168451662180323194828514316327126544738502554127
  ( 87 digits)
SNFS difficulty: 138 digits.
Divisors found:
 r1=515100320152004920978466573096213025512461 (pp42)
 r2=550200369707475541148787748643398354924032907 (pp45)
Version: GGNFS-0.77.1-20060513-pentium3
Total time: 21.08 hours.
Scaled time: 13.20 units (timescale=0.626).
Factorization parameters were as follows:
n: 283408386584072121357621650236515295775168451662180323194828514316327126544738502554127
m: 1000000000000000000000000000
c5: 1000
c0: 3
skew: 1
type: snfs

Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1750001)
Primes: RFBsize:78498, AFBsize:64158, largePrimes:1602887 encountered
Relations: rels:1611027, finalFF:169149
Max relations in full relation-set: 28
Initial matrix: 142722 x 169149 with sparse part having weight 16717764.
Pruned matrix : 135569 x 136346 with weight 11997191.
Total sieving time: 19.46 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 1.25 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 21.08 hours.
 --------- CPU info (if available) ----------
x86info v1.12b.  Dave Jones 2001-2003
Feedback to <davej@redhat.com>.

Found 1 CPU
--------------------------------------------------------------------------
Family: 6 Model: 8 Stepping: 10 Type: 0 Brand: 2
CPU Model: Pentium III-M (Coppermine) [cD0] Original OEM
Instruction TLB: 4KB pages, 4-way associative, 32 entries
Instruction TLB: 4MB pages, fully associative, 2 entries
Data TLB: 4KB pages, 4-way associative, 64 entries
L2 unified cache:
        Size: 256KB     8-way associative.
        line size=32 bytes.
L1 Instruction cache:
        Size: 16KB      4-way associative.
        line size=32 bytes.
Data TLB: 4MB pages, 4-way associative, 8 entries
L1 Data cache:
        Size: 16KB      4-way associative.
        line size=32 bytes.
1.0Ghz processor (estimate).

Jun 3, 2006

By Tyler Cadigan / PRIMO 2.2.0 beta 6

The following 227 prime numbers under 1000 digits were certified by PRIMO.

(10767+53)/9, (10684+71)/9, (10720+71)/9, (11·10876+7)/9, (11·10811+43)/9, (11·10812+43)/9, (11·10547+61)/9, (4·10887+11)/3, (13·10735+23)/9, (13·10529+41)/9, (14·10537+31)/9, (14·10831+31)/9, (5·10629+7)/3, (5·10720+7)/3, (17·10843+1)/9, 2·10761+9, (19·10543-1)/9, (19·10584-1)/9, (19·10833-1)/9, (19·10754+17)/9, (19·10951+17)/9, (7·10657+17)/3, (22·10499+41)/9, (23·10733+31)/9, (25·10936-61)/9, (25·10482-7)/9, (26·10876-71)/9, (26·10494-53)/9, (26·10598-53)/9, (26·10449-17)/9, 3·10484-7, 3·10865-7, 3·10593+7, (28·10692+53)/9, (28·10797+71)/9, (29·10649-11)/9, (29·10949-11)/9, (29·10963-11)/9, (29·10519+61)/9, (29·10603+61)/9, (10978+11)/3, (31·10758+23)/9, (31·10512+41)/9, (32·10957+31)/9, (11·10673-17)/3, (11·10780-17)/3, (11·10498+1)/3, (34·10776+11)/9, (35·10538-71)/9, (35·10509+1)/9, (35·10710+1)/9, 4·10949-9, (37·10589-1)/9, (37·10973-1)/9, (37·10513+53)/9, (38·10630+7)/9, (38·10724+7)/9, (13·10715-7)/3, (13·10804-7)/3, (13·10456+11)/3, (13·10467+11)/3, (13·10607+11)/3, (13·10828+11)/3, (13·10638+17)/3, (4·10722+23)/9, (41·10702-23)/9, (41·10621+31)/9, (14·10652+1)/3, (43·10925-61)/9, (44·10595-17)/9, (44·10637-17)/9, (44·10776-17)/9, (44·10618+1)/9, 5·10495-3, 5·10966-3, 5·10531+3, 5·10706+3, 5·10757+9, (46·10447+17)/9, (46·10487+17)/9, (46·10445+71)/9, (46·10543+71)/9, (46·10633+71)/9, (46·10757+71)/9, (47·10494-11)/9, (47·10614-11)/9, (47·10710-11)/9, (47·10475+7)/9, (47·10505+7)/9, (47·10835+7)/9, (47·10922+7)/9, (47·10638+43)/9, (16·10575+17)/3, (16·10715+17)/3, (49·10476-31)/9, (49·10834-31)/9, (49·10795-13)/9, (49·10564+23)/9, (49·10620+23)/9, (49·10619+41)/9, (49·10759+41)/9, (5·10540-23)/9, (5·10528+13)/9, (5·10960+13)/9, (17·10868-11)/3, (17·10651+7)/3, (17·10884+7)/3, (17·10938+7)/3, (52·10866-7)/9, (52·10992-7)/9, (53·10816-71)/9, (53·10858-71)/9, (53·10462-17)/9, (53·10608+1)/9, 6·10806+7, (55·10533-1)/9, (55·10616-1)/9, (55·10718-1)/9, (55·10787-1)/9, (55·10647+17)/9, (55·10973+53)/9, (55·10953+71)/9, (56·10433-11)/9, (56·10766-11)/9, (19·10755-7)/3, (19·10455+11)/3, (58·10613-31)/9, (58·10470-13)/9, (58·10887+23)/9, (58·10627+41)/9, (58·10687+41)/9, (58·10699+41)/9, (59·10597-41)/9, (59·10681-41)/9, (59·10617-23)/9, (59·10696+13)/9, (61·10713+11)/9, (62·10732-17)/9, (62·10501+1)/9, (62·10515+1)/9, (62·10627+1)/9, (62·10641+1)/9, (62·10725+1)/9, 7·10568-9, 7·10639-9, 7·10842-9, 7·10969-9, (64·10938+17)/9, (65·10837+7)/9, (22·10489-7)/3, (22·10592-7)/3, (22·10634-7)/3, (22·10908-1)/3, (67·10451+41)/9, (67·10772+41)/9, (68·10734-41)/9, (68·10931-41)/9, (68·10646-23)/9, (68·10814-23)/9, (68·10967+31)/9, (23·10434-17)/3, (23·10721-17)/3, (23·10822-17)/3, (23·10883-17)/3, (23·10498-11)/3, (23·10868-11)/3, (23·10879-11)/3, (23·10717+7)/3, (23·10968+7)/3, (7·10624+11)/9, 8·10698+9, (73·10474-1)/9, (73·10902-1)/9, (73·10745+17)/9, (73·10641+53)/9, (73·10675+53)/9, (73·10594+71)/9, (74·10436+7)/9, (74·10524+43)/9, (74·10530+43)/9, (74·10657+43)/9, (25·10848+17)/3, (76·10486-31)/9, (76·10627-31)/9, (76·10999-31)/9, (76·10442-13)/9, (76·10469+41)/9, (77·10471-41)/9, (77·10637+31)/9, (26·10481-11)/3, (26·10608-11)/3, (26·10741-11)/3, (26·10879-11)/3, (26·10453+7)/3, (26·10611+7)/3, (26·10883+7)/3, (79·10480-61)/9, 9·10549-7, 9·10765-7, 9·10973-7, 9·10588+7, 9·10776+7, 9·10906+7, (82·10473+53)/9, (82·10685+53)/9, (82·10701+53)/9, (83·10520-11)/9, (83·10456+7)/9, (83·10678+7)/9, (83·10471+43)/9, (83·10561+43)/9, (83·10664+43)/9, (28·10448+11)/3, (28·10539+11)/3, (28·10784+11)/3, (28·10814+11)/3, (85·10581-13)/9, (86·10573-41)/9, (86·10897-41)/9, (86·10981-41)/9, (29·10635-17)/3, (29·10940-17)/3, (29·10944-17)/3, (88·10784-61)/9, (88·10447-43)/9, (89·10529-17)/9, 10990-3.

Jun 2, 2006 (4th)

By Wataru Sakai / GMP-ECM 6.0.1, GMP-ECM 6.1

(61·10163-7)/9 = 6(7)163<164> = 9266672567<10> · 5673581071735727<16> · C139

C139 = P35(1305...) · P35(2240...) · P70

P35(1305...) = 13053999710108279553984814365912541<35>

P35(2240...) = 22402313059656738339109313460161689<35>

P70 = 4408286195992575892384026018410003380146235251197963945518892063985397<70>

(61·10169-7)/9 = 6(7)169<170> = 679517 · 2099650316119<13> · C152

C152 = P33 · C120

P33 = 462133680259364512974037301324911<33>

C120 = [102795098400219410634465090516194534805474053557213593780153631997610268197607479386423556429973192979895429973931816909<120>]

(61·10170-7)/9 = 6(7)170<171> = 89 · 59149 · 73106034559740600637<20> · C145

C145 = P33 · C112

P33 = 455443373077175325700179430733987<33>

C112 = [3866894270110480495299331929349939555976910470220605286134629327779460046947883016645268141896942460825185552203<112>]

(61·10172-7)/9 = 6(7)172<173> = 1155709 · 4691776423<10> · C158

C158 = P30 · P42 · P86

P30 = 609460208105001402610217070871<30>

P42 = 463915191687646936303192442868799163452747<42>

P86 = 44209700384489934180137596183593901714505219083957722275135118923645544441308317835503<86>

(61·10193-7)/9 = 6(7)193<194> = 59 · 3853 · C189

C189 = P30 · P160

P30 = 163127799506136496038335489929<30>

P160 = 1827714372782507311292761526282412035783631956330528107609297122108841522030987601896279600559024296237981269384421792628912505034582472939235971142099110239319<160>

(61·10196-7)/9 = 6(7)196<197> = 4159 · 4464781 · 226180181 · C179

C179 = P38 · C142

P38 = 15615154400366770009282227004370183921<38>

C142 = [1033468904117966617164744053188712951295398238274545348816534213750285722018672609129914860028868584067980435445547786740892587358674249064463<142>]

(61·10199-7)/9 = 6(7)199<200> = 67 · 2686555097433200453529295711<28> · C171

C171 = P27 · P33 · P112

P27 = 605308283558156762793357649<27>

P33 = 181507461190783917343467817300507<33>

P112 = 3427249105123054795888760122109345886233343024535902715535737986060352180735446845218692299323082077938308290447<112>

(2·10159+7)/9 = (2)1583<159> = 298723 · 134414293495679<15> · C139

C139 = P35 · P105

P35 = 28564470286657715379909548819111177<35>

P105 = 193752446812631227185571963969853916284322191569677049783345080351097717812535867500285661692155668121347<105>

(2·10170+7)/9 = (2)1693<170> = 12930304574921414314033<23> · C148

C148 = P43 · P105

P43 = 3177578812262362929721778663715578834608987<43>

P105 = 540856932080673148371720800720497574973083187669508000817425748253849426512467650834585100482455000456813<105>

(2·10174+7)/9 = (2)1733<174> = 32653 · C169

C169 = P34 · C135

P34 = 8605748596807443176651449709360011<34>

C135 = [790816538438140615000153862079160056073471252421369321942539171949977923538944145405594829029895279514855025343464426448291871504794881<135>]

(2·10187+7)/9 = (2)1863<187> = 3 · 7121 · 703861 · 9726089 · 765326106386707<15> · 437824737463030830793<21> · C134

C134 = P28 · P32 · P75

P28 = 5263877762821122828884893157<28>

P32 = 48391846941817862159960485307009<32>

P75 = 178022660365682865284769924756205427705493239580961443647315723443038756623<75>

(2·10197+7)/9 = (2)1963<197> = 1621 · 141974874916545385999<21> · 2232227063658151482511<22> · C152

C152 = P32 · C120

P32 = 43577960060843625073819999006811<32>

C120 = [992630718271618283341033880453341958342128797919820395767331503484855179680778194512437518931403483604755119718794009097<120>]

Jun 2, 2006 (3rd)

By Makoto Kamada / GGNFS-0.77.1-20060513-pentium4

(8·10183+1)/9 = (8)1829<183> = 72 · 43 · 461 · 467 · 27107 · 9068209 · 23313817858784804426409706148665366375211175744287<50> · C114

C114 = P53 · P62

P53 = 17172336853874519123559347693340353363432157819381763<53>

P62 = 19912205285236655490930714577233779462660321205072785210366107<62>

Number: 88889_183
N=341939096661584400227553288107254525079031934616327634095069075719584264530732473440793216775647315692905629106641
  ( 114 digits)
SNFS difficulty: 124 digits.
Divisors found:
 r1=17172336853874519123559347693340353363432157819381763 (pp53)
 r2=19912205285236655490930714577233779462660321205072785210366107 (pp62)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 3.48 hours.
Scaled time: 3.06 units (timescale=0.879).
Factorization parameters were as follows:
n: 341939096661584400227553288107254525079031934616327634095069075719584264530732473440793216775647315692905629106641
m: 10000000000000000000000000000000
c4: 1
c2: -5
c0: 25
skew: 2.24
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 850001)
Primes: RFBsize:78498, AFBsize:63591, largePrimes:1360471 encountered
Relations: rels:1359532, finalFF:174303
Max relations in full relation-set: 28
Initial matrix: 142154 x 174303 with sparse part having weight 7785807.
Pruned matrix : 128927 x 129701 with weight 4603124.
Total sieving time: 3.19 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.23 hours.
Time per square root: 0.02 hours.
Prototype def-par.txt line would be:
snfs,124,4,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 3.48 hours.
 --------- CPU info (if available) ----------

Jun 2, 2006 (2nd)

By Bryan Koen / GMP-ECM 6.1

10138+3 = 1(0)1373<139> = 103 · 990513749998083607<18> · C118

C118 = P32 · C87

P32 = 34585142462197870945875655226509<32>

C87 = [283408386584072121357621650236515295775168451662180323194828514316327126544738502554127<87>]

Jun 2, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(8·10177+1)/9 = (8)1769<177> = 7 · 29 · 163 · 10723 · 6035986569923<13> · 380857470122232181070000528210631041570306701<45> · C112

C112 = P32 · P80

P32 = 54739137296048956120640580620887<32>

P80 = 19908513669930269360597071221167439859525827759440362292604313670802851972278387<80>

Number: 88889_177
N=1089774863138580484872984968817045844294765683283798979147942631744722199904541170863376042427550881656470869269
  ( 112 digits)
Divisors found:
 r1=54739137296048956120640580620887 (pp32)
 r2=19908513669930269360597071221167439859525827759440362292604313670802851972278387 (pp80)
Version: GGNFS-0.77.1
Total time: 39.45 hours.
Scaled time: 23.51 units (timescale=0.596).
Factorization parameters were as follows:
name: 88889_177
n: 1089774863138580484872984968817045844294765683283798979147942631744722199904541170863376042427550881656470869269
skew: 36330.36
# norm 2.48e+15
c5: 5820
c4: -160561218
c3: -103428289141967
c2: 106685185438483196
c1: 22587835698887125868428
c0: 5319801337068504126612240
# alpha -6.19
Y1: 124019362819
Y0: -2847625443342581414407
# Murphy_E 9.82e-10
# M 622533092526007148420631005709468983895694441684678411183890427592736842958130944535980867733197098436365974294
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2450001)
Relations: rels:7552865, finalFF:730865
Initial matrix: 500372 x 730865 with sparse part having weight 57563517.
Pruned matrix : 402098 x 404663 with weight 19977007.
Polynomial selection time: 0.50 hours.
Total sieving time: 33.31 hours.
Total relation processing time: 0.60 hours.
Matrix solve time: 4.61 hours.
Time per square root: 0.43 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 39.45 hours.
 --------- CPU info (if available) ----------

Jun 1, 2006 (2nd)

By Kazumaro Aoki / GMP-ECM

(10577-1)/9 = (1)577<577> = 8147324243<10> · C567

C567 = P36 · C531

P36 = 938481850248139268016449056596865441<36>

C531 = [145317063102710861820499228904524399066849909129219189300595865487766749556421082708313313982046013295421851928598056080304609057683996269997168542682627544996557610063342531571550391683940782938558316925981737405043174224057225444684519563619355417209749868847265821610326528137035528572329838382261312815748193325315149971534888035173399493417165233051071970445677091792860412089498091494812744864695247159254664667237171078605676809481110779919742695465749073598859163974452510897573796809940497098416296446123048494164664199197<531>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jun 1, 2006

By Alexander Mkrtychyan / GGNFS-0.77.1-20060513-pentium4

10135+3 = 1(0)1343<136> = 113 · 209694391 · 3187745395872205735627<22> · C104

C104 = P31 · P73

P31 = 4126491370074199286802782631529<31>

P73 = 3208264562687349553112271518304371303840051419576548379085824235751916727<73>

Number: 10003_135
N=13238876030844222881517187707728521701393691806109836301501637811754088940555731331591745916106732685583
  ( 104 digits)
SNFS difficulty: 135 digits.
Divisors found:
 r1=4126491370074199286802782631529 (pp31)
 r2=3208264562687349553112271518304371303840051419576548379085824235751916727 (pp73)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 5.14 hours.
Scaled time: 3.29 units (timescale=0.639).
Factorization parameters were as follows:
n: 13238876030844222881517187707728521701393691806109836301501637811754088940555731331591745916106732685583
m: 1000000000000000000000000000
c5: 1
c0: 3
skew: 1.25
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Sieved special-q in [400000, 1000001)
Relations: rels:1483040, finalFF:174625
Initial matrix: 142575 x 174625 with sparse part having weight 11401173.
Pruned matrix : 136556 x 137332 with weight 6638985.
Total sieving time: 4.66 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.35 hours.
Time per square root: 0.06 hours.
Prototype def-par.txt line would be:
snfs,135,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 5.14 hours.
 --------- CPU info (if available) ----------
Number: 10003_135
N=13238876030844222881517187707728521701393691806109836301501637811754088940555731331591745916106732685583
  ( 104 digits)
Divisors found:
 r1=4126491370074199286802782631529 (pp31)
 r2=3208264562687349553112271518304371303840051419576548379085824235751916727 (pp73)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 12.23 hours.
Scaled time: 10.47 units (timescale=0.856).
Factorization parameters were as follows:
name: 10003_135
n: 13238876030844222881517187707728521701393691806109836301501637811754088940555731331591745916106732685583
skew: 15091.32
# norm 1.78e+014
c5: 15300
c4: 42172857
c3: -16843114753885
c2: -6385923654261920
c1: 1080586713066062557585
c0: 1600614640292011265372783
# alpha -5.36
Y1: 85171659001
Y0: -61295925167544543480
# Murphy_E 2.14e-009
# M 1415068216635383107428986942648757487027085459449481691813363559400817105834292943797372282379140929763
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Sieved special-q in [1150000, 2050001)
Relations: rels:4579325, finalFF:479215
Initial matrix: 338276 x 479215 with sparse part having weight 37900481.
Pruned matrix : 287943 x 289698 with weight 14497215.
Total sieving time: 10.16 hours.
Total relation processing time: 0.21 hours.
Matrix solve time: 1.68 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 12.23 hours.
 --------- CPU info (if available) ----------

May 2006

May 31, 2006 (4th)

By Alexander Mkrtychyan / GGNFS-0.77.1-20060513-pentium4

10125+9 = 1(0)1249<126> = 7 · 13 · 384889 · 723939179 · C109

C109 = P27 · P83

P27 = 104798542417408554023904481<27>

P83 = 37632735246204919539474660114544096567452721600807355325578711593030532758062764009<83>

Number: 10009_125
N=3943855800982512204047076283279173934267476357842898027812986502106895423798672694305963146974921925060624329
  ( 109 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=104798542417408554023904481 (pp27)
 r2=37632735246204919539474660114544096567452721600807355325578711593030532758062764009 (pp83)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.96 hours.
Scaled time: 1.68 units (timescale=0.856).
Factorization parameters were as follows:
n: 3943855800982512204047076283279173934267476357842898027812986502106895423798672694305963146974921925060624329
m: 10000000000000000000000000
c5: 1
c0: 9
skew: 1.55
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Sieved special-q in [400000, 600001)
Relations: rels:2183785, finalFF:208639
Initial matrix: 113175 x 208639 with sparse part having weight 18310937.
Pruned matrix : 100818 x 101447 with weight 4612940.
Total sieving time: 1.74 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.96 hours.
 --------- CPU info (if available) ----------

May 31, 2006 (3rd)

By Alexander Mkrtychyan / GGNFS-0.77.1-20060513-pentium4

10126+3 = 1(0)1253<127> = 523 · 219931704421459<15> · C109

C109 = P54 · P56

P54 = 225003335227519500209690385071854069954197019410358111<54>

P56 = 38638611863595333536671213995256267949387191415100091789<56>

Number: 10003_126
N=8693816537870552796189791836347215234147282169892521208207622196514133941968184404004410089386067533460650579
  ( 109 digits)
SNFS difficulty: 126 digits.
Divisors found:
 r1=225003335227519500209690385071854069954197019410358111 (pp54)
 r2=38638611863595333536671213995256267949387191415100091789 (pp56)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.71 hours.
Scaled time: 2.32 units (timescale=0.856).
Factorization parameters were as follows:
n: 8693816537870552796189791836347215234147282169892521208207622196514133941968184404004410089386067533460650579
m: 10000000000000000000000000
c5: 10
c0: 3
skew: 1
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Sieved special-q in [400000, 700001)
Relations: rels:2364119, finalFF:237060
Initial matrix: 113082 x 237060 with sparse part having weight 23525055.
Pruned matrix : 102455 x 103084 with weight 5247156.
Total sieving time: 2.45 hours.
Total relation processing time: 0.08 hours.
Matrix solve time: 0.14 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,126,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.71 hours.
 --------- CPU info (if available) ----------

May 31, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(5·10160+31)/9 = (5)1599<160> = 3 · 83 · 191 · 11897 · 28176527153<11> · 18501477700637<14> · 113560929621493<15> · C114

C114 = P42 · P73

P42 = 110326591238035710584592040607678556416233<42>

P73 = 1503329914327084129827562239789927074395898119591880527859360579326768337<73>

Number: 55559_160
N=165857264953875455413997705152619856437429539839930319261236162874151164125325354773712814415336747189600137214521
  ( 114 digits)
Divisors found:
 r1=110326591238035710584592040607678556416233 (pp42)
 r2=1503329914327084129827562239789927074395898119591880527859360579326768337 (pp73)
Version: GGNFS-0.77.1
Total time: 62.57 hours.
Scaled time: 37.29 units (timescale=0.596).
Factorization parameters were as follows:
name: 55559_160
n: 165857264953875455413997705152619856437429539839930319261236162874151164125325354773712814415336747189600137214521
skew: 66068.60
# norm 7.20e+15
c5: 3600
c4: -247115952
c3: 212958230220305
c2: -666236161802342372
c1: -347144910357299009278472
c0: -149742468887770791438169544
# alpha -5.62
Y1: 269559540643
Y0: -8564195791010614904981
# Murphy_E 5.45e-10
# M 48686816090489950110783223909642057313547960725390427311092854386814467166976067367315514213453959993934165254017
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2950001)
Relations: rels:7451217, finalFF:605225
Initial matrix: 500754 x 605225 with sparse part having weight 50049963.
Pruned matrix : 460141 x 462708 with weight 28300107.
Total sieving time: 53.74 hours.
Total relation processing time: 0.63 hours.
Matrix solve time: 7.64 hours.
Time per square root: 0.57 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 62.57 hours.
 --------- CPU info (if available) ----------

May 31, 2006

By Makoto Kamada / GGNFS-0.77.1-20060513-pentium4

10137+3 = 1(0)1363<138> = C138

C138 = P36 · P45 · P58

P36 = 485528403184829992818506125204327553<36>

P45 = 148422974169957271956708475508014083532747879<45>

P58 = 1387663704324682066869289940523411644503592736304905992069<58>

Number: 10003_137
N=100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
  ( 138 digits)
SNFS difficulty: 137 digits.
Divisors found:
 r1=485528403184829992818506125204327553 (pp36)
 r2=148422974169957271956708475508014083532747879 (pp45)
 r3=1387663704324682066869289940523411644503592736304905992069 (pp58)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 8.57 hours.
Scaled time: 7.53 units (timescale=0.879).
Factorization parameters were as follows:
n: 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003
m: 1000000000000000000000000000
c5: 100
c0: 3
skew: 1
type: snfs
Factor base limits: 1000000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 43/43
Sieved algebraic special-q in [400000, 1525001)
Primes: RFBsize:78498, AFBsize:64158, largePrimes:1561033 encountered
Relations: rels:1553398, finalFF:160894
Max relations in full relation-set: 28
Initial matrix: 142720 x 160894 with sparse part having weight 14946696.
Pruned matrix : 137740 x 138517 with weight 11497237.
Total sieving time: 7.96 hours.
Total relation processing time: 0.07 hours.
Matrix solve time: 0.50 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000
total time: 8.57 hours.
 --------- CPU info (if available) ----------

May 30, 2006 (8th)

By Wojciech Florek / GMP-ECM 6.0.1 B1=250000

10165+3 = 1(0)1643<166> = 38239 · 1693194240447509<16> · C146

C146 = P31 · P115

P31 = 1588184880884744278485835046657<31>

P115 = 9724910962239622540990620193028590711568046948990342160048211399738346880582051939871864183726938718963260603503529<115>

May 30, 2006 (7th)

By Kazumaro Aoki / GMP-ECM

10283+1 = 1(0)2821<284> = 11 · 1699 · 241117 · 61945573305222690279363663578823967<35> · 151168348012920493188164812150408056175148228488823<51> · C189

C189 = P47 · P142

P47 = 49019999488937337866558715558211303750925973449<47>

P142 = 4834389726736518293852244130660191969670797610633948645694761977558159678896763591712097243317272920296826630341374217553659008741548305187653<142>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

May 30, 2006 (6th)

By Wojciech Florek / Msieve v. 1.03

10139+3 = 1(0)1383<140> = 13 · 327203583643<12> · 21557806404758500426320572531<29> · C99

C99 = P46 · P54

P46 = 1048720107311272779271661501804277089838257303<46>

P54 = 103985894904565220127485054041767990985479311662142569<54>

Tue May 30 01:53:59 2006  Msieve v. 1.03
Tue May 30 01:53:59 2006  random seeds: e5a24ffa 3215051b
Tue May 30 01:53:59 2006  factoring 109052098863174370952569599747648629418311788803478577891274670334454933699104045854505718091431407 (99 digits)
Tue May 30 01:54:00 2006  using multiplier of 17
Tue May 30 01:54:00 2006  sieve interval: 9 blocks of size 65536
Tue May 30 01:54:00 2006  processing polynomials in batches of 6
Tue May 30 01:54:00 2006  using a sieve bound of 2538791 (92941 primes)
Tue May 30 01:54:00 2006  using large prime bound of 380818650 (28 bits)
Tue May 30 01:54:00 2006  using double large prime bound of 2787999993955500 (43-52 bits)
Tue May 30 01:54:00 2006  using trial factoring cutoff of 57 bits
Tue May 30 01:54:00 2006  polynomial 'A' values have 13 factors
Tue May 30 09:38:34 2006  93395 relations (22839 full + 70556 combined from 1378715 partial), need 93037
Tue May 30 09:38:35 2006  begin with 1378715 relations
Tue May 30 09:38:36 2006  reduce to 218992 relations in 11 passes
Tue May 30 09:38:36 2006  attempting to read 22839 full and 218992 partial relations
Tue May 30 09:38:41 2006  recovered 22839 full and 218992 partial relations
Tue May 30 09:38:41 2006  recovered 230899 polynomials
Tue May 30 09:38:41 2006  attempting to build 70556 cycles
Tue May 30 09:38:41 2006  found 70556 cycles in 6 passes
Tue May 30 09:38:42 2006  distribution of cycle lengths:
Tue May 30 09:38:42 2006     length 2 : 16484
Tue May 30 09:38:42 2006     length 3 : 16165
Tue May 30 09:38:42 2006     length 4 : 12533
Tue May 30 09:38:42 2006     length 5 : 9319
Tue May 30 09:38:42 2006     length 6 : 6470
Tue May 30 09:38:42 2006     length 7 : 4127
Tue May 30 09:38:42 2006     length 8 : 2464
Tue May 30 09:38:42 2006     length 9+: 2994
Tue May 30 09:38:42 2006  largest cycle: 21 relations
Tue May 30 09:38:42 2006  92941 x 93005 system, weight 6096558 (avg 65.55/col)
Tue May 30 09:38:42 2006  reduce to 91325 x 91389 in 3 passes
Tue May 30 09:42:18 2006  lanczos halted after 1447 iterations
Tue May 30 09:42:18 2006  recovered 62 nontrivial dependencies
Tue May 30 09:43:31 2006  prp46 factor: 1048720107311272779271661501804277089838257303
Tue May 30 09:43:31 2006  prp54 factor: 103985894904565220127485054041767990985479311662142569
Tue May 30 09:43:32 2006  elapsed time 07:49:33

May 30, 2006 (5th)

By Alexander Mkrtychyan / GGNFS-0.77.1-20060513-pentium4

10124+3 = 1(0)1233<125> = 7 · 43 · 8179 · 23257479000261691<17> · C102

C102 = P42 · P60

P42 = 278215836815846300810499872638251601851541<42>

P60 = 627753020605636868785440299879864836902467148030812554348147<60>

Number: 10003_124
N=174650831941472467445289919450500673291473034301660439617172819294158790322600074782094487475522444527
  ( 102 digits)
SNFS difficulty: 125 digits.
Divisors found:
 r1=278215836815846300810499872638251601851541 (pp42)
 r2=627753020605636868785440299879864836902467148030812554348147 (pp60)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 2.02 hours.
Scaled time: 1.30 units (timescale=0.640).
Factorization parameters were as follows:
n: 174650831941472467445289919450500673291473034301660439617172819294158790322600074782094487475522444527
m: 10000000000000000000000000
c5: 1
c0: 30
skew: 1.97
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Sieved special-q in [400000, 600001)
Relations: rels:2190943, finalFF:218685
Initial matrix: 113035 x 218685 with sparse part having weight 19064751.
Pruned matrix : 99519 x 100148 with weight 4369458.
Total sieving time: 1.81 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.12 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,125,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 2.02 hours.
 --------- CPU info (if available) ----------

May 30, 2006 (4th)

By Makoto Kamada / GGNFS-0.77.1-20060513-pentium4

10116+9 = 1(0)1159<117> = 111256744554457<15> · C102

C102 = P28 · P28 · P47

P28 = 3052729705599278798406752741<28>

P28 = 5505231043723870085469276793<28>

P47 = 53482259761111102005149456829292624252000374149<47>

Number: 10009_116
N=898821913228396280023466116957629527519011387394111616097834533727168556480812558017319934505640764337
  ( 102 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=3052729705599278798406752741 (pp28)
 r2=5505231043723870085469276793 (pp28)
 r3=53482259761111102005149456829292624252000374149 (pp47)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.32 hours.
Scaled time: 1.17 units (timescale=0.880).
Factorization parameters were as follows:
n: 898821913228396280023466116957629527519011387394111616097834533727168556480812558017319934505640764337
m: 100000000000000000000000
c5: 10
c0: 9
skew: 1
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:64158, largePrimes:1940389 encountered
Relations: rels:1896820, finalFF:138845
Max relations in full relation-set: 28
Initial matrix: 113323 x 138845 with sparse part having weight 10525760.
Pruned matrix : 102932 x 103562 with weight 6044808.
Total sieving time: 1.08 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.17 hours.
Time per square root: 0.04 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.32 hours.
 --------- CPU info (if available) ----------

May 30, 2006 (3rd)

By Makoto Kamada / GGNFS-0.77.1-20060513-pentium4

10116+3 = 1(0)1153<117> = 613 · 5581 · C110

C110 = P32 · P39 · P40

P32 = 31409912863227233240324396659219<32>

P39 = 285562837995982349446361585842661944753<39>

P40 = 3258810312307206854209463561699139379393<40>

Number: 10003_116
N=29229911670129924034382560499340427043163518264164157522332383263771015210369135785508569771653007041778020451
  ( 110 digits)
SNFS difficulty: 116 digits.
Divisors found:
 r1=31409912863227233240324396659219 (pp32)
 r2=285562837995982349446361585842661944753 (pp39)
 r3=3258810312307206854209463561699139379393 (pp40)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.75 hours.
Scaled time: 1.54 units (timescale=0.879).
Factorization parameters were as follows:
n: 29229911670129924034382560499340427043163518264164157522332383263771015210369135785508569771653007041778020451
m: 100000000000000000000000
c5: 10
c0: 3
skew: 1
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 550001)
Primes: RFBsize:49098, AFBsize:63918, largePrimes:2331143 encountered
Relations: rels:2714082, finalFF:499083
Max relations in full relation-set: 28
Initial matrix: 113082 x 499083 with sparse part having weight 42387208.
Pruned matrix : 65921 x 66550 with weight 6428247.
Total sieving time: 1.57 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.09 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.75 hours.
 --------- CPU info (if available) ----------

May 30, 2006 (2nd)

By Makoto Kamada / GGNFS-0.77.1-20060513-pentium4

10114+9 = 1(0)1139<115> = 61 · 197 · C110

C110 = P41 · P70

P41 = 28209372385446691031827707934227981145697<41>

P70 = 2949921878782510902524946201902765360019176183479097760119909220054841<70>

Number: 10009_114
N=83215444786552384122493134725805109428309894316385121078472164433718898227511026046434218190896230340351169177
  ( 110 digits)
SNFS difficulty: 115 digits.
Divisors found:
 r1=28209372385446691031827707934227981145697 (pp41)
 r2=2949921878782510902524946201902765360019176183479097760119909220054841 (pp70)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.29 hours.
Scaled time: 1.14 units (timescale=0.879).
Factorization parameters were as follows:
n: 83215444786552384122493134725805109428309894316385121078472164433718898227511026046434218190896230340351169177
m: 100000000000000000000000
c5: 1
c0: 90
skew: 2.46
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 400000)
Primes: RFBsize:49098, AFBsize:64158, largePrimes:2037023 encountered
Relations: rels:2085053, finalFF:208794
Max relations in full relation-set: 28
Initial matrix: 113320 x 208794 with sparse part having weight 16430199.
Pruned matrix : 86059 x 86689 with weight 4402841.
Total sieving time: 1.12 hours.
Total relation processing time: 0.04 hours.
Matrix solve time: 0.10 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,115,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.29 hours.
 --------- CPU info (if available) ----------

May 30, 2006

By Makoto Kamada / GGNFS-0.77.1-20060513-pentium4

10111+3 = 1(0)1103<112> = 22483 · C107

C107 = P49 · P59

P49 = 3811103616383696520035255018963138889550371472027<49>

P59 = 11670648336895389594887395705639732998619139278066767263683<59>

Number: 10003_111
N=44478050082284392652226126406618333852243917626651247609304808077213894942845705644264555441889427567495441
  ( 107 digits)
SNFS difficulty: 111 digits.
Divisors found:
 r1=3811103616383696520035255018963138889550371472027 (pp49)
 r2=11670648336895389594887395705639732998619139278066767263683 (pp59)
Version: GGNFS-0.77.1-20060513-pentium4
Total time: 1.46 hours.
Scaled time: 1.26 units (timescale=0.864).
Factorization parameters were as follows:
n: 44478050082284392652226126406618333852243917626651247609304808077213894942845705644264555441889427567495441
m: 10000000000000000000000
c5: 10
c0: 3
skew: 1
type: snfs
Factor base limits: 600000/800000
Large primes per side: 3
Large prime bits: 25/25
Max factor residue bits: 46/46
Sieved algebraic special-q in [400000, 500001)
Primes: RFBsize:49098, AFBsize:63918, largePrimes:2285539 encountered
Relations: rels:2658142, finalFF:499848
Max relations in full relation-set: 28
Initial matrix: 113082 x 499848 with sparse part having weight 39448818.
Pruned matrix : 61151 x 61780 with weight 5357858.
Total sieving time: 1.31 hours.
Total relation processing time: 0.06 hours.
Matrix solve time: 0.06 hours.
Time per square root: 0.03 hours.
Prototype def-par.txt line would be:
snfs,111,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000
total time: 1.46 hours.
 --------- CPU info (if available) ----------

May 29, 2006 (2nd)

100...003 and 100...009 have been extended to n=200. The factors contained in 100...003, 100...009, 99...991 and 99...997 are shared with Wojciech Florek's Numbers b^n +/- (b-1).

May 29, 2006

By Alexander Mkrtychyan / ggnfs-0.77.1-20050930-win32, ggnfs-0.77.1-20060513-win32 gnfs

(10177+17)/9 = (1)1763<177> = 79 · 199 · 337 · 1892299672990464278460298053559<31> · C140

C140 = P41 · P99

P41 = 30718605547911357038884474798678757669593<41>

P99 = 360791261643161040204601470623121686876253222118849993349356095607539068590369608206576778840865487<99>

From dependence 0, sqrt obtained:
r1=30718605547911357038884474798678757669593 (pp41)
r2=360791261643161040204601470623121686876253222118849993349356095607539068590369608206576778840865487 (pp99)

Sieving time: ~100hrs 3x(2xXeon 2GHz HT)
Special-q: [3700000;4285000)U[4700000;5285000)U[5700000;6275000)U[6700000;7275000)U[7700000;8275000)U[8700000;9275000)
Matbuild time: 1h 13m (P4 3GHz)
Matsolve time: 65hrs (Xeon 2GHz)
SQRT time: 23m (Xeon 2GHz)

May 28, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(10187-7)/3 = (3)1861<187> = 353 · 280452841 · 1622017637<10> · 6455829493<10> · 8153771179<10> · 8323772467<10> · 13844844491<11> · 133121560007<12> · C116

C116 = P32 · P85

P32 = 17112512897645193474162457303709<32>

P85 = 1502130221517405323788789034763018633547019554207566438289495865206761369751410755243<85>

Number: 33331_187
N=25705222789659230129577349579323241908332956518982930455730238052034344376144780365717653648473188667077721115096287
  ( 116 digits)
Divisors found:
 r1=17112512897645193474162457303709 (pp32)
 r2=1502130221517405323788789034763018633547019554207566438289495865206761369751410755243 (pp85)
Version: GGNFS-0.77.1
Total time: 74.90 hours.
Scaled time: 44.64 units (timescale=0.596).
Factorization parameters were as follows:
name: 33331_187
n: 25705222789659230129577349579323241908332956518982930455730238052034344376144780365717653648473188667077721115096287
skew: 72066.11
# norm 4.77e+15
c5: 16020
c4: 1079678044
c3: -226377956377577
c2: -3869740926659501127
c1: 593017781651556008797213
c0: 556666633407509921583325059
# alpha -5.61
Y1: 29630664371
Y0: -17420947106597594755066
# Murphy_E 4.96e-10
# M 19075954865955788364877833372874227080287775471724129794572307966875364161158480220873129933185096115271356398268504
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2250000, 3630001)
Relations: rels:7413410, finalFF:711122
Initial matrix: 631991 x 711122 with sparse part having weight 52523327.
Pruned matrix : 591074 x 594297 with weight 34326604.
Polynomial selection time: 1.58 hours.
Total sieving time: 60.71 hours.
Total relation processing time: 0.96 hours.
Matrix solve time: 11.04 hours.
Time per square root: 0.62 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 74.90 hours.
 --------- CPU info (if available) ----------

May 27, 2006

By Tyler Cadigan / PRIMO 2.2.0 beta 5, PRIMO 2.2.0 beta 6

(13·103883+23)/9 = 144...447<3884> and (13·103883+41)/9 = 144...449<3884> are twin primes. PRIMO took 61 days to certify them. These numbers are the new largest known quasi-repdigit twin primes in our tables. Congratulations!

[PRIMO - Primality Certificate]
Version=2.2.0 beta 5
WebSite=http://www.ellipsa.net/
Format=3
ID=B2CD301B487E4
Created=03/01/2006 07:58:02 AM
TestCount=555
Status=Candidate certified prime

[Running Times]
Initialization=1mn 13s
1stPhase=717h 33mn 5s
2ndPhase=199h 0mn 10s
Total=916h 34mn 29s
[PRIMO - Primality Certificate]
Version=2.2.0 beta 6
WebSite=http://www.ellipsa.net/
Format=3
ID=B2D1401C3126D
Created=05/04/2006 08:13:59 am
TestCount=525
Status=Candidate certified prime

[Running Times]
Initialization=1mn 17s
1stPhase=435h 46mn 42s
2ndPhase=120h 53mn 59s
Total=556h 42mn 0s

May 26, 2006

By Alexander Mkrtychyan / ggnfs-0.77.1-20050930-win32, ggnfs-0.77.1-20060513-win32 gnfs

(10180+17)/9 = (1)1793<180> = 6949 · 135862068644287<15> · 21633659135200744087543<23> · 57990409560719099220689<23> · C116

C116 = P58 · P59

P58 = 1382900513606693483258913500529894818988671399169846834029<58>

P59 = 67835941890955693798711513601062800007163705809229580442097<59>

From dependence 2, sqrt obtained:
r1=67835941890955693798711513601062800007163705809229580442097 (pp59)
r2=1382900513606693483258913500529894818988671399169846834029 (pp58)

---
name: 11113_180
n: 93810358881996442890482228144067883749540447348259571159075789651402467670223973413339539712829879169409153603718813
skew: 175108.69
# norm 1.75e+016
c5: 5400
c4: -1726380600
c3: -432331060735484
c2: 49069046496066798379
c1: 6386726768458004938997316
c0: -195736233629971911011199858171
# alpha -6.42
Y1: 118668961433
Y0: -28052497025194315455812
# Murphy_E 4.47e-010
# M 21556650053594647587355239452989933796097336626550949729236432534682743476314564571653393032526111986106295322015595
type: gnfs
rlim: 4200000
alim: 4200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6

special-q: [2100000;3300000) U [3800000;4050000)
largePrimes: 7643593 , relations: 7698454, finalFF:735738
Pruning matrix with wt=0.700
Initial matrix is 592789 x 735738 with sparse part having weight 60694738.
(total weight is 105658690)
Matrix pruned to 534537 x 537564 with weight 32218417.
Matrix solve time: 11 hrs
Each dependency: 24 min

May 25, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

6·10154-1 = 5(9)154<155> = 57413 · 33391993 · 394480713417379755453806059<27> · C116

C116 = P55 · P62

P55 = 5080508476226699401820394941107809615305588790497635369<55>

P62 = 15615853062739861486377064170042789464317919964935221145123641<62>

Number: 59999_154
N=79336473848760530612842941919437624337465023282039573568924868671690972576856766205762376956791968689234595639658529
  ( 116 digits)
Divisors found:
 r1=5080508476226699401820394941107809615305588790497635369 (pp55)
 r2=15615853062739861486377064170042789464317919964935221145123641 (pp62)
Version: GGNFS-0.77.1
Total time: 71.45 hours.
Scaled time: 42.59 units (timescale=0.596).
Factorization parameters were as follows:
name: 59999_154
n: 79336473848760530612842941919437624337465023282039573568924868671690972576856766205762376956791968689234595639658529
skew: 84818.07
# norm 2.28e+16
c5: 29880
c4: 7478564061
c3: -707415992953978
c2: -45326205609016815484
c1: 1923709240675668423295402
c0: 33553695631315758691438543975
# alpha -7.35
Y1: 1705761963619
Y0: -19267108168052096703534
# Murphy_E 5.23e-10
# M 66752713575719543916592226157126688247860915181985985556033446618000744146215247187696635904247103461998592722806763
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2250000, 3570001)
Relations: rels:7595337, finalFF:785196
Initial matrix: 631739 x 785196 with sparse part having weight 56191010.
Pruned matrix : 561458 x 564680 with weight 27895824.
Total sieving time: 60.75 hours.
Total relation processing time: 1.09 hours.
Matrix solve time: 9.02 hours.
Time per square root: 0.60 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 71.45 hours.
 --------- CPU info (if available) ----------

May 22, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(22·10158-1)/3 = 7(3)158<159> = 140489219953<12> · 35002292573981<14> · 12758191547884466113<20> · C116

C116 = P46 · P70

P46 = 5876416527844272249936979378582409414757015853<46>

P70 = 1989116612667541745797449592887591507231608864101217927853626043037229<70>

Number: 73333_158
N=11688877738489155829430414188785043880605496839583412226210933921576972975907322546275114248757018500186648622191337
  ( 116 digits)
Divisors found:
 r1=5876416527844272249936979378582409414757015853 (pp46)
 r2=1989116612667541745797449592887591507231608864101217927853626043037229 (pp70)
Version: GGNFS-0.77.1
Total time: 78.52 hours.
Scaled time: 46.80 units (timescale=0.596).
Factorization parameters were as follows:
name: 73333_158
n: 11688877738489155829430414188785043880605496839583412226210933921576972975907322546275114248757018500186648622191337
skew: 59680.44
# norm 3.24e+16
c5: 20880
c4: -14234941084
c3: -306085187616580
c2: 23180516622910676703
c1: -735129018559166322145374
c0: 4488697936590608689274471535
# alpha -6.93
Y1: 486245336687
Y0: -14112712835610901808786
# Murphy_E 4.83e-10
# M 2568106766109560019945838462360232314677097972922575724213417769912041924975690663254191959635629891932025334885188
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2250000, 3690001)
Relations: rels:7460294, finalFF:721699
Initial matrix: 631607 x 721699 with sparse part having weight 54496744.
Pruned matrix : 587098 x 590320 with weight 34434946.
Polynomial selection time: 1.53 hours.
Total sieving time: 64.01 hours.
Total relation processing time: 1.17 hours.
Matrix solve time: 11.13 hours.
Time per square root: 0.67 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 78.52 hours.
 --------- CPU info (if available) ----------

May 19, 2006

By Yousuke Koide / GMP-ECM

101490+1 = 1(0)14891<1491> = 101 · 3541 · 8941 · 10729 · 27961 · 62581 · 607921 · 14118155281<11> · 4672884738461<13> · 72286688991301<14> · 171815892427926701<18> · 136916416686052955621<21> · 2336398996447692315465181<25> · [110870679844269144354635709949582391774770890704083103791132633566371413253392265378550591815806580691669808595307539634355488864836833845471616794677024940025967620229919340559408262151273358247434378152195260280636870443948931086228877135378433246056449430881437009<267>] · C533 · [1351888791527812046439213882009622550983970447446930813907281321570614318590099348850147937665737601917016027689304215555619864311672420525464165912633730679733873139241622895458014281474880533521107162485558617384106966419668546077494971073918410836418351615825596959802566688270975816957817343681670940963553941306251076786071118381886951748734183323759331738970862212863946579098193981677634489961869774727417167109001620173536142186561428201966969394669482772192463087452587648096715535089953833204308363926463253547939370366391026176469926869119483259090839941<565>]

C533 = P32 · C502

P32 = 43449727365272099794386367962241<32>

C502 = [1605214440709619357797351581919800889833597416421394148739815672950024771161380823847360755208273655227157019000219766490046550207325155036864476602837123952047383195091299758360303040822482624716944164463773873136231905729534814986307576307291846151794615420341552185181793289760376366513402259834628028778708825939521820938434639815230158850634413284564675945198522078882483236008364966125191436705573836033815481341830782769681163394145324260216840198126909976526595416165428782222227927578041059481<502>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

May 18, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

6·10153-1 = 5(9)153<154> = 72 · 11923 · 10612859 · 331784113069<12> · 453413972988539<15> · C115

C115 = P54 · P62

P54 = 210419824853341366020370755446106047880424773709398731<54>

P62 = 30570327461743607247656827644966362380207522643930113459529683<62>

Number: 59999_153
N=6432602950209381566071417300565692922172746250322495126280992600135969399574714874192832413021554182913335977032273
  ( 115 digits)
Divisors found:
 r1=210419824853341366020370755446106047880424773709398731 (pp54)
 r2=30570327461743607247656827644966362380207522643930113459529683 (pp62)
Version: GGNFS-0.77.1
Total time: 74.60 hours.
Scaled time: 49.61 units (timescale=0.665).
Factorization parameters were as follows:
name: 59999_153
n: 6432602950209381566071417300565692922172746250322495126280992600135969399574714874192832413021554182913335977032273
skew: 105280.31
# norm 6.40e+15
c5: 3360
c4: 1711138388
c3: -142704087242572
c2: -16509405547813587843
c1: 579448197690139623628968
c0: 15834339481339862133738235344
# alpha -6.16
Y1: 916937538077
Y0: -18047092579177005337355
# Murphy_E 5.51e-10
# M 4649560124782638886169002085810032125698866907620478245677898408391415163706005214228115241540314236068560646898293
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 3150001)
Relations: rels:7537636, finalFF:591893
Initial matrix: 500171 x 591893 with sparse part having weight 53046021.
Pruned matrix : 466490 x 469054 with weight 32722150.
Total sieving time: 65.33 hours.
Total relation processing time: 0.80 hours.
Matrix solve time: 7.93 hours.
Time per square root: 0.53 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 74.60 hours.
 --------- CPU info (if available) ----------

May 15, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(10171+11)/3 = (3)1707<171> = 92679287 · 994403167 · 417175914199627907<18> · 42988602995074769083067<23> · C114

C114 = P42 · P72

P42 = 532370738642252747881930955732927552264431<42>

P72 = 378832148738346714803246790370049786475497092748031158119297214036870927<72>

Number: 33337_171
N=201679150845265397972899579405414196358211817136533655146698091272809044950702835327119509077953012871064520097537
  ( 114 digits)
Divisors found:
 r1=532370738642252747881930955732927552264431 (pp42)
 r2=378832148738346714803246790370049786475497092748031158119297214036870927 (pp72)
Version: GGNFS-0.77.1
Total time: 60.55 hours.
Scaled time: 36.21 units (timescale=0.598).
Factorization parameters were as follows:
name: 33337_171
n: 201679150845265397972899579405414196358211817136533655146698091272809044950702835327119509077953012871064520097537
skew: 64839.26

May 12, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(8·10194-17)/9 = (8)1937<194> = 3 · 457 · 7442198479<10> · 1853420236219<13> · 47262295153011259<17> · 15350897443886512393<20> · 64765061725005467929<20> · C114

C114 = P34 · P80

P34 = 6480369962419216676886015131553803<34>

P80 = 15436388905337558778371403302481752050799648156400720007183437167938419834568313<80>

Number: 88887_194
N=100033510990370769037783221436892148654237355566140936043342879059476911987097644903473741174361430890787438444339
  ( 114 digits)
Divisors found:
 r1=6480369962419216676886015131553803 (pp34)
 r2=15436388905337558778371403302481752050799648156400720007183437167938419834568313 (pp80)
Version: GGNFS-0.77.1
Total time: 59.27 hours.
Scaled time: 39.41 units (timescale=0.665).
Factorization parameters were as follows:
name: 88887_194
n: 100033510990370769037783221436892148654237355566140936043342879059476911987097644903473741174361430890787438444339
skew: 94843.55
# norm 3.78e+15
c5: 6720
c4: -454079855
c3: -166276676958541
c2: 4321868868486253437
c1: 621457987802746553015556
c0: -5759405241914086523773708032
# alpha -5.97
Y1: 1235364142463
Y0: -6832132952966350514215
# Murphy_E 6.59e-10
# M 53414084420105239531409507853870439225520878623788372429017774638301052821831186082132921294698619636722904152636
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2850001)
Relations: rels:7428947, finalFF:618021
Initial matrix: 501237 x 618021 with sparse part having weight 51636023.
Pruned matrix : 454628 x 457198 with weight 27725778.
Polynomial selection time: 0.75 hours.
Total sieving time: 50.46 hours.
Total relation processing time: 0.67 hours.
Matrix solve time: 6.82 hours.
Time per square root: 0.57 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 59.27 hours.
 --------- CPU info (if available) ----------

May 9, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(64·10187-1)/9 = 7(1)187<188> = 3059423027<10> · 774835058906615644573<21> · 2096821980403022549357<22> · 46631924364211658379013<23> · C114

C114 = P34 · P80

P34 = 3085197246316846058441513572039351<34>

P80 = 99439936186422677023881388364394444639121093342721552571149678501567263064669351<80>

Number: 71111_187
N=306791817296274137578369995378342769784629428227128004530748464743913733873267850246802709850429363527789575631201
  ( 114 digits)
Divisors found:
 r1=3085197246316846058441513572039351 (pp34)
 r2=99439936186422677023881388364394444639121093342721552571149678501567263064669351 (pp80)
Version: GGNFS-0.77.1
Total time: 66.32 hours.
Scaled time: 44.11 units (timescale=0.665).
Factorization parameters were as follows:
name: 71111_187
n: 306791817296274137578369995378342769784629428227128004530748464743913733873267850246802709850429363527789575631201
skew: 72723.60
# norm 8.36e+15
c5: 4200
c4: 1314878496
c3: 29893165368154
c2: 5806505690884697260
c1: -80974786490363044819303
c0: -2809595739939450546389912905
# alpha -5.91
Y1: 506287004443
Y0: -9391120872173951113476
# Murphy_E 5.91e-10
# M 64411780652946857169721256341933818960526809823175485053028889724667874325524578817371689180174804384560712691116
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 3050001)
Relations: rels:7784965, finalFF:703564
Initial matrix: 500178 x 703564 with sparse part having weight 64780933.
Pruned matrix : 427184 x 429748 with weight 27215548.
Polynomial selection time: 0.52 hours.
Total sieving time: 58.35 hours.
Total relation processing time: 0.75 hours.
Matrix solve time: 6.21 hours.
Time per square root: 0.49 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 66.32 hours.
 --------- CPU info (if available) ----------

May 8, 2006

By Yousuke Koide / GMP-ECM

101005+1 = 1(0)10041<1006> = 7 · 11 · 13 · 211 · 241 · 2011 · 2161 · 7237 · 9091 · 667321 · 248807851 · 7261216121<10> · 17830074841<11> · 851109498533797<15> · 45360300267343173645804799921<29> · 909090909090909090909090909090909090909090909090909090909090909091<66> · 220589842618680198991086731354678488275926380957742565496334997548411735059<75> · 302763019793435602569276039549096923630299122171140405303248730561741324305632792351835552866724155290700915085510738521559595248967375329278966176208018813174111240588000435579287968883246599299199382818469156370627492652751047813638818869931<243> · C523

C523 = P34 · C489

P34 = 5106142986008803018248662015009851<34>

C489 = [267065612248820557472520439776822436976316860200284961217319474767187378351419204646394707262722878914653395748869244344163867301798774915535042661263712198199655751422924668127752305623311241735515907241278561718322243002304418362598142142784047872257429459694724497453620868115224924909852592025982594685275509236743201047056443487859885626143200492047910061842042588027369301270574181306219963521753550999023466384773034942701929137632741459562769524551431233366749180168445321428112521<489>]

(101095-1)/9 = (1)1095<1095> = 3 · 31 · 37 · 41 · 271 · 439 · 2906161 · 30528601 · 743778751 · 2212293763<10> · 12171337159<11> · 1399205517511<13> · 99519941206321<14> · 1855193842151350117<19> · 49207341634646326934001739482502131487446637<44> · 39316310783659104892252157287077969239619734325044334592964583271<65> · 23593748551050409936688015200253053030029532433958916533719315706853<68> · [900009000090000900009000090000900009000090000900009000090000900009000090090900909009090090900909009090090900909009090090900909009090090900909009099090990909909099090990909909099090990909909099090990909909099090990909909999099990999909999099990999909999099990999909999099990999909999099991<288>] · C534

C534 = P36 · C499

P36 = 140932038048905130657965837325339961<36>

C499 = [2490959198534119854148888244888389656922469923333114578224491510740768956555767426487650605866819367218146558537719339947893409283320637700994215368076762244767408218909879904099720709997732498013277342080382591987824100057995391141148714118030303561287868930859755521892342961834650557591057337986666940122597723149999708447139377583307317514714358416876794090235604232173146119518484368738494673569394646876952276579416547854836399176089562703592384079831887087898586536197356767893761165757641671<499>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

May 6, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

10176-3 = (9)1757<176> = 1630871011403<13> · 274954356330508669<18> · 6165326947505579813146109111140967<34> · C113

C113 = P53 · P61

P53 = 15902473362316519828155848907387241210869028241932019<53>

P61 = 2274568355541311973196278737571018169468417735311027313697927<61>

Number: 99997_176
N=36171262684763804729310148527389239248018395875233064507433824238903582995595207747275554709544383072041835224613
  ( 113 digits)
Divisors found:
 r1=15902473362316519828155848907387241210869028241932019 (pp53)
 r2=2274568355541311973196278737571018169468417735311027313697927 (pp61)
Version: GGNFS-0.77.1
Total time: 49.15 hours.
Scaled time: 31.46 units (timescale=0.640).
Factorization parameters were as follows:
name: 99997_176
n: 36171262684763804729310148527389239248018395875233064507433824238903582995595207747275554709544383072041835224613
skew: 21661.12
# norm 1.39e+15
c5: 18480
c4: -1274308388
c3: -2753156212614
c2: -566135503557535436
c1: -1770382572121760880459
c0: 12586420686444448843600627
# alpha -5.30
Y1: 186177921679
Y0: -4553366263117725452040
# Murphy_E 7.67e-10
# M 6503063031704603377893240417849562075913973347253991849218632153429208960877388456019300122795172030561087003516
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2650001)
Relations: rels:7231586, finalFF:566384
Initial matrix: 501020 x 566384 with sparse part having weight 46763514.
Pruned matrix : 469008 x 471577 with weight 31217684.
Total sieving time: 40.71 hours.
Total relation processing time: 0.63 hours.
Matrix solve time: 7.33 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 49.15 hours.
 --------- CPU info (if available) ----------

May 4, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(22·10195-1)/3 = 7(3)195<196> = 760607 · 924361 · 7110820979199464413<19> · 225671089237444355780867<24> · 1468739043177098162139599627<28> · C115

C115 = P47 · P68

P47 = 57840971850648197321146788506896562701289609689<47>

P68 = 76510951515688690163170103291651427855005889299208107899216779746183<68>

Number: 73333_195
N=4425467792885258554902155078021991736153936106228595784249517804196388210518384921317149581681328539846156557567087
  ( 115 digits)
Divisors found:
 r1=57840971850648197321146788506896562701289609689 (pp47)
 r2=76510951515688690163170103291651427855005889299208107899216779746183 (pp68)
Version: GGNFS-0.77.1
Total time: 84.49 hours.
Scaled time: 50.36 units (timescale=0.596).
Factorization parameters were as follows:
name: 73333_195
n: 4425467792885258554902155078021991736153936106228595784249517804196388210518384921317149581681328539846156557567087
skew: 170663.23
# norm 9.92e+15
c5: 1260
c4: 133094852
c3: -235094834885984
c2: -2109515795186569345
c1: 1527791730117853107692802
c0: -2793794243224810862467149600
# alpha -5.77
Y1: 302054157823
Y0: -20375937126109800578251
# Murphy_E 5.19e-10
# M 3076403489535678031464462710394205254422024861907700313351362960154556084852305858936583388784869574395611274292560
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 3450001)
Relations: rels:7869880, finalFF:687897
Initial matrix: 500521 x 687897 with sparse part having weight 66175633.
Pruned matrix : 440257 x 442823 with weight 30310998.
Polynomial selection time: 0.52 hours.
Total sieving time: 75.79 hours.
Total relation processing time: 0.78 hours.
Matrix solve time: 6.82 hours.
Time per square root: 0.59 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 84.49 hours.
 --------- CPU info (if available) ----------

April 2006

Apr 30, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(2·10166+43)/9 = (2)1657<166> = 23 · 239 · 223681 · 4808529001<10> · 27380724157<11> · 49555413624314842798663<23> · C114

C114 = P48 · P67

P48 = 109487586728603959180419389601246000593684286667<48>

P67 = 2529994022553427102516108528949076661299677585064796901468164965163<67>

Number: 22227_166
N=277002939967167951016685502103671381318776877865988131419624426806168301114704336309326219472752500352276560381721
  ( 114 digits)
Divisors found:
 r1=109487586728603959180419389601246000593684286667 (pp48)
 r2=2529994022553427102516108528949076661299677585064796901468164965163 (pp67)
Version: GGNFS-0.77.1
Total time: 68.07 hours.
Scaled time: 40.57 units (timescale=0.596).
Factorization parameters were as follows:
name: 22227_166
n: 277002939967167951016685502103671381318776877865988131419624426806168301114704336309326219472752500352276560381721
skew: 35022.57
# norm 2.16e+15
c5: 18240
c4: 3324342576
c3: -75210684545821
c2: -3889995031532597485
c1: 41149321063516891001327
c0: 225554783497329843951341475
# alpha -5.11
Y1: 661875331123
Y0: -6859467162763553226608
# Murphy_E 5.83e-10
# M 169113702666968308599370405410246605720862169449212140169193171897561787349105029174955912873471203511474794908184
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 3050001)
Relations: rels:7820687, finalFF:710792
Initial matrix: 500744 x 710792 with sparse part having weight 65707739.
Pruned matrix : 426298 x 428865 with weight 27132479.
Total sieving time: 60.31 hours.
Total relation processing time: 0.73 hours.
Matrix solve time: 6.55 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 68.07 hours.
 --------- CPU info (if available) ----------

Apr 27, 2006 (2nd)

By Yousuke Koide / GMP-ECM

10957+1 = 1(0)9561<958> = 7 · 112 · 13 · 23 · 59 · 1277 · 4093 · 8779 · 357281 · 599144041 · 49561573447<11> · 183411838171<12> · 638453709757<12> · 135080726389891<15> · 8793273568581345414847<22> · 154083204930662557781201849<27> · 1274194732898148471766404179653<31> · [486459602951209423461970749393767073577709990315453869054236545173346054197523047637756449380382360041196303992701358542477479985899282299202659134981413322115768441437335973512015267176836292140179486592703400778357473505777445415009505803673230073891473294849<261>] · C539

C539 = P33 · C506

P33 = 156318278601913796169958831669567<33>

C506 = [66203514277021933018367219154147693778936535037473098541895109470133101615260456904766124804243260059004061482523868396627422842510506272739618129760738873068588643277236787555047257507825557038938807521179427472188374447895999544336201041507230424796520553176789792857470904436544840504491242651630080934330545370540473441479395984110121956451559196947095558755351350931089697373180296334055005865225493893072152234214689358450841228924816239504156756948896041357344696275396252307079534359595606264813659<506>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 27, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(4·10175+23)/9 = (4)1747<175>= 74 · 151 · 4077068417<10> · 912028673482967<15> · 18287204296526384115739261382729<32> · C114

C114 = P43 · P72

P43 = 1474496589385636624872422204643590358428021<43>

P72 = 122264617559167997611060160283499497988751361155452737911400912906085147<72>

Number: 44447_175
N=180278761593532432612303389060257361960331553150960921382583597306562657112851496908359299109733878279188096704087
  ( 114 digits)
Divisors found:
 r1=1474496589385636624872422204643590358428021 (pp43)
 r2=122264617559167997611060160283499497988751361155452737911400912906085147 (pp72)
Version: GGNFS-0.77.1
Total time: 66.44 hours.
Scaled time: 40.99 units (timescale=0.617).
Factorization parameters were as follows:
name: 44447_175
n: 180278761593532432612303389060257361960331553150960921382583597306562657112851496908359299109733878279188096704087
skew: 37257.24
# norm 1.97e+15
c5: 2640
c4: -3066352960
c3: -2045340552093
c2: 4202550017261824270
c1: 5428663167547359316208
c0: -351827258170714110587019840
# alpha -5.13
Y1: 940460856101
Y0: -9265702850142573753067
# Murphy_E 5.77e-10
# M 73472187332863004272367469093365019774637426525363658693875390400459913791531866622534228469633558335064213728171
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 3050001)
Relations: rels:7715758, finalFF:666113
Initial matrix: 501371 x 666113 with sparse part having weight 60549670.
Pruned matrix : 442462 x 445032 with weight 28621695.
Polynomial selection time: 0.59 hours.
Total sieving time: 57.53 hours.
Total relation processing time: 0.71 hours.
Matrix solve time: 7.08 hours.
Time per square root: 0.52 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 66.44 hours.
 --------- CPU info (if available) ----------

Apr 24, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(5·10164-41)/9 = (5)1631<164> = 3 · 117526809611<12> · 54250638606310858569979433501919015383<38> · C115

C115 = P43 · P73

P43 = 1474584781590694929005726294763938095505713<43>

P73 = 1969675536474541734600499776776117471857256864782569029241086440347327593<73>

Number: 55551_164
N=2904453570756846986973383368766510254862338723725138737049038603407688954012735912987940359365696468744723414038809
  ( 115 digits)
Divisors found:
 r1=1474584781590694929005726294763938095505713 (pp43)
 r2=1969675536474541734600499776776117471857256864782569029241086440347327593 (pp73)
Version: GGNFS-0.77.1
Total time: 67.75 hours.
Scaled time: 40.38 units (timescale=0.596).
Factorization parameters were as follows:
name: 55551_164
n: 2904453570756846986973383368766510254862338723725138737049038603407688954012735912987940359365696468744723414038809
skew: 80450.98
# norm 1.20e+16
c5: 17820
c4: 4393654356
c3: -433753330947111
c2: -27350320194916868196
c1: 1177687194802812552792514
c0: 15113021087910275283692837108
# alpha -6.45
Y1: 2090837063779
Y0: -11026236084453321843579
# Murphy_E 5.28e-10
# M 223818122459110710984661179910979783697925729433915265008233972170338542245360401390459830340040811696130589483131
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 3050001)
Relations: rels:7459470, finalFF:591118
Initial matrix: 500042 x 591118 with sparse part having weight 51454791.
Pruned matrix : 465016 x 467580 with weight 31354404.
Total sieving time: 58.56 hours.
Total relation processing time: 0.63 hours.
Matrix solve time: 7.92 hours.
Time per square root: 0.64 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 67.75 hours.
 --------- CPU info (if available) ----------

Apr 23, 2006

By Bruce Dodson / GMP-ECM

10399+1 = 1(0)3981<400> = 72 · 11 · 13 · 127 · 2689 · 459691 · 909091 · 1458973 · 425991366045253<15> · 909090909090909091<18> · 247025236977306025681323889<27> · 753201806271328462547977919407<30> · 61828645758322140842666144519962696417487<41> · 72021403933746126426491665754465510017877<41> · 17499101101496101893247811440257935152097401<44> · C159

C159 = P49 · P110

P49 = 9284668536078237580134472469990637899155265743957<49>

P110 = 13147963643704652632557279758698587212033283223333451187877069162714784603584406816150353817835190742091970171<110>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 22, 2006 (2nd)

By Yousuke Koide / GMP-ECM

10903+1 = 1(0)9021<904> = 72 · 11 · 13 · 127 · 2689 · 3613 · 459691 · 909091 · 57009401 · 2182600451<10> · 212057054080446499<18> · 120525789336558438197<21> · 7306116556571817748755241<25> · 304768036847074491064894608014695867632997<42> · 3605696680890791382725432167911038465896663<43> · 6798855735656881396055959081077830421892567<43> · 1752088930844817629923654387608505754917704006063078641900632201094124478044555887071171166365583553287053602700568010683873135238140340718711012045219107751867190380847<169> · C504

C504 = P38 · C467

P38 = 43304701938592897922269981296083376277<38>

C467 = [21013886489517971344330040348864764437934906646797649893170202970198245328335882505499980396675911865555101856779577300554075531457771872695017237088972173632109249163225374752369335580275541978505985802453671153658648150573384500193528998265661485199395999980819844420791561304482876541398168140686809355351611618717081565145452820471364641262390976246981616092354714230772892990579479051048942179341131112862748124387554407607082664991040927358250555874030530718383<467>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 22, 2006

Jason Papadopoulos's Msieve Version 1.06 was released.

Apr 21, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(2·10167-17)/3 = (6)1661<167> = 7 · 7461472332473<13> · 431563732881502259<18> · 5375549665816933543013<22> · C114

C114 = P35 · P37 · P44

P35 = 13261436963852796014111335957348117<35>

P37 = 1573557102101571405377857101955399229<37>

P44 = 26366061185051453095178144268786977977763221<44>

Number: 66661_167
N=550197165033613611769376863626601856258906596716272891854586217441612353242352244972984468385524424237232803855253
  ( 114 digits)
Divisors found:
 r1=13261436963852796014111335957348117 (pp35)
 r2=1573557102101571405377857101955399229 (pp37)
 r3=26366061185051453095178144268786977977763221 (pp44)
Version: GGNFS-0.77.1
Total time: 61.41 hours.
Scaled time: 36.60 units (timescale=0.596).
Factorization parameters were as follows:
name: 66661_167
n: 550197165033613611769376863626601856258906596716272891854586217441612353242352244972984468385524424237232803855253
skew: 70471.01
# norm 4.20e+15
c5: 1800
c4: 1368602079
c3: -12250040256487
c2: -1093635789305396793
c1: 39849855690633737457906
c0: -1783344159885267576523734080
# alpha -5.53
Y1: 805473164171
Y0: -12503883379418569316817
# Murphy_E 5.79e-10
# M 529423451654234320505526908635372534366477001369404131995810074889560862579154671691751730713159012157786351594722
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2950001)
Relations: rels:7611348, finalFF:653939
Initial matrix: 500098 x 653939 with sparse part having weight 56597179.
Pruned matrix : 441743 x 444307 with weight 26893096.
Total sieving time: 53.70 hours.
Total relation processing time: 0.64 hours.
Matrix solve time: 6.54 hours.
Time per square root: 0.53 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 61.41 hours.
 --------- CPU info (if available) ----------

Apr 19, 2006

By Yousuke Koide / GMP-ECM

10888+1 = 1(0)8871<889> = 17 · 593 · 1777 · 5882353 · 7228321 · 9999999900000001<16> · 14645119755678294049<20> · 1686340623946037268128160202360893760539460370996627318701517706745362561551433406408094266441822934232698145025463743674536256340640809274873526138279915682968128161887015177082630691231028669477234384485666273187182124789224283305059021924114671146711635919055647554806087689713153457<286> · C547

C547 = P34 · P514

P34 = 2430356574005120498845908043009873<34>

P514 = 2187319485856065660460480283212234313654078652411870459451330169647543812240431617143716447792186692975247051510538424479092940669136785288465781753693717009207146283270615110366556378727360748704592078063629885737548293485907528075546515396905912717472464716164833417809029422074335902030196371245199471373470169818790769381981258258611278976650676287419191207657093916768283363951628318877273133525031558244951861839766442570991470244423599118239355710932138403326127489420348476636642367374646669593814227877889<514>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 18, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(10162+11)/3 = (3)1617<162> = 1433 · 124841369 · 1336592833641954403<19> · 36720308617555078459<20> · C113

C113 = P35 · P79

P35 = 15839391943642481226131981562976091<35>

P79 = 2396790507959344653148912568029143521446310165683450943135628493061398785885083<79>

Number: 33337_162
N=37963704262370013974982229977530646773584991859960923446485591042890017200918324520218776946038568609153002550553
  ( 113 digits)
Divisors found:
 r1=15839391943642481226131981562976091 (pp35)
 r2=2396790507959344653148912568029143521446310165683450943135628493061398785885083 (pp79)
Version: GGNFS-0.77.1
Total time: 57.23 hours.
Scaled time: 37.88 units (timescale=0.662).
Factorization parameters were as follows:
name: 33337_162
n: 37963704262370013974982229977530646773584991859960923446485591042890017200918324520218776946038568609153002550553
skew: 82628.90
# norm 5.80e+15
c5: 5400
c4: 2402492435
c3: -113085781430568
c2: -14669915217540964944
c1: 360170614013768543148208
c0: 13321767032890434723398144064
# alpha -6.38
Y1: 693271831747
Y0: -5880177126467717739035
# Murphy_E 6.89e-10
# M 34645119737512916872622338715117151998917211253417099047843164366198507059196910860745581897837412972482767998816
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2850001)
Relations: rels:7665727, finalFF:700241
Initial matrix: 500331 x 700241 with sparse part having weight 60604941.
Pruned matrix : 422361 x 424926 with weight 24830799.
Polynomial selection time: 0.52 hours.
Total sieving time: 50.08 hours.
Total relation processing time: 0.70 hours.
Matrix solve time: 5.45 hours.
Time per square root: 0.48 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 57.23 hours.
 --------- CPU info (if available) ----------

Apr 16, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(82·10165-1)/9 = 9(1)165<166> = 3 · 4651 · 3815909 · 109337069 · 24597499837<11> · 119473647151415430355631209<27> · C111

C111 = P44 · P68

P44 = 52584546422938872199993496426580755318657669<44>

P68 = 10127846063825475829007266635111227567710236342483257149233524822111<68>

Number: 91111_165
N=532568191507609461751810844266510060172332169466526373634275624269343840855863338282742074685691230272530919259
  ( 111 digits)
Divisors found:
 r1=52584546422938872199993496426580755318657669 (pp44)
 r2=10127846063825475829007266635111227567710236342483257149233524822111 (pp68)
Version: GGNFS-0.77.1
Total time: 47.69 hours.
Scaled time: 28.42 units (timescale=0.596).
Factorization parameters were as follows:
name: 91111_165
n: 532568191507609461751810844266510060172332169466526373634275624269343840855863338282742074685691230272530919259
skew: 44253.41
# norm 2.76e+15
c5: 13260
c4: -2952571022
c3: -64159933967618
c2: 5169908297278730197
c1: 65757180348379498133862
c0: -972969186385581959161825911
# alpha -6.14
Y1: 183357985723
Y0: -2092994245773555980588
# Murphy_E 8.58e-10
# M 266349246250008411579281465016211195175095228656302106749506815357893863129981722202192551134409014791788528244
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1600000, 2500001)
Relations: rels:7502896, finalFF:632541
Initial matrix: 459786 x 632541 with sparse part having weight 56622491.
Pruned matrix : 394614 x 396976 with weight 24147845.
Polynomial selection time: 0.50 hours.
Total sieving time: 41.44 hours.
Total relation processing time: 0.68 hours.
Matrix solve time: 4.57 hours.
Time per square root: 0.49 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 47.69 hours.
 --------- CPU info (if available) ----------

Apr 13, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(83·10176+61)/9 = 9(2)1759<177> = 977189933 · 677436880567<12> · 4398981358728402973<19> · 4561677112603872026693843<25> · C113

C113 = P40 · P73

P40 = 7192656946027737524918319855947986687571<40>

P73 = 9652098648828096511437545492127071883766346870809662669210109599313691731<73>

Number: 92229_176
N=69424234390238348459735580768786661626522690519560994858731457507032720590703701430297457624005875684018103175401
  ( 113 digits)
Divisors found:
 r1=7192656946027737524918319855947986687571 (pp40)
 r2=9652098648828096511437545492127071883766346870809662669210109599313691731 (pp73)
Version: GGNFS-0.77.1
Total time: 60.14 hours.
Scaled time: 39.99 units (timescale=0.665).
Factorization parameters were as follows:
name: 92229_176
n: 69424234390238348459735580768786661626522690519560994858731457507032720590703701430297457624005875684018103175401
skew: 34725.81
# norm 9.38e+15
c5: 27840
c4: 1952949260
c3: 239570943857341
c2: 28653622092714987
c1: 4208411463039264573491
c0: -524927595336302835681939143
# alpha -6.17
Y1: 829057423733
Y0: -4779333281932956287892
# Murphy_E 6.01e-10
# M 1944097459749997755277490881319499555332311992419460999696824029213840783552124833372077496272187035996537581197
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2950001)
Relations: rels:7512522, finalFF:623442
Initial matrix: 499633 x 623442 with sparse part having weight 54825480.
Pruned matrix : 451822 x 454384 with weight 29284529.
Polynomial selection time: 0.50 hours.
Total sieving time: 51.68 hours.
Total relation processing time: 0.79 hours.
Matrix solve time: 6.71 hours.
Time per square root: 0.46 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 60.14 hours.
 --------- CPU info (if available) ----------

Apr 12, 2006

By Yousuke Koide / GMP-ECM

10816+1 = 1(0)8151<817> = 97 · 353 · 449 · 641 · 1409 · 69857 · 206209 · 58627969 · 3156663361<10> · 66554101249<11> · 75118313082913<14> · 39127329514182768921189838418689<32> · 8274466617334672110426476083265843201<37> · [20613661601050142213000575997849301836417547662874985098970766781932900988120507408603473644982986488160619644274811516746717894883553676903578704941377044565165542482689618096760494994922455997632250274389555329<212>] · C471

C471 = P37 · P435

P37 = 4444442797021732533861519689020084897<37>

P435 = 182168885688800471032070314606442908018600300417083944518739710393647902382617378829742666164078393724922058999479539245587167427080499185116669904781913921946772253903767015005946741838709655930349163084737589584381983926389625045094948824590259228606134828950677303795021460411056135766667281810175120746691826141507834669471110707839979934576289109001841823875933756134673970083682689775540524930437792688282436257038622290979346977<435>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 11, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(22·10168-1)/3 = 7(3)168<169> = 7 · 56123 · 446327841017<12> · 430461185535167573<18> · 1409905188331436013487<22> · C113

C113 = P56 · P58

P56 = 13084049258809821588896439090996621938307031288296648457<56>

P58 = 5266746964258109491400138988161479038453646038826462079387<58>

Number: 73333_168
N=68910376714040195406347745240503361261758316416576282636203495308149851640887510416264286216165380927075165055859
  ( 113 digits)
Divisors found:
 r1=13084049258809821588896439090996621938307031288296648457 (pp56)
 r2=5266746964258109491400138988161479038453646038826462079387 (pp58)
Version: GGNFS-0.77.1
Total time: 53.51 hours.
Scaled time: 31.89 units (timescale=0.596).
Factorization parameters were as follows:
name: 73333_168
n: 68910376714040195406347745240503361261758316416576282636203495308149851640887510416264286216165380927075165055859
skew: 36941.64
# norm 5.22e+15
c5: 15600
c4: 4190341915
c3: 3039365141531
c2: -8922979585383379554
c1: 94148034217382755246189
c0: -5421494257068971161432225
# alpha -6.41
Y1: 975922912999
Y0: -5358309014913334727634
# Murphy_E 7.37e-10
# M 6599696211979593814265749664234017177559052514922972069100058083737370758216219483967420220531197055536338039220
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2750001)
Relations: rels:7879379, finalFF:790755
Initial matrix: 500653 x 790755 with sparse part having weight 69627103.
Pruned matrix : 390126 x 392693 with weight 22520690.
Polynomial selection time: 0.53 hours.
Total sieving time: 46.94 hours.
Total relation processing time: 0.63 hours.
Matrix solve time: 4.96 hours.
Time per square root: 0.46 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 53.51 hours.
 --------- CPU info (if available) ----------

Apr 9, 2006

By Yousuke Koide / GMP-ECM

10849+1 = 1(0)8481<850> = 7 · 11 · 13 · 1699 · 241117 · 9170899 · 715880197 · 7198295568559013885196835567543447<34> · 61945573305222690279363663578823967<35> · 151168348012920493188164812150408056175148228488823<51> · [236981781933948043228112220789227624908212542569354344676500735171191136986262759275099377257787061318322981899812820646487731505276950534191352836827590738081581753192002166353465640625197<189>] · C515

C515 = P34 · C482

P34 = 1941850545413860134349140850659019<34>

C482 = [11974596042808172532294983252939558878410189694663843068971765344308532913676645715309213363442627278076993492211166595880998184306177956628823075306750747898909101048339462363861018906574913448147471222095530123865763276293471254728437236511524459858068517800257650185047651380759211520548387242736820413514544025166081207894531393549080448211783134185139166833148694113912674297086397341821453080768324146339882473885456877565040591000305223469402926705116035907018404340127773009<482>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 8, 2006 (2nd)

By Yousuke Koide / GMP-ECM

10816+1 = 1(0)8151<817> = 97 · 353 · 449 · 641 · 1409 · 69857 · 206209 · 58627969 · 3156663361<10> · 66554101249<11> · 75118313082913<14> · 8274466617334672110426476083265843201<37> · [20613661601050142213000575997849301836417547662874985098970766781932900988120507408603473644982986488160619644274811516746717894883553676903578704941377044565165542482689618096760494994922455997632250274389555329<212>] · C503

C503 = P32 · C471

P32 = 39127329514182768921189838418689<32>

C471 = [809639191841064628525439231464999860397773607701980496081352666339504925459847421412079302897545851796994671960772729238488139832762235263695725908656072122047265685298946436141716959730769253735737488429705565187437664314635095937428340389980720185899033798436170265716087449200924809607342324420823123105586292160476218717903066160195563389157166475672526475982627558029455580472138762318157710719436530508723203208044400504432618748282362705740783507784354366160306369<471>]

10822+1 = 1(0)8211<823> = 101 · 9901 · 718606649 · 40160350429<11> · 144389656548047821<18> · 2834523818368583744706086149<28> · [3430756550790484778909640352209879033892610315578901813821345434990400007261052844057102137330186660253398361164679549479441003751370060990401385264590147924466884786339105844110638415462294590233248989402615229312388735660453351624541145759819967937881<253>] · C500

C500 = P35 · C466

P35 = 16254031864650930002850269462824009<35>

C466 = [1518251219423747541558249786341574895284479899305883251990246801255766909229333395434458469693549966383795065664136418817339096752250299235950034967670343929013892055001964056060297891256021051404942653075694117320359458606226902427876452489321855322434222068318126282515684656661189152027802914755789408960326502178798522971472567196598942110678827737509377973305601271034834784135339840915115044044544939389765778113496729595022312073212316740002281949880005471741<466>]

10837+1 = 1(0)8361<838> = 7 · 11 · 13 · 19 · 373 · 1117 · 5023 · 44641 · 52579 · 70541929 · 3590254957<10> · 14175966169<11> · 261315626851<12> · 909090909090909090909090909091<30> · 183372282864547916749018225828651<33> · 18381907262281244633158190677786966663091011<44> · 4887054837129490444185770642291712106451445708466643483270887621857163512076927093556902832792696796518529880218993484798134507347686651311824503<145> · C525

C525 = P36 · C490

P36 = 108131551600520034721722272883130729<36>

C490 = [7045616588486799878229908819910336923888220571062351357216159107348231895397024661050209344237746338927104332618758413991185539098879237656670503260201568098865214938494573500927612773398337686887554455654975502630496905550466931864411689596634310312025533326809689061042921776515817300848267597128380147428873265628242289520724784622861753110448953054107116821206466090015933935448825960415332332679426815216857782017220038922288778308959959611010035857100841026102213598239576198581831053<490>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Apr 8, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(34·10190-7)/9 = 3(7)190<191> = 37 · 109 · 6609437 · 60793981 · 16209889148099957<17> · 3026164475092149900973<22> · 5559395425785366046547<22> · C113

C113 = P47 · P67

P47 = 17700270697562795473798575278495575252228893343<47>

P67 = 4829510199492607911626007156104654630552733041153862475787361617117<67>

Number: 37777_190
N=85483637867659658567202674170495654476226505771174948815394154314847353949058264254404667624789110546175796152131
  ( 113 digits)
Divisors found:
 r1=17700270697562795473798575278495575252228893343 (pp47)
 r2=4829510199492607911626007156104654630552733041153862475787361617117 (pp67)
Version: GGNFS-0.77.1
Total time: 57.54 hours.
Scaled time: 38.27 units (timescale=0.665).
Factorization parameters were as follows:
name: 37777_190
n: 85483637867659658567202674170495654476226505771174948815394154314847353949058264254404667624789110546175796152131
skew: 29076.08
# norm 1.07e+16
c5: 36540
c4: -12185242756
c3: 256023137714363
c2: 11051642456086268502
c1: 18000780073429467449288
c0: -153367693679452411321236672
# alpha -6.17
Y1: 878574755927
Y0: -4718764285096744772323
# Murphy_E 6.34e-10
# M 75966605504227469208499904048510806763470040437426901577401200590832189731289766473179388615073537509657719698494
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2850001)
Relations: rels:7507727, finalFF:633645
Initial matrix: 500994 x 633645 with sparse part having weight 54977270.
Pruned matrix : 448761 x 451329 with weight 28155882.
Total sieving time: 50.19 hours.
Total relation processing time: 0.63 hours.
Matrix solve time: 6.24 hours.
Time per square root: 0.49 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 57.54 hours.
 --------- CPU info (if available) ----------

Apr 6, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(61·10173-7)/9 = 6(7)173<174> = 71 · 233 · 24742957991<11> · 31809119701353051742109<23> · 39660267116313906346259099<26> · C112

C112 = P28 · P29 · P56

P28 = 3760357206641161646188454939<28>

P29 = 17434053596101093960844893121<29>

P56 = 20021041886655596186926329100373757874861254953098046101<56>

Number: 67777_173
N=1312544851288681061657320385726742235100077386920141929455960788027209627857570783929880133267056183525631510519
  ( 112 digits)
Divisors found:
 r1=3760357206641161646188454939 (pp28)
 r2=17434053596101093960844893121 (pp29)
 r3=20021041886655596186926329100373757874861254953098046101 (pp56)
Version: GGNFS-0.77.1
Total time: 43.90 hours.
Scaled time: 26.21 units (timescale=0.597).
Factorization parameters were as follows:
name: 67777_173
n: 1312544851288681061657320385726742235100077386920141929455960788027209627857570783929880133267056183525631510519
skew: 24484.59
# norm 3.26e+15
c5: 20160
c4: -6931159530
c3: -62708438404343
c2: 2275074974729497200
c1: 32786546490054575521986
c0: 5415945762602193956372053
# alpha -6.42
Y1: 308438021903
Y0: -2305306742891941527290
# Murphy_E 8.41e-10
# M 54595772227758935359404905948683395924693960067717954361230432600020289149931447345402724142563475095733714275
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2550001)
Relations: rels:7400610, finalFF:656339
Initial matrix: 500217 x 656339 with sparse part having weight 52225852.
Pruned matrix : 433326 x 435891 with weight 23330329.
Total sieving time: 37.25 hours.
Total relation processing time: 0.59 hours.
Matrix solve time: 5.59 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 43.90 hours.
 --------- CPU info (if available) ----------

Apr 4, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(25·10189-7)/9 = 2(7)189<190> = 23 · 53 · 37013 · 547635411247<12> · 330088629807359<15> · 3327653778948571<16> · 22683909170999073431738750101<29> · C112

C112 = P39 · P73

P39 = 856086520823564452415849992209116593237<39>

P73 = 5270401796810904687788561074505843101960974063751693547717781294407477621<73>

Number: 27777_189
N=4511919937574110062022680359046714142686606807038938468754742182604387963067074666966204626047764872601837449177
  ( 112 digits)
Divisors found:
 r1=856086520823564452415849992209116593237 (pp39)
 r2=5270401796810904687788561074505843101960974063751693547717781294407477621 (pp73)
Version: GGNFS-0.77.1
Total time: 57.21 hours.
Scaled time: 34.09 units (timescale=0.596).
Factorization parameters were as follows:
name: 27777_189
n: 4511919937574110062022680359046714142686606807038938468754742182604387963067074666966204626047764872601837449177
skew: 148044.23
# norm 4.56e+15
c5: 720
c4: -73626874
c3: -110867117727798
c2: 454455646419441839
c1: 510055059250966394606382
c0: 3954090739576303650823513256
# alpha -5.57
Y1: 234260784469
Y0: -5746536105901399508307
# Murphy_E 7.19e-10
# M 3185822251552743801476745947087601288349612792255263001652175728055263652166107759270387802466612664245102359504
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2850001)
Relations: rels:7502977, finalFF:656719
Initial matrix: 500172 x 656719 with sparse part having weight 54894770.
Pruned matrix : 438101 x 440665 with weight 25287702.
Polynomial selection time: 0.50 hours.
Total sieving time: 50.16 hours.
Total relation processing time: 0.64 hours.
Matrix solve time: 5.43 hours.
Time per square root: 0.48 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 57.21 hours.
 --------- CPU info (if available) ----------

Apr 1, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(83·10169+61)/9 = 9(2)1689<170> = 3 · 112 · 306725482387<12> · 158097431899383477583<21> · 5128036316381592220298959<25> · C112

C112 = P50 · P62

P50 = 19700081684465458593403806555789969994895088533657<50>

P62 = 51860316780454489279897084658059454426917923044301608049721421<62>

Number: 92229_168
N=1021652476757208163560581079259281054181213711730300692671570682687015568804053712776559333447913768270232366597
  ( 112 digits)
Divisors found:
 r1=19700081684465458593403806555789969994895088533657 (pp50)
 r2=51860316780454489279897084658059454426917923044301608049721421 (pp62)
Version: GGNFS-0.77.1
Total time: 48.14 hours.
Scaled time: 28.69 units (timescale=0.596).
Factorization parameters were as follows:
name: 92229_168
n: 1021652476757208163560581079259281054181213711730300692671570682687015568804053712776559333447913768270232366597
skew: 42379.53
# norm 2.26e+15
c5: 5700
c4: 2476189901
c3: 2818036125079
c2: -3965150761651559721
c1: 20159536553490602897396
c0: 628219114223343985647383680
# alpha -5.92
Y1: 299274416299
Y0: -2822810127643404054087
# Murphy_E 8.41e-10
# M 998581722717076005120486833807822888215121894318500192856457073627922103911622034888560960264551830549271253187
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2650001)
Relations: rels:7817263, finalFF:794068
Initial matrix: 500946 x 794068 with sparse part having weight 68271744.
Pruned matrix : 385474 x 388042 with weight 21626578.
Polynomial selection time: 0.52 hours.
Total sieving time: 41.98 hours.
Total relation processing time: 0.73 hours.
Matrix solve time: 4.45 hours.
Time per square root: 0.47 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 48.14 hours.
 --------- CPU info (if available) ----------

March 2006

Mar 30, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

2·10168-9 = 1(9)1671<169> = 7 · 1087 · 8537489959<10> · 367694783292840547667053261930530350154041<42> · C113

C113 = P53 · P61

P53 = 17966034076031944574391153471623679589453353622292711<53>

P61 = 4660500063909969005743702902671272798968399002082218677735511<61>

Number: 19991_168
N=83730702959555558644286753585554649649572317505120979221312693092511006979457450320140886370830911981249481160321
  ( 113 digits)
Divisors found:
 r1=17966034076031944574391153471623679589453353622292711 (pp53)
 r2=4660500063909969005743702902671272798968399002082218677735511 (pp61)
Version: GGNFS-0.77.1
Total time: 58.38 hours.
Scaled time: 34.80 units (timescale=0.596).
Factorization parameters were as follows:
name: 19991_168
n: 83730702959555558644286753585554649649572317505120979221312693092511006979457450320140886370830911981249481160321
skew: 62536.04
# norm 1.67e+15
c5: 4800
c4: 542418002
c3: -30527202903432
c2: -187460816726501101
c1: 39811099175404160316726
c0: -1109743373310044488384538995
# alpha -5.38
Y1: 185480496509
Y0: -7052262054420382279818
# Murphy_E 6.92e-10
# M 75632762796499756649388024022841439022310180894940132867887513639978626189449917333412097122871594278740117554634
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2850001)
Relations: rels:7719597, finalFF:707777
Initial matrix: 500741 x 707777 with sparse part having weight 61382861.
Pruned matrix : 422570 x 425137 with weight 24650963.
Total sieving time: 51.42 hours.
Total relation processing time: 0.60 hours.
Matrix solve time: 5.83 hours.
Time per square root: 0.53 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 58.38 hours.
 --------- CPU info (if available) ----------

Mar 29, 2006

By CWI

10238+1 = 1(0)2371<239> = 29 · 101 · 281 · 2381 · 28559389 · 121499449 · 1491383821<10> · 275855329893529<15> · 2324557465671829<16> · 20087794479102305428621<23> · C152

C152 = P64 · P89

P64 = 5582637833682557709253612812885341475900082138954691763178176941<64>

P89 = 13712255219708533473813623053189821987961076229175414555827926545777661379291311684923609<89>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 27, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(68·10198+13)/9 = 7(5)1977<199> = 33 · 2837 · 7305413 · 124068676637<12> · 403212889427768888832067867<27> · 1562091434865214888463863633<28> · C123

C123 = P57 · P66

P57 = 258170928787318894541525466230371667081514748966348106999<57>

P66 = 669249700255497765647229643415437163131542241223547798847162206127<66>

Number: 75557_198
N=172780816705596629436477571893915454694951908049723289731935734705261274963726310234006475949636958455314893409923089382873
  ( 123 digits)
Divisors found:
 r1=258170928787318894541525466230371667081514748966348106999 (pp57)
 r2=669249700255497765647229643415437163131542241223547798847162206127 (pp66)
Version: GGNFS-0.77.1
Total time: 257.55 hours.
Scaled time: 161.74 units (timescale=0.628).
Factorization parameters were as follows:
name: 75557_198
n: 172780816705596629436477571893915454694951908049723289731935734705261274963726310234006475949636958455314893409923089382873
skew: 242002.32
# norm 4.69e+16
c5: 5040
c4: 620918512
c3: -1283681869942759
c2: -25445850424152104787
c1: 26848786049597838801584727
c0: 58141808848337734262122548867
# alpha -5.97
Y1: 1075588169161
Y0: -509346087624359811646142
# Murphy_E 2.15e-10
# M 4224800078277202070226350581168509253931390803546482563682347130827643033159196813348775910046698793869083997859267081664
type: gnfs
rlim: 5000000
alim: 5000000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 5000000/5000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2500000, 7780001)
Relations: rels:8271672, finalFF:788713
Initial matrix: 697784 x 788713 with sparse part having weight 89212794.
Pruned matrix : 662576 x 666128 with weight 65904764.
Total sieving time: 227.99 hours.
Total relation processing time: 4.58 hours.
Matrix solve time: 24.26 hours.
Time per square root: 0.72 hours.
Prototype def-par.txt line would be:
gnfs,122,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.4,2.4,60000
total time: 257.55 hours.
 --------- CPU info (if available) ----------

Mar 23, 2006

By Kazumaro Aoki / GMP-ECM

(10371-1)/9 = (1)371<371> = 107 · 239 · 2969 · 4649 · 51199 · 1659431 · 1325815267337711173<19> · 47198858799491425660200071<26> · C304

C304 = P50 · C255

P50 = 26628696860763170757415075888614691991511099147227<50>

C255 = [222341721027911715633671961706217915116678982524266600828809108331318320649681568887402437710769278163500186590283610898584016236491957089336867945678571711723875925300701888125177904675751179148227068623232948215760382265117676642381699264210177060167843<255>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 21, 2006

By Bruce Dodson / GMP-ECM

10283+1 = 1(0)2821<284> = 11 · 1699 · 241117 · 61945573305222690279363663578823967<35> · C239

C239 = P51 · C189

P51 = 151168348012920493188164812150408056175148228488823<51>

C189 = [236981781933948043228112220789227624908212542569354344676500735171191136986262759275099377257787061318322981899812820646487731505276950534191352836827590738081581753192002166353465640625197<189>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 20, 2006

By Torbjörn Granlund / GMP-ECM

10395+1 = 1(0)3941<396> = 11 · 1423 · 9091 · 9615060929<10> · 6295632499623851<16> · 4539787279569136988691351491<28> · 24966203549341539495819194854679625225811<41> · 66443174541490579097997510158021076958392938976011506949065646573<65> · C229

C229 = P47 · P182

P47 = 36135553580039597739744803188558136917651907171<47>

P182 = 42660530392229903351072436102344244250617560023502875336329183331096805000157530395542396500243031769146588091361465456452731316179986315200680926557940585563325081869311166989363491<182>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 15, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(32·10183-23)/9 = 3(5)1823<184> = 11 · 19 · 17397387712532638583<20> · 90684212543160708737<20> · 15029772282548630768461<23> · C120

C120 = P40 · P81

P40 = 1923668077538699854190851222644599554517<40>

P81 = 372960566449273440535593005370695937455230440600272291890122994647120883283696071<81>

Number: 35553_183
N=717452335859218360167438927623765212076802428464127319102516042017826581473819680378277934646358498808266801495823202707
  ( 120 digits)
Divisors found:
 r1=1923668077538699854190851222644599554517 (pp40)
 r2=372960566449273440535593005370695937455230440600272291890122994647120883283696071 (pp81)
Version: GGNFS-0.77.1
Total time: 146.56 hours.
Scaled time: 87.35 units (timescale=0.596).
Factorization parameters were as follows:
name: 35553_183
n: 717452335859218360167438927623765212076802428464127319102516042017826581473819680378277934646358498808266801495823202707
skew: 103830.10
# norm 4.16e+16
c5: 18360
c4: 9620368916
c3: 7177488075314
c2: -81657829878091490664
c1: 1933461944338510949361607
c0: -313681924961620863382406111
# alpha -5.66
Y1: 1710720816299
Y0: -131335908490248459876552
# Murphy_E 2.70e-10
# M 481970025387192072510914688544626149162622798462491063577737582196652254614879116165880736905817348899803797752005002797
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2250000, 5190001)
Relations: rels:7895878, finalFF:708277
Initial matrix: 631562 x 708277 with sparse part having weight 69096069.
Pruned matrix : 599687 x 602908 with weight 50233403.
Polynomial selection time: 1.50 hours.
Total sieving time: 125.46 hours.
Total relation processing time: 2.04 hours.
Matrix solve time: 16.85 hours.
Time per square root: 0.70 hours.
Prototype def-par.txt line would be:
gnfs,119,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 146.56 hours.
 --------- CPU info (if available) ----------

Mar 15, 2006

By Makoto Kamada / PFGW

(14·1011279-11)/3 = 4(6)112783<11280> is PRP. This is the 26th prime or PRP of the form 466...663 including 43.

(14·1019677-11)/3 = 4(6)196763<19678> is PRP. This is the 27th prime or PRP of the form 466...663 including 43.

Primality testing (14*10^11279-11)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 167
Running N-1 test using base 193
Running N-1 test using base 223
Running N+1 test using discriminant 3, base 1+sqrt(3)
Running N+1 test using discriminant 3, base 3+sqrt(3)
Running N+1 test using discriminant 3, base 4+sqrt(3)
Calling N+1 BLS with factored part 0.04% and helper 0.01% (0.13% proof)
(14*10^11279-11)/3 is Fermat and Lucas PRP! (136.2094s+0.0010s)
Primality testing (14*10^19677-11)/3 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 139
Running N+1 test using discriminant 191, base 2+sqrt(191)
Calling N-1 BLS with factored part 0.18% and helper 0.04% (0.57% proof)
(14*10^19677-11)/3 is Fermat and Lucas PRP! (208.3531s+0.0015s)

Note:

(14·1011279-11)/3-1 = 42·R11279, 11279 is prime.
(14·1019677-11)/3-1 = 42·R19677, 19677 = 3 · 7 · 937.

Mar 12, 2006

By Yousuke Koide / GMP-ECM

10563+1 = 1(0)5621<564> = 11 · 12498601 · 579098423 · 5089082809028683211<19> · 29283791702184825961<20> · C508

C508 = P35 · P474

P35 = 36265008707438890601092610924794499<35>

P474 = 232401494054570096143564993567696213375160353588417043090684984008451459670563877848647221789116648084601933880604986363761579421580159899581971059471764334988754554032162111036734709558829222890387903668986840084368851089124293184850568488971261475110622313574444779882860262870083592445443612475383694609460996337539641013578225997858543638658915937776380907660097061600787534395165252920449980799649154737825244060326194223564696221792437925158704683354257701429283783173<474>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 9, 2006 (2nd)

By Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, Msieve v. 1.03

(86·10159+31)/9 = 9(5)1589<160> = 11 · 79 · 11174459 · 1502356653904533350741<22> · C129

C129 = P35 · P95

P35 = 32925940611028209913897631506414729<35>

P95 = 19892914848838805121187170889842741939087687000043733872145367908159923963535199308109148910261<95>

(86·10197+31)/9 = 9(5)1969<198> = 11 · 383 · 389 · 6551821 · 889779406597<12> · 16240097980183799<17> · 6326590128437676415873<22> · C135

C135 = P36 · P50 · P51

P36 = 257061712718000124573629082190241723<36>

P50 = 17202872520442432210877384770546939996230403362031<50>

P51 = 220127243508692213597620396060520447620885683353701<51>

(83·10152+61)/9 = 9(2)1519<153> = 53 · 49553849717<11> · 317701005474431<15> · C127

C127 = P34 · P47(1095...) · P47(2796...)

P34 = 3608239190673295798991471185907989<34>

P47(1095...) = 10951667146070503349365880660080570035257139853<47>

P47(2796...) = 27969723271484245196929127184512281242928180627<47>

(83·10158+61)/9 = 9(2)1579<159> = C159

C159 = P39 · C121

P39 = 117545651888135840815842818880953169751<39>

C121 = [7845651518440422046274124148055206572053296058018576850355756519442414234698093136206369834368093919414710356459458036979<121>]

(83·10165+61)/9 = 9(2)1649<166> = 11 · 53 · 15467 · 624066075792757767593189<24> · C136

C136 = P32 · P43 · P62

P32 = 77015221797071783144018776142779<32>

P43 = 1363983398260425583802572468420050762256249<43>

P62 = 15600722535588390596249739026257013695088784067038703180701031<62>

(83·10170+61)/9 = 9(2)1699<171> = 7883 · 19441 · 2000351 · 2106457109<10> · C148

C148 = P32 · P117

P32 = 10246654667775461302966534591093<32>

P117 = 139374886901991284309920528691380173177220939093427095206182914573598399192602401679574826904949867314936196243568889<117>

(83·10182+61)/9 = 9(2)1819<183> = 773 · 5849 · C177

C177 = P26 · P152

P26 = 18323924688912353458934957<26>

P152 = 11131558409804658552975136550245961802897585754926764622588590174425550785078755590086633257634460716644299002312941445512090775542751313517232875571261<152>

(83·10187+61)/9 = 9(2)1869<188> = 3 · 11 · 92051 · 30067547 · C175

C175 = P32 · C143

P32 = 84311270917687423566615482497229<32>

C143 = [11975936863183358248554497011506440623051685644174883289393187724496404341718218435134527037287517064098894745988460538796464883046662025611401<143>]

(83·10188+61)/9 = 9(2)1879<189> = 446309 · 1434847 · 11812329767321731<17> · C162

C162 = P33 · P129

P33 = 813358403948275531485764881346537<33>

P129 = 149891436995987972781929490337435011368175402050551513955225614585203280820778471440295188112515448467155816910188061801267258909<129>

Mar 9, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

3·10167-1 = 2(9)167<168> = 7 · 7643 · 5308447 · 22854213927330216399615920416772214007<38> · C119

C119 = P59 · P61

P59 = 39688758719895871031552328771144713882109670630545445702193<59>

P61 = 1164549798963657623144995222566231913164712125722393092919267<61>

Number: 29999_167
N=46219535988371850084418374386615219342097027661120626172731378243865022947240172061060017102055950948979932685073852531
  ( 119 digits)
Divisors found:
 r1=39688758719895871031552328771144713882109670630545445702193 (pp59)
 r2=1164549798963657623144995222566231913164712125722393092919267 (pp61)
Version: GGNFS-0.77.1
Total time: 127.93 hours.
Scaled time: 76.25 units (timescale=0.596).
Factorization parameters were as follows:
name: 29999_167
n: 46219535988371850084418374386615219342097027661120626172731378243865022947240172061060017102055950948979932685073852531
skew: 124276.53
# norm 6.35e+16
c5: 3780
c4: 9000258924
c3: -554045092292200
c2: -39482819237992107286
c1: 3932121986615762035288899
c0: 70617401508006264190233896568
# alpha -6.80
Y1: 977912957527
Y0: -104103375987437644398895
# Murphy_E 3.22e-10
# M 38938266427990170016457106322341826580574242911371250299063807152482269131899914371350670090841862042894144699664069961
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2250000, 4770001)
Relations: rels:7833087, finalFF:739482
Initial matrix: 632170 x 739482 with sparse part having weight 66718778.
Pruned matrix : 591810 x 595034 with weight 42684964.
Polynomial selection time: 1.71 hours.
Total sieving time: 109.90 hours.
Total relation processing time: 1.73 hours.
Matrix solve time: 13.85 hours.
Time per square root: 0.75 hours.
Prototype def-par.txt line would be:
gnfs,118,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 127.93 hours.
 --------- CPU info (if available) ----------

Mar 6, 2006 (2nd)

By Bruce Dodson / GMP-ECM

10610+1 = 1(0)6091<611> = 101 · 3541 · 6101 · 21961 · 27961 · 51241 · 1587221 · 9818561 · 81183810541<11> · 217345835281<12> · 555818110301<12> · 28474644365651641<17> · 8950221294967070861<19> · 17751033585336286181<20> · 17716886277230798340041<23> · 101444162656037151745878558385892753596849<42> · 75743388768260974116327848920184337528059461788181539337429709<62> · [24117462560776940857674798510867129035516104161041003845211930699998253738773357627145166937584558542746371549244626963892247670300659074689156318263222623146762142584127818541<176>] · C185

C185 = P50 · P136

P50 = 39069669288697789469488625615834711944836425801981<50>

P136 = [1642269048916396301246801744101379821902073519810571143520576971928815724659633161556699837755221303434764527770131486856721570324295821<136>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 6, 2006

By Yousuke Koide / GMP-ECM

10557+1 = 1(0)5561<558> = 11 · 88007 · 179268223 · 344577275324047<15> · C529

C529 = P38 · C491

P38 = 20862619931001299769258280552030071437<38>

C491 = [80155126803992958974081271951622621798563080439375689086151511748888857024774801881444988889327039297111156006793190146899843106382703618789533002233930062113834145634448902443144669556151584614671871116613397376475754027410164847877952704878442901102913032214159979400648826552464374616727772570384213045693621664436916530380113597719242206587830138898336553329158672161855285016711264338141948902686341480347249217048265971292294117681897203483787177184016190823523188622792220861985797929<491>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Mar 3, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(14·10178-41)/9 = 1(5)1771<179> = 18077 · 970583 · 1735406205257<13> · 1745824177303<13> · 390328319148709270682251559<27> · C117

C117 = P41 · P76

P41 = 82809502531065408728209262767741242648467<41>

P76 = 9053460294396930637785159619418341915179225744274958113717340351294912094247<76>

Number: 15551_178
N=749712543163762808092051180657424884788820203073702176064721437535025801283241160904783569650296980815170595794069349
  ( 117 digits)
Divisors found:
 r1=82809502531065408728209262767741242648467 (pp41)
 r2=9053460294396930637785159619418341915179225744274958113717340351294912094247 (pp76)
Version: GGNFS-0.77.1
Total time: 90.52 hours.
Scaled time: 60.19 units (timescale=0.665).
Factorization parameters were as follows:
name: 15551_178
n: 749712543163762808092051180657424884788820203073702176064721437535025801283241160904783569650296980815170595794069349
skew: 37242.91
# norm 6.09e+15
c5: 64800
c4: 6759976239
c3: -240101464909709
c2: -7631822091175545737
c1: 136429241778261841168464
c0: 1961043974935176328332864300
# alpha -5.23
Y1: 3236659220977
Y0: -25862042449072322628529
# Murphy_E 4.05e-10
# M 349385423445357336464828299975167497040480146975800760950577244763433429412923324641596525897204278449812482008715321
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2250000, 3990001)
Relations: rels:7690204, finalFF:756389
Initial matrix: 631392 x 756389 with sparse part having weight 61408642.
Pruned matrix : 578158 x 581378 with weight 35000223.
Polynomial selection time: 2.42 hours.
Total sieving time: 74.78 hours.
Total relation processing time: 1.15 hours.
Matrix solve time: 11.46 hours.
Time per square root: 0.70 hours.
Prototype def-par.txt line would be:
gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 90.52 hours.
 --------- CPU info (if available) ----------

February 2006

Feb 28, 2006

By Greg Childers

(34·1015768-43)/9 = 3(7)157673<15769> is prime!

It was proved using the CHG code of John Renze. The method of proof and the certificates are available at http://www.pa.uky.edu/~childers/certs/P15769.zip

Congratulations!

The related informations are here: Primality proof of (34*10^15768-43)/9 - need help! (Yahoo! Groups primeform)

Feb 27, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(4·10165-7)/3 = 1(3)1641<166> = 11 · 172 · 15451 · 9309257 · 118373216867<12> · 1155975658715129283281353<25> · C116

C116 = P42 · P75

P42 = 205021964377232851384274581785018821440921<42>

P75 = 103937930788557133839808815846377770465549706196596461958171966641700024737<75>

Number: 13331_165
N=21309558743574854304397255469491373814945851188552387301145377958263470546801882078579306491878134755335591684062777
  ( 116 digits)
Divisors found:
 r1=205021964377232851384274581785018821440921 (pp42)
 r2=103937930788557133839808815846377770465549706196596461958171966641700024737 (pp75)
Version: GGNFS-0.77.1
Total time: 82.16 hours.
Scaled time: 54.56 units (timescale=0.664).
Factorization parameters were as follows:
name: 13331_165
n: 21309558743574854304397255469491373814945851188552387301145377958263470546801882078579306491878134755335591684062777
skew: 74051.52
# norm 2.34e+16
c5: 15480
c4: 3522388296
c3: -263035411418048
c2: 17484999314447126873
c1: 419940854699164050454894
c0: -9021914749412741504826452520
# alpha -6.42
Y1: 232981020679
Y0: -16895086808506470960631
# Murphy_E 4.68e-10
# M 14447464806211217445904309749906213471132462194430118712249412815602202665304715034718787861457069930890043834109555
type: gnfs
rlim: 4500000
alim: 4500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.4
alambda: 2.4
qintsize: 60000
Factor base limits: 4500000/4500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [2250000, 3810001)
Relations: rels:7611728, finalFF:765966
Initial matrix: 632522 x 765966 with sparse part having weight 59940352.
Pruned matrix : 572389 x 575615 with weight 32817222.
Total sieving time: 69.56 hours.
Total relation processing time: 1.39 hours.
Matrix solve time: 10.53 hours.
Time per square root: 0.69 hours.
Prototype def-par.txt line would be:
gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000
total time: 82.16 hours.
 --------- CPU info (if available) ----------

Feb 24, 2006

By Yousuke Koide / GMP-ECM

10526+1 = 1(0)5251<527> = 101 · 5261 · 119929 · C516

C516 = P35 · C482

P35 = 13268398183394556944627542607703521<35>

C482 = [11826809890140660378338391428621739420944914204418270540548648343005259897590744879396431744264495055674553364129755077045241978687202365722448940256802260852123723223687570098653961560376654250917493622678295282473622845068332813346356170074002662358220640333931566540952269342710885379205798802761321264162169247021611517911394262594009242131813723180126329212661624008170532159618167368524165159364853029744154010198135065779112334150003021894547007767944159586907077014505010249<482>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 23, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(28·10157+17)/9 = 3(1)1563<158> = 35 · 11 · 15241 · 30689 · 20857099 · 305736526979514144882409<24> · C115

C115 = P52 · P63

P52 = 5531052712936917961623275670908807144590636709264557<52>

P63 = 705523257741806994604431331044786408191814533429843056689276487<63>

Number: 31113_157
N=3902286328772913985808676036444149479620450834825575137775166222776897795611767518523557612486876817421306202571259
  ( 115 digits)
Divisors found:
 r1=5531052712936917961623275670908807144590636709264557 (pp52)
 r2=705523257741806994604431331044786408191814533429843056689276487 (pp63)
Version: GGNFS-0.77.1
Total time: 72.69 hours.
Scaled time: 48.34 units (timescale=0.665).
Factorization parameters were as follows:
name: 31113_157
n: 3902286328772913985808676036444149479620450834825575137775166222776897795611767518523557612486876817421306202571259
skew: 111063.39
# norm 1.68e+16
c5: 4200
c4: 3846257440
c3: -55901044728118
c2: -31732745539522374884
c1: -796641630993524085413841
c0: 32181874432829360357010466365
# alpha -6.43
Y1: 1288462748353
Y0: -15617352258803599959586
# Murphy_E 4.96e-10
# M 2091860557216746714576578794995371925399048065820019879931480116988906787342221899432500462446408416880157916828661
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 3150001)
Relations: rels:7440531, finalFF:577703
Initial matrix: 499902 x 577703 with sparse part having weight 50403483.
Pruned matrix : 469571 x 472134 with weight 32720714.
Polynomial selection time: 0.50 hours.
Total sieving time: 62.31 hours.
Total relation processing time: 0.91 hours.
Matrix solve time: 8.41 hours.
Time per square root: 0.56 hours.
Prototype def-par.txt line would be:
gnfs,114,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 72.69 hours.
 --------- CPU info (if available) ----------

Feb 21, 2006

By Makoto Kamada / GGNFS-0.77.1-20050930-pentium4

(7·10151-1)/3 = 2(3)151<152> = 17 · 4794211 · C144

C144 = P62 · P83

P62 = 21673976374827387979429628274383243276327347868031316908486251<62>

P83 = 13209066428165039913538933609092428550233210679041990355672812502768300544328111909<83>

Number: 23333_151
N=286292993697574666040961059240887337977030230507454208631953796597032317092590274755426950561506653034048690773755526175623222322447946115863159
  ( 144 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=21673976374827387979429628274383243276327347868031316908486251 (pp62)
 r2=13209066428165039913538933609092428550233210679041990355672812502768300544328111909 (pp83)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 26.78 hours.
Scaled time: 16.44 units (timescale=0.614).
Factorization parameters were as follows:
n: 286292993697574666040961059240887337977030230507454208631953796597032317092590274755426950561506653034048690773755526175623222322447946115863159
m: 1000000000000000000000000000000
c5: 70
c0: -1
skew: 1
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 2100001)
Primes: RFBsize:176302, AFBsize:176833, largePrimes:5577813 encountered
Relations: rels:5534752, finalFF:516451
Max relations in full relation-set: 28
Initial matrix: 353202 x 516451 with sparse part having weight 46378725.
Pruned matrix : 284926 x 286756 with weight 24102058.
Total sieving time: 23.94 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 2.51 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 26.78 hours.
 --------- CPU info (if available) ----------

Feb 20, 2006 (2nd)

By Herman te Riele / GMP-ECM

10382+1 = 1(0)3811<383> = 101 · 77929 · 106961 · C371

C371 = P47 · C324

P47 = 13968004259021399202183274452648726337203224861<47>

C324 = [850393064402012666744482907848502515341494454491910072839871008358233226408384942430276781401143673123159329816093549352983410346709470834405150582792012803493237246693515128580540497732985722494237458711874709969154969748305639862674398403145342742584691000307403742442619500709721633892588569975004520484288234238028276889<324>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 20, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(71·10162-17)/9 = 7(8)1617<163> = 3 · 243502289 · 116444549857<12> · 128270027616314750452923569549<30> · C114

C114 = P43 · P72

P43 = 3386184936137402790776200334857258952729771<43>

P72 = 213518991010401372381688432413728927073750464555050022709806288337774787<72>

Number: 78887_162
N=723014790938678651721147391990553557307168178882364588086043927423948319684735855253124973472587538762189468083777
  ( 114 digits)
Divisors found:
 r1=3386184936137402790776200334857258952729771 (pp43)
 r2=213518991010401372381688432413728927073750464555050022709806288337774787 (pp72)
Version: GGNFS-0.77.1
Total time: 65.96 hours.
Scaled time: 39.38 units (timescale=0.597).
Factorization parameters were as follows:
name: 78887_162
n: 723014790938678651721147391990553557307168178882364588086043927423948319684735855253124973472587538762189468083777
skew: 46149.34
# norm 7.15e+15
c5: 12060
c4: -2736605976
c3: -44691865616191
c2: -3100143244501198126
c1: 20887871137226227608648
c0: 1061224024356544925135754180
# alpha -5.93
Y1: 762409635149
Y0: -9027378239651588136263
# Murphy_E 5.82e-10
# M 605779985268998323829240402100043274437028440935658503297164474505831869806567549361974091435657964544874132311457
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2950001)
Relations: rels:7527514, finalFF:620031
Initial matrix: 501181 x 620031 with sparse part having weight 52823587.
Pruned matrix : 455494 x 458063 with weight 28473787.
Total sieving time: 57.75 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 6.99 hours.
Time per square root: 0.60 hours.
Prototype def-par.txt line would be:
gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 65.96 hours.
 --------- CPU info (if available) ----------

Feb 18, 2006

By Wataru Sakai / GMP-ECM 6.0.1 B1=11000000

(86·10156+31)/9 = 9(5)1559<157> = 13 · 487 · 53117 · 33675667 · 16469890637<11> · C131

C131 = P35 · P97

P35 = 45896092494621654893425012753765729<35>

P97 = 1116265380604458192056463779508427484700133652377805812712655330066850140540194073278282658605887<97>

(86·10172+31)/9 = 9(5)1719<173> = 32 · 23 · 59 · 79 · 1791454139<10> · 398614507270289<15> · C144

C144 = P34 · P111

P34 = 1342363415950343403713077647628357<34>

P111 = 103318380622337348816390846078358788840032723949972204188865763768829298668657709947217898275209152529423007011<111>

(86·10175+31)/9 = 9(5)1749<176> = 3 · 11 · 2849423 · C169

C169 = P36 · C133

P36 = 662096372245323070905807054281026159<36>

C133 = [1534842682831474675191613986513705075285853096908253230732277917454586669752032261197652469052432398524331417918409196804434169528839<133>]

(86·10184+31)/9 = 9(5)1839<185> = 3 · 349 · 13883077929495122457509792250269<32> · C151

C151 = P40 · P112

P40 = 3240633863300248064298285243088031837323<40>

P112 = 2028586508296212038657801271877882169058285697615801859876284958434006470077093431789681527730924938652681378831<112>

(86·10193+31)/9 = 9(5)1929<194> = 3 · 11 · 2699 · 46103930161<11> · 8491960607515969<16> · C163

C163 = P33 · C131

P33 = 193493468565567926104105693906747<33>

C131 = [14162074932095004056081428092843431186530927733017519258696552135554878856011970657843644107064766187698663624963481176743381279999<131>]

Feb 17, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(61·10153-7)/9 = 6(7)153<154> = 3 · 251 · 67901 · 16902449019944461<17> · 104893886986106263<18> · C113

C113 = P36

P36 = 517325769482943481148002669266260899<36>

P78 = 144528086508799010588986000906479628320347052391513546996479503285853448618037<78>

Number: 67777_153
N=74768103565061870641605399739627354138013930489466959869231758097217372256549377910964390885085630752041839235263
  ( 113 digits)
Divisors found:
 r1=517325769482943481148002669266260899 (pp36)
 r2=144528086508799010588986000906479628320347052391513546996479503285853448618037 (pp78)
Version: GGNFS-0.77.1
Total time: 61.92 hours.
Scaled time: 36.84 units (timescale=0.595).
Factorization parameters were as follows:
name: 67777_153
n: 74768103565061870641605399739627354138013930489466959869231758097217372256549377910964390885085630752041839235263
skew: 55526.94
# norm 8.28e+15
c5: 12120
c4: -3386768743
c3: -88626093878374
c2: 243661300839375176
c1: 105379193533510512818766
c0: 1364060466056181859258457439
# alpha -5.81
Y1: 950254522657
Y0: -5728577268569493660032
# Murphy_E 6.06e-10
# M 16703589613663589708930353481129128065019775689439043582974894461469132433722410551782136824363891658249732324655
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2950001)
Relations: rels:7552137, finalFF:638676
Initial matrix: 500743 x 638676 with sparse part having weight 56983765.
Pruned matrix : 448464 x 451031 with weight 28731156.
Polynomial selection time: 0.51 hours.
Total sieving time: 53.34 hours.
Total relation processing time: 0.95 hours.
Matrix solve time: 6.62 hours.
Time per square root: 0.52 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 61.92 hours.
 --------- CPU info (if available) ----------

Feb 14, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(71·10160-17)/9 = 7(8)1597<161> = 89 · 3491 · 78791 · 163337 · 494927 · 20992251737<11> · 25597988189016413<17> · C113

C113 = P53 · P61

P53 = 11466231815762675161044743195594232084784560019479973<53>

P61 = 6469758533064433639393094558069579940474812145379136995723789<61>

Number: 78887_160
N=74183751132125462572090856533831080834569538057811826337065936337992030749034836183025904719268995337840525177697
  ( 113 digits)
Divisors found:
 r1=11466231815762675161044743195594232084784560019479973 (pp53)
 r2=6469758533064433639393094558069579940474812145379136995723789 (pp61)
Version: GGNFS-0.77.1
Total time: 53.10 hours.
Scaled time: 31.65 units (timescale=0.596).
Factorization parameters were as follows:
name: 78887_160
n: 74183751132125462572090856533831080834569538057811826337065936337992030749034836183025904719268995337840525177697
skew: 38798.92
# norm 5.62e+15
c5: 39840
c4: -3837797312
c3: -158075269926546
c2: 997159671338664115
c1: 26196821511285852635928
c0: 601719853765070500366044775
# alpha -6.41
Y1: 475417808587
Y0: -4508154323163695216034
# Murphy_E 7.04e-10
# M 29623494024761047815194465994502172767121530326872775601150064441321500367062841145203088741769412509398727691366
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2750001)
Relations: rels:7649183, finalFF:703646
Initial matrix: 500694 x 703646 with sparse part having weight 60474912.
Pruned matrix : 420736 x 423303 with weight 24158497.
Polynomial selection time: 0.56 hours.
Total sieving time: 45.88 hours.
Total relation processing time: 0.66 hours.
Matrix solve time: 5.49 hours.
Time per square root: 0.51 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 53.10 hours.
 --------- CPU info (if available) ----------

Feb 14, 2006

By Maksym Voznyy / GGNFS-0.77.1-20050930-pentium4

(7·10159-43)/9 = (7)1583<159> = 2198881 · 107554406636101703<18> · 108269558050928644841579<24> · C113

C113 = P54 · P59

P54 = 508913280753558081579008581881689241407143447291728103<54>

P59 = 59686408469391464479233088678668511871451520317771224765303<59>

Number: c113
N=30375205950554965254665724980216207052946917800227062425483231705034695663566872449662848892149586008209464410209
  ( 113 digits)
SNFS difficulty: 160 digits.
Divisors found:
 r1=508913280753558081579008581881689241407143447291728103 (pp54)
 r2=59686408469391464479233088678668511871451520317771224765303 (pp59)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: -568.07 hours.
Scaled time: -263.02 units (timescale=0.463).
Factorization parameters were as follows:
n: 30375205950554965254665724980216207052946917800227062425483231705034695663566872449662848892149586008209464410209
m: 100000000000000000000000000000000
c5: 7
c0: -430
skew: 2.5
type: snfs
qintsize: 10000
Factor base limits: 4000000/4000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [2000000, 3790001)
Primes: RFBsize:283146, AFBsize:283047, largePrimes:5637721 encountered
Relations: rels:5645068, finalFF:636944
Max relations in full relation-set: 28
Initial matrix: 566258 x 636944 with sparse part having weight 41222443.
Pruned matrix : 513332 x 516227 with weight 29866484.
Total sieving time: 64.60 hours.
Total relation processing time: -645.06 hours.
Matrix solve time: 12.25 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000
total time: -568.07 hours.
 --------- CPU info (if available) ----------

Feb 12, 2006

By Patrick Keller / GMP-ECM B1=1000000

(85·10186+41)/9 = 9(4)1859<187> = 72 · 73 · 2963 · 13879 · 15569 · 249311 · C167

C167 = P38 · C130

P38 = 13535091039564671486279847232684736987<38>

C130 = [1222093145661488304689087334206869992908799364801631751346153045069664958899170583005647688332917002870930209205870065660169052657<130>]

Feb 11, 2006

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

(37·10168-1)/9 = 4(1)168<169> = 681773 · 358640627 · 925410356462034774743<21> · 2027784404324172549427<22> · C112

C112 = P56 · P57

P56 = 61132896250125153035803780936000573049046898692303340201<56>

P57 = 146564511853610321058927580714084417649617753103996081381<57>

Number: 41111_168
N=8959913097096997938824188495967634805981158290247231678875205600280440323115153722167798653658628998881324897581
  ( 112 digits)
Divisors found:
 r1=61132896250125153035803780936000573049046898692303340201 (pp56)
 r2=146564511853610321058927580714084417649617753103996081381 (pp57)
Version: GGNFS-0.77.1
Total time: 49.32 hours.
Scaled time: 32.79 units (timescale=0.665).
Factorization parameters were as follows:
name: 41111_168
n: 8959913097096997938824188495967634805981158290247231678875205600280440323115153722167798653658628998881324897581
skew: 40427.59
# norm 2.40e+15
c5: 26100
c4: 2196431592
c3: -127573556116769
c2: -3240983120379717400
c1: 93050782877412745697718
c0: 784802897791216925783383232
# alpha -5.73
Y1: 331254086647
Y0: -3214636746423654432877
# Murphy_E 7.34e-10
# M 6577919040614998762593170428792988826678863704808659218722799705188626767732335579311257019642666960033159299411
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2650001)
Relations: rels:7281400, finalFF:599694
Initial matrix: 500888 x 599694 with sparse part having weight 47516870.
Pruned matrix : 457312 x 459880 with weight 26788343.
Polynomial selection time: 0.51 hours.
Total sieving time: 41.75 hours.
Total relation processing time: 0.62 hours.
Matrix solve time: 5.95 hours.
Time per square root: 0.49 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 49.32 hours.
 --------- CPU info (if available) ----------

Feb 10, 2006 (2nd)

By Patrick Keller / GGNFS-0.77.1-20050930-pentium4 gnfs

(10187+53)/9 = (1)1867<187> = 7 · 71 · 197 · 4523 · 90019 · 131374937 · 44730961183<11> · 764090474173501457<18> · 1003033405098351401377991<25> · C112

C112 = P38 · P75

P38 = 16462583911544611673142425725427372749<38>

P75 = 375919771891371586331252948799948552812814320677059444957657343601244135613<75>

Number: 2
N=6188610788770414212796511211495988489540391349491968058312867831046678507555599713712584325000581110482056610137
  ( 112 digits)
Divisors found:
 r1=16462583911544611673142425725427372749 (pp38)
 r2=375919771891371586331252948799948552812814320677059444957657343601244135613 (pp75)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 27.41 hours.
Scaled time: 18.26 units (timescale=%1.3lf).
Factorization parameters were as follows:
name: 2
n: 6188610788770414212796511211495988489540391349491968058312867831046678507555599713712584325000581110482056610137
skew: 21795.31
# norm 8.31e+014
c5: 38880
c4: -120636723
c3: -5646870886264
c2: -84505874040617561
c1: -12229642424486779772215
c0: -10006425163572188338251900
# alpha -5.32
Y1: 1030176524267
Y0: -2756598296849159231369
# Murphy_E 7.71e-010
# M 3327217392231341839193020182372575084355003187604176097066870872073360700330416454572036356484618763494826886338
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 200000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2750001)
Relations: rels:7750950, finalFF:745908
Initial matrix: 500763 x 745908 with sparse part having weight 63844677.
Pruned matrix : 405254 x 407821 with weight 22768815.
Polynomial selection time: 0.52 hours.
Total sieving time: 22.26 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 4.08 hours.
Time per square root: 0.23 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,200000
total time: 27.41 hours.
 --------- CPU info (if available) ----------

Feb 10, 2006

By Maksym Voznyy / GGNFS-0.77.1-20050930-pentium4

(46·10151-1)/9 = 5(1)151<152> = 3 · 100613 · 11252677 · 17561028246989<14> · 254884347047509<15> · C112

C112 = P36 · P77

P36 = 163142891746432375615001387087556691<36>

P77 = 20607383487557504808781535006630386430436651273368978693125608058034215922407<77>

Number: c112
N=3361948133487812075077922500985184449851754373875089188887233786612314488240147798191074701287201289454469675237
  ( 112 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=163142891746432375615001387087556691 (pp36)
 r2=20607383487557504808781535006630386430436651273368978693125608058034215922407 (pp77)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 40.64 hours.
Scaled time: 19.02 units (timescale=0.468).
Factorization parameters were as follows:
n: 3361948133487812075077922500985184449851754373875089188887233786612314488240147798191074701287201289454469675237
m: 1000000000000000000000000000000
c5: 460
c0: -1
skew: 0.4
type: snfs
qintsize: 20000
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1200000, 1960001)
Primes: RFBsize:176302, AFBsize:176118, largePrimes:5294119 encountered
Relations: rels:5123433, finalFF:422966
Max relations in full relation-set: 28
Initial matrix: 352487 x 422966 with sparse part having weight 34954044.
Pruned matrix : 312226 x 314052 with weight 22744841.
Total sieving time: 31.87 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 8.25 hours.
Time per square root: 0.10 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 40.64 hours.
 --------- CPU info (if available) ----------

Feb 9, 2006 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1 gnfs

8·10158-3 = 7(9)1577<159> = 47 · 73 · 163 · 7715837 · 5875170743947<13> · 18583538108533323516211<23> · C112

C112 = P30 · P82

P30 = 288901606894446877454247126479<30>

P82 = 5877596490240672347764431371309125446211638140185245222440610912673511074017720739<82>

Number: 79997_158
N=1698047070707691395420746408981023416719231061576173416181875824650185270803056769051905000529016826215834347981
  ( 112 digits)
Divisors found:
 r1=288901606894446877454247126479 (pp30)
 r2=5877596490240672347764431371309125446211638140185245222440610912673511074017720739 (pp82)
Version: GGNFS-0.77.1
Total time: 49.27 hours.
Scaled time: 32.76 units (timescale=0.665).
Factorization parameters were as follows:
name: 79997_158
n: 1698047070707691395420746408981023416719231061576173416181875824650185270803056769051905000529016826215834347981
skew: 34286.38
# norm 4.83e+15
c5: 9000
c4: -4462864515
c3: -64241300805211
c2: 1453846801432205282
c1: -26683572554404993280571
c0: 263662311370362904945670067
# alpha -6.21
Y1: 359421792191
Y0: -2851982598484250583104
# Murphy_E 7.76e-10
# M 1118129559379046546854714597668784376529084592686110336061756095364521516843937336546128904918463162740256522637
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2650001)
Relations: rels:7253879, finalFF:587691
Initial matrix: 500957 x 587691 with sparse part having weight 45582024.
Pruned matrix : 461255 x 463823 with weight 27086263.
Polynomial selection time: 0.50 hours.
Total sieving time: 41.11 hours.
Total relation processing time: 0.75 hours.
Matrix solve time: 6.45 hours.
Time per square root: 0.45 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 49.27 hours.
 --------- CPU info (if available) ----------

Feb 9, 2006 (2nd)

By Patrick Keller / GGNFS-0.77.1-20050930-pentium4 gnfs

(79·10165-7)/9 = 8(7)165<166> = 181787 · 6947861 · 471250250494729967<18> · 146631661811942550414576793<27> · C111

C111 = P33 · P78

P33 = 505183798145073606671326082895157<33>

P78 = 199086528382066627439016425618280593244587507522519767719428521573572672432733<78>

Number: 2
N=100575288567569414650753061908992433831162812137784021232130567965686212874475190732266862757968646178973974081
  ( 111 digits)
Divisors found:
 r1=505183798145073606671326082895157 (pp33)
 r2=199086528382066627439016425618280593244587507522519767719428521573572672432733 (pp78)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 25.27 hours.
Scaled time: 16.88 units (timescale=%1.3lf).
Factorization parameters were as follows:
name: 2
n: 100575288567569414650753061908992433831162812137784021232130567965686212874475190732266862757968646178973974081
skew: 41634.78
# norm 4.86e+015
c5: 14160
c4: 2304193002
c3: -83720342315739
c2: 1686585772450806812
c1: 45998111723386131551140
c0: -776680905380863451921695600
# alpha -6.55
Y1: 767339486963
Y0: -1480056448132856254239
# Murphy_E 9.24e-010
# M 1117747378090499295948109067179419719161638564223783773069029778808966385056414571852861383687546909976534536
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1600000, 2350001)
Relations: rels:7212017, finalFF:564444
Initial matrix: 459888 x 564444 with sparse part having weight 45344626.
Pruned matrix : 415592 x 417955 with weight 24057004.
Total sieving time: 20.47 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 4.22 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 25.27 hours.
 --------- CPU info (if available) ----------

Feb 9, 2006

By Patrick Keller / GGNFS-0.77.1-20050930-pentium4 gnfs

(5·10167+13)/9 = (5)1667<167> = 32 · 4027 · 10463 · 12941 · 44897457148379489<17> · 1519650041086432620438421693<28> · C111

C111 = P37 · P75

P37 = 1001555099341379538477781614644711869<37>

P75 = 165668185679698740547711081846511427600993641940174707427260998637343088981<75>

Number: 2
N=165925816166136783147225072078845728669837032683683114399003933918276111210507446722985872485375711425173815489
  ( 111 digits)
Divisors found:
 r1=1001555099341379538477781614644711869 (pp37)
 r2=165668185679698740547711081846511427600993641940174707427260998637343088981 (pp75)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 26.12 hours.
Scaled time: 17.27 units (timescale=%1.3lf).
Factorization parameters were as follows:
name: 2
n: 165925816166136783147225072078845728669837032683683114399003933918276111210507446722985872485375711425173815489
skew: 39402.35
# norm 2.87e+015
c5: 2760
c4: -1796268948
c3: -3542165988808
c2: -153924170064893167
c1: -1523943674560155151998
c0: -77864042459289411013639504
# alpha -5.39
Y1: 325574065619
Y0: -2268867260185188064005
# Murphy_E 7.81e-010
# M 68795449822125752170511759654875711714200059898916396981004545201485519359004288023996397211130284425818863789
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1600000, 2500001)
Relations: rels:7293097, finalFF:562048
Initial matrix: 461329 x 562048 with sparse part having weight 47664987.
Pruned matrix : 421158 x 423528 with weight 26372876.
Total sieving time: 20.36 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 5.19 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,200000
total time: 26.12 hours.
 --------- CPU info (if available) ----------

Feb 7, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1

(83·10151+61)/9 = 9(2)1509<152> = 3 · 11 · 17 · 733 · 40329493663<11> · C136

C136 = P58 · P79

P58 = 4266817943380179456442463705074607914097928139686406991771<58>

P79 = 1303292406197656724391669573637441907482304621617005899880147521482913023505621<79>

Number: 92229_151
N=5560911424235291114762797245319179861381456751514177216307994652416449166451578809099682022150998090569967412440150646011850523319244791
  ( 136 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=4266817943380179456442463705074607914097928139686406991771 (pp58)
 r2=1303292406197656724391669573637441907482304621617005899880147521482913023505621 (pp79)
Version: GGNFS-0.77.1
Total time: 51.11 hours.
Scaled time: 30.46 units (timescale=0.596).
Factorization parameters were as follows:
name: 92229_151
n: 5560911424235291114762797245319179861381456751514177216307994652416449166451578809099682022150998090569967412440150646011850523319244791
m: 1000000000000000000000000000000
c5: 830
c0: 61
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2500001)
Relations: rels:5525717, finalFF:420091
Initial matrix: 352078 x 420091 with sparse part having weight 41285447.
Pruned matrix : 342863 x 344687 with weight 26911075.
Total sieving time: 45.82 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 4.78 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 51.11 hours.
 --------- CPU info (if available) ----------

Feb 7, 2006

By Patrick Keller / GGNFS-0.77.1-20050930-pentium4 gnfs

(85·10174+41)/9 = 9(4)1739<175> = 7 · 2017 · 11063449 · 13431161 · 862560884921<12> · 617545692656011875106207177777<30> · C115

C115 = P45 · P70

P45 = 950310447883283935373995072876758274438818959<45>

P70 = 8892912596211804531600808855278331945835416961840108159359737857615713<70>

Feb 5, 2006 (4th)

By Yousuke Koide / GMP-ECM B1=48e6, GGNFS-0.77.1 gnfs

10465+1 = 1(0)4641<466> = 7 · 11 · 13 · 211 · 241 · 373 · 2161 · 9091 · 11161 · 44641 · 3590254957<10> · 3925963357681<13> · 5167617497664851<16> · 22672589441232691<17> · 909090909090909090909090909091<30> · 6548241632713397411808073416931<31> · 553114664478262993662992814601370587114291<42> · 18381907262281244633158190677786966663091011<44> · 4857900688365130469291831549890842547443917376935406225054646143856579892970236911030721<88> · C152

C152 = P46 · P49 · P58

P46 = 3093888678771257769541252942946202755752229401<46>

P49 = 1158334526259936604206939942487445760921582415411<49>

P58 = 3092189186638711651761630213691413266133197806226014052371<58>

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Feb 5, 2006 (3rd)

By Sinkiti Sibata / GGNFS-0.77.1

(8·10152-71)/9 = (8)1511<152> = 3 · 43 · 1853927 · 4204279 · 7297846909<10> · 54055784093<11> · C117

C117 = P50 · P67

P50 =41852930861153999543319597376037498948438646374273<50>

P67 = 5354400016690058007150197629839830971822257922958622091177046313833<67>

Number: 88881_152
N=224097333701490818996657378545506420449477157334788271342455411233177004466153550173305245966022827936168245135218409
  ( 117 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=41852930861153999543319597376037498948438646374273 (pp50)
 r2=5354400016690058007150197629839830971822257922958622091177046313833 (pp67)
Version: GGNFS-0.77.1
Total time: 47.04 hours.
Scaled time: 28.04 units (timescale=0.596).
Factorization parameters were as follows:
name: 88881_152
n: 224097333701490818996657378545506420449477157334788271342455411233177004466153550173305245966022827936168245135218409
m: 1000000000000000000000000000000
c5: 800
c0: -71
skew: 2
type: snfs
 
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2400001)
Relations: rels:5420617, finalFF:427342
Initial matrix: 352737 x 427342 with sparse part having weight 39372434.
Pruned matrix : 342345 x 344172 with weight 24241100.
Total sieving time: 41.88 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 4.69 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 47.04 hours.
 --------- CPU info (if available) ----------

Feb 5, 2006 (2nd)

By Patrick Keller / GMP-ECM B1=1000000, Msieve v. 1.03

(29·10184+7)/9 = 3(2)1833<185> = 3 · 1609 · 141209 · 51361763 · 40099719731363732494892431187567<32> · C137

C137 = P38 · P44 · P55

P38 = 92263672187280138504843095427211568801<38>

P44 = 37954749951041472756030401435183280403544987<44>

P55 = 6554471536158162812921217408651094733184278319197338043<55>

Sat Feb 04 12:56:59 2006  
Sat Feb 04 12:56:59 2006  
Sat Feb 04 12:56:59 2006  Msieve v. 1.03
Sat Feb 04 12:56:59 2006  random seeds: ea6ba580 6866eb26
Sat Feb 04 12:56:59 2006  factoring 248773328216101756750898896613176208821881925232865782829696275230827569801647842746392670997040441 (99 digits)
Sat Feb 04 12:57:01 2006  using multiplier of 1
Sat Feb 04 12:57:01 2006  sieve interval: 9 blocks of size 65536
Sat Feb 04 12:57:01 2006  processing polynomials in batches of 6
Sat Feb 04 12:57:01 2006  using a sieve bound of 2577437 (94049 primes)
Sat Feb 04 12:57:01 2006  using large prime bound of 386615550 (28 bits)
Sat Feb 04 12:57:01 2006  using double large prime bound of 2864855634283950 (43-52 bits)
Sat Feb 04 12:57:01 2006  using trial factoring cutoff of 56 bits
Sat Feb 04 12:57:01 2006  polynomial 'A' values have 13 factors
Sat Feb 04 21:41:54 2006  56404 relations (17959 full + 38445 combined from 1160498 partial), need 94145
Sat Feb 04 21:41:55 2006  elapsed time 08:44:56
Sat Feb 04 22:05:29 2006  
Sat Feb 04 22:05:29 2006  
Sat Feb 04 22:05:29 2006  Msieve v. 1.03
Sat Feb 04 22:05:29 2006  random seeds: d6651c40 32698dee
Sat Feb 04 22:05:29 2006  factoring 248773328216101756750898896613176208821881925232865782829696275230827569801647842746392670997040441 (99 digits)
Sat Feb 04 22:05:30 2006  using multiplier of 1
Sat Feb 04 22:05:30 2006  sieve interval: 9 blocks of size 65536
Sat Feb 04 22:05:30 2006  processing polynomials in batches of 6
Sat Feb 04 22:05:30 2006  using a sieve bound of 2577437 (94049 primes)
Sat Feb 04 22:05:30 2006  using large prime bound of 386615550 (28 bits)
Sat Feb 04 22:05:30 2006  using double large prime bound of 2864855634283950 (43-52 bits)
Sat Feb 04 22:05:30 2006  using trial factoring cutoff of 56 bits
Sat Feb 04 22:05:30 2006  polynomial 'A' values have 13 factors
Sat Feb 04 22:05:44 2006  restarting with 17959 full and 1160498 partial relations
Sun Feb 05 00:06:02 2006  94364 relations (21827 full + 72537 combined from 1416464 partial), need 94145
Sun Feb 05 00:06:19 2006  begin with 1416464 relations
Sun Feb 05 00:06:20 2006  reduce to 227453 relations in 12 passes
Sun Feb 05 00:06:20 2006  attempting to read 21827 full and 227453 partial relations
Sun Feb 05 00:06:35 2006  recovered 21827 full and 227453 partial relations
Sun Feb 05 00:06:35 2006  recovered 240062 polynomials
Sun Feb 05 00:06:35 2006  attempting to build 72537 cycles
Sun Feb 05 00:06:35 2006  found 72537 cycles in 6 passes
Sun Feb 05 00:06:36 2006  distribution of cycle lengths:
Sun Feb 05 00:06:36 2006     length 2 : 16159
Sun Feb 05 00:06:36 2006     length 3 : 15890
Sun Feb 05 00:06:36 2006     length 4 : 12995
Sun Feb 05 00:06:36 2006     length 5 : 9994
Sun Feb 05 00:06:36 2006     length 6 : 6811
Sun Feb 05 00:06:36 2006     length 7 : 4521
Sun Feb 05 00:06:36 2006     length 8 : 2736
Sun Feb 05 00:06:36 2006     length 9+: 3431
Sun Feb 05 00:06:36 2006  largest cycle: 22 relations
Sun Feb 05 00:06:37 2006  94049 x 94113 system, weight 6254417 (avg 66.46/col)
Sun Feb 05 00:06:37 2006  reduce to 92804 x 92868 in 3 passes
Sun Feb 05 00:10:09 2006  lanczos halted after 1470 iterations
Sun Feb 05 00:10:09 2006  recovered 61 nontrivial dependencies
Sun Feb 05 00:11:12 2006  prp44 factor: 37954749951041472756030401435183280403544987
Sun Feb 05 00:11:12 2006  prp55 factor: 6554471536158162812921217408651094733184278319197338043
Sun Feb 05 00:11:13 2006  elapsed time 02:05:44

Feb 5, 2006

By Maksym Voznyy / GGNFS-0.77.1-20050930-pentium4 gnfs

(86·10190+31)/9 = 9(5)1899<191> = 32 · 67 · 5471 · 611551 · 73815411636669551483<20> · 3170631581865285261257<22> · 6091316752293331060196299481596117<34> · C104

C104 = P33 · P71

P33 = 457211761022060630937323603497523<33>

P71 = 72663753848976855418724955088071884465133486342364370534508053286036233<71>

Number: c104
N=33222722859764244370420434977799235487750656254904937398689327484258018049044115562830311699136103750859
  ( 104 digits)
Divisors found:
 r1=457211761022060630937323603497523 (pp33)
 r2=72663753848976855418724955088071884465133486342364370534508053286036233 (pp71)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 16.86 hours.
Scaled time: 7.82 units (timescale=0.464).
Factorization parameters were as follows:
name: c104
n: 33222722859764244370420434977799235487750656254904937398689327484258018049044115562830311699136103750859
skew: 27227.55
# norm 1.38e+014
c5: 1200
c4: -337183344
c3: -2381651633066
c2: 248938736692896209
c1: 1114387600843598108660
c0: -8590490841004470211810724
# alpha -5.80
Y1: 4931580409
Y0: -122589077603127855687
# Murphy_E 2.20e-009
# M 18111450033633959611018991800622801867540539784088860242535444057580236296942281954789823965040069650824
type: gnfs
rlim: 2300000
alim: 2300000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 10000
Factor base limits: 2300000/2300000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1150000, 1880001)
Primes: RFBsize:169511, AFBsize:169766, largePrimes:4290847 encountered
Relations: rels:4240040, finalFF:381754
Max relations in full relation-set: 28
Initial matrix: 339352 x 381754 with sparse part having weight 25810384.
Pruned matrix : 304178 x 305938 with weight 16837141.
Total sieving time: 13.97 hours.
Total relation processing time: 0.26 hours.
Matrix solve time: 2.44 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000
total time: 16.86 hours.
 --------- CPU info (if available) ----------

Feb 4, 2006 (2nd)

By Patrick Keller / GMP-ECM B1=1000000

(35·10173-53)/9 = 3(8)1723<174> = 11 · 19 · C172

C172 = P36 · C137

P36 = 106607187862536784442950213557216101<36>

C137 = [17453911169924557576039346133779902931162217477346570291829558559498426489621005591757758283994513516027454699330159557616319274222151687<137>]

(35·10194-53)/9 = 3(8)1933<195> = 61 · 617 · 7789 · 2163952582499<13> · 2326287941625511<16> · C159

C159 = P34 · P125

P34 = 6746993270905212529064277315866309<34>

P125 = 39057761165108223751807608888821277864278277187051226632566244066718880660497494906726063888182641266851221458785471976443931<125>

Feb 4, 2006

By Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, msieve 0.87

(86·10160+31)/9 = 9(5)1599<161> = 3 · 53 · 1613 · 3079 · 459013 · C147

C147 = P32 · P116

P32 = 14670887812170112648165750204273<32>

P116 = 17969391859802737625411698238094111071046415301119204415487275818924623166672293418294215899020175769928316811952687<116>

(86·10161+31)/9 = 9(5)1609<162> = 11 · 89 · 6781 · 10463 · 219000841 · 8485143186446374631<19> · C124

C124 = P35 · P44 · P47

P35 = 11172612558877304373318878010640487<35>

P44 = 11130475485219139561224467027642134977104237<44>

P47 = 59531916804317723800843666035300551575340273843<47>

(86·10165+31)/9 = 9(5)1649<166> = 11 · 198206262227<12> · 282920348903<12> · 56062580707273403<17> · C126

C126 = P33 · P93

P33 = 377200546525010742136261811904529<33>

P93 = 732548361104222114744378742455560736263367357613585076402263537276085872187790224738590321427<93>

(86·10185+31)/9 = 9(5)1849<186> = 11 · 79 · 109 · 89785291 · 1340814637898597<16> · C158

C158 = P30 · C129

P30 = 106445252032344079296136072207<30>

C129 = [787244138386490929876920510164611857119065256566549011183789719145870310160312863127858597915954078318413882086128479743889883711<129>]

(86·10190+31)/9 = 9(5)1899<191> = 32 · 67 · 5471 · 611551 · 73815411636669551483<20> · 3170631581865285261257<22> · C138

C138 = P34 · C104

P34 = 6091316752293331060196299481596117<34>

C104 = [33222722859764244370420434977799235487750656254904937398689327484258018049044115562830311699136103750859<104>]

(86·10199+31)/9 = 9(5)1989<200> = 32 · 11 · 53 · 541 · 89137 · 76090631637580657<17> · C172

C172 = P43 · P130

P43 = 4579335276299329109975930690686129256408537<43>

P130 = 1083817023802321703870503348039561161116538975431193722884499511083415580850112440288729259296754840574728575471510509230597499349<130>

Feb 3, 2006 (2nd)

By Patrick Keller / GMP-ECM B1=1000000

(29·10159+7)/9 = 3(2)1583<160> = 112 · C158

C158 = P33 · P125

P33 = 372612991204438824699686544369853<33>

P125 = 71468081761631228566085263364605922699893745503722687075347744609858409705036759488616306116194486173125016207819151185682771<125>

Feb 3, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(2·10153+43)/9 = (2)1527<153> = 233 · 705525417997694941<18> · C133

C133 = P62 · P71

P62 = 96031666888365515991851317657490644554037610309664332640312809<62>

P71 = 14076815976438800641016953391829954431437624223094892290351236824633151<71>

Number: 22227_153
N=1351820102698192661030117440553977431729482875555439502902724093183979899791774244560611952035579693882883059470179897275225311331159
  ( 133 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=96031666888365515991851317657490644554037610309664332640312809 (pp62)
 r2=14076815976438800641016953391829954431437624223094892290351236824633151 (pp71)
Version: GGNFS-0.77.1
Total time: 61.83 hours.
Scaled time: 36.91 units (timescale=0.597).
Factorization parameters were as follows:
name: 22227_153
n: 1351820102698192661030117440553977431729482875555439502902724093183979899791774244560611952035579693882883059470179897275225311331159
m: 10000000000000000000000000000000
c5: 1
c0: 2150
skew: 1
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1500000, 3000001)
Relations: rels:5698313, finalFF:582672
Initial matrix: 434096 x 582672 with sparse part having weight 46776643.
Pruned matrix : 402398 x 404632 with weight 22177700.
Total sieving time: 56.12 hours.
Total relation processing time: 0.51 hours.
Matrix solve time: 5.00 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 61.83 hours.
 --------- CPU info (if available) ----------

Feb 2, 2006 (3rd)

By Patrick Keller / GMP-ECM B1=1000000, GGNFS-0.77.1-20050930-pentium4 gnfs

(85·10168+41)/9 = 9(4)1679<169> = 7 · C169

C169 = P35 · C134

P35 = 30130007026272762236778552242458213<35>

C134 = [44779490028988984693345170298727232692672656093119287564674642677206820719270872412399590798774417897156369411429035099199813230155339<134>]

(85·10157+41)/9 = 9(4)1569<158> = 3 · 11 · 59 · 1450887150073<13> · C143

C143 = P29 · P114

P29 = 34449651002043481561963796153<29>

P114 = 970492098520818280676751308577374007361564345427698728787511704586443471464476736368328800135769189312717343166243<114>

(85·10164+41)/9 = 9(4)1639<165> = 13 · 9275757052376397976700267<25> · C139

C139 = P32 · P53 · P56

P32 = 26101001656469946963507262643981<32>

P53 = 14014284289662546774664694573536712383889671549051637<53>

P56 = 21411919469099025577565743587014582313214956323407880927<56>

Number: 1
N=300072726627314093320520489979175841355383288041487938215482381207181324448972896973431534123803458670427499
  ( 108 digits)
Divisors found:
 r1=14014284289662546774664694573536712383889671549051637 (pp53)
 r2=21411919469099025577565743587014582313214956323407880927 (pp56)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 14.13 hours.
Scaled time: 9.34 units (timescale=%1.3lf).
Factorization parameters were as follows:
name: 1
n: 300072726627314093320520489979175841355383288041487938215482381207181324448972896973431534123803458670427499
skew: 14413.92
# norm 2.07e+015
c5: 68040
c4: -5486491074
c3: -107839267366391
c2: 814095232497087056
c1: 297733551779803293509
c0: 3472766926728906384353725
# alpha -6.26
Y1: 281101122991
Y0: -337985656024213877229
# Murphy_E 1.25e-009
# M 240851906692879690151436063888151202315772228258486233467638719578063636840097221853916840815252756913542175
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Sieved special-q in [1250000, 2600001)
Relations: rels:4653173, finalFF:470989
Initial matrix: 365488 x 470989 with sparse part having weight 38723282.
Pruned matrix : 330933 x 332824 with weight 19140939.
Total sieving time: 11.34 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 2.40 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 14.13 hours.
 --------- CPU info (if available) ----------

Feb 2, 2006 (2nd)

By Patrick Keller / GMP-ECM B1=1000000

(85·10163+41)/9 = 9(4)1629<164> = 32 · 11 · 31 · 157 · C159

C159 = P32 · P128

P32 = 13105568177894521477105321529233<32>

P128 = 14956294955922037005060865998514952333966593107588242623067398373503949070814552736812565807968312337312378522414968886212851241<128>

Feb 2, 2006

By Makoto Kamada / GGNFS-0.77.1-20050930-pentium4

(10154-7)/3 = (3)1531<154> = 210030505454134151<18> · 2949482315206615051<19> · C118

C118 = P39 · P79

P39 = 988766704612729363725673840229579328631<39>

P79 = 5441977445653925374118919046362314202378090727425848505434921132007141558367001<79>

Number: 33331_154
N=5380846105516030294514527973878351422932507055981674764039604926065238659321190766317777113182762829421115190284905631
  ( 118 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=988766704612729363725673840229579328631 (pp39)
 r2=5441977445653925374118919046362314202378090727425848505434921132007141558367001 (pp79)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 34.82 hours.
Scaled time: 21.38 units (timescale=0.614).
Factorization parameters were as follows:
name: 33331_154
n: 5380846105516030294514527973878351422932507055981674764039604926065238659321190766317777113182762829421115190284905631
m: 10000000000000000000000000000000
c5: 1
c0: -70
skew: 5
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved algebraic special-q in [1500000, 2600001)
Primes: RFBsize:216816, AFBsize:217251, largePrimes:5599946 encountered
Relations: rels:5549582, finalFF:541091
Max relations in full relation-set: 28
Initial matrix: 434131 x 541091 with sparse part having weight 42032926.
Pruned matrix : 365380 x 367614 with weight 26967032.
Total sieving time: 29.75 hours.
Total relation processing time: 0.24 hours.
Matrix solve time: 4.74 hours.
Time per square root: 0.09 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 34.82 hours.
 --------- CPU info (if available) ----------

Feb 1, 2006 (2nd)

By Patrick Keller / GMP-ECM B1=1000000

(85·10183+41)/9 = 9(4)1829<184> = 11 · 280294841 · 127720032577<12> · 532735528664257<15> · C149

C149 = P32 · P117

P32 = 48044979146898568326453523893341<32>

P117 = 937022319203434101741528181490976533217713016698050847685313060556924953332107679500036871906546985351198581558955351<117>

Feb 1, 2006

By Patrick Keller / GMP-ECM B1=1000000

(85·10160+41)/9 = 9(4)1599<161> = 3 · 50179757 · 14484627089<11> · C143

C143 = P34 · P109

P34 = 4356375194869062990627509092203103<34>

P109 = 9942463665136438161089813056493194640029957518925315720288546609296010178713411105011178503140721671112406457<109>

(85·10171+41)/9 = 9(4)1709<172> = 112 · 427052687177<12> · 919355421421<12> · 1442197769764018515817<22> · C126

C126 = P33 · P93

P33 = 728961914628469704246275138502451<33>

P93 = 189102158969065391485449428344208719851426050660814594754935684284783697027367063614273413071<93>

January 2006

Jan 31, 2006 (3rd)

By Patrick Keller / GMP-ECM B1=1000000

(85·10195+41)/9 = 9(4)1949<196> = 11 · 251 · 2161031 · 27117551 · 1356870133<10> · 1739134559<10> · C161

C161 = P32 · C129

P32 = 25433652459414927499870617826399<32>

C129 = [972564350491546545147205599284218262224405374403653035025318106240841093313007765387765814323889960983051835806443072289350847213<129>]

(85·10153+41)/9 = 9(4)1529<154> = 11 · 677 · C151

C151 = P30 · P121

P30 = 532169908190609312922547459373<30>

P121 = 2383113620910345920040953299352597741758366084543329896306152414094100094570766140265306051858235710984214902514068075779<121>

(85·10191+41)/9 = 9(4)1909<192> = 11 · 994241 · 3853279 · 101912461631<12> · C168

C168 = P29 · C140

P29 = 14619811588998591301047585107<29>

C140 = [15041548193948732237377921782760162860444904346066707049385208315027780859557363470765425247552446374119213069706352597065891744437122468593<140>]

Jan 31, 2006 (2nd)

By Patrick Keller / GMP-ECM B1=1000000

(35·10195-53)/9 = 3(8)1943<196> = 11 · 353 · C193

C193 = P32 · C161

P32 = 13489623807653598428959653177019<32>

C161 = [74243477544933195199721018884564753532476736984037248212062263178045358729126496935286755527092585387779607938542329058870850264718140427333783944788315471979579<161>]

Jan 31, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(2·10154+7)/9 = (2)1533<154> = 3 · 13 · 83 · 227 · 62851 · 910523 · 11950907 · 226326480869<12> · C119

C119 = P34 · P85

P34 = 2678614065727037627558566220314891<34>

P85 = 7294061730828789765648309600745906429764528886149847086345196093357863550959590237333<85>

Number: 22223_154
N=19537976348479297709241108486263881541684093534372921346678597304513214562602235530128310041656777831832213020684025703
  ( 119 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=2678614065727037627558566220314891 (pp34)
 r2=7294061730828789765648309600745906429764528886149847086345196093357863550959590237333 (pp85)
Version: GGNFS-0.77.1
Total time: 44.63 hours.
Scaled time: 26.60 units (timescale=0.596).
Factorization parameters were as follows:
name: 22223_154
n: 19537976348479297709241108486263881541684093534372921346678597304513214562602235530128310041656777831832213020684025703
m: 10000000000000000000000000000000
c5: 1
c0: 35
skew: 2
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1500000, 2600001)
Relations: rels:5734822, finalFF:622092
Initial matrix: 433711 x 622092 with sparse part having weight 48174864.
Pruned matrix : 382626 x 384858 with weight 19449566.
Total sieving time: 39.59 hours.
Total relation processing time: 0.39 hours.
Matrix solve time: 4.49 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 44.63 hours.
 --------- CPU info (if available) ----------

Jan 30, 2006 (2nd)

By CWI / GMP-ECM

(10383-1)/9 = (1)383<383> = 852559 · 1628675880394909638591813700831880313095925587<46> · C331

C331 = P47 · C285

P47 = 23181229247696012268805890210990826546682789683<47>

C285 = [345192952476958960147823998139683616642758281269013129543194636356033777495389903234686281133559196454018224515556815842464194616108378684266847054423006039422253677029609403326167675526846676838304378980263488424464689785323765671486102372923974370891369373572968024442734473362642049<285>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 30, 2006

By Patrick Keller / GMP-ECM B1=1000000, Msieve v. 1.03

(29·10197+7)/9 = 3(2)1963<198> = 11 · 21487 · 43969 · 344695237 · 1684161325078097<16> · 4370874144876529<16> · 1167476286104917223<19> · C131

C131 = P32 · P41 · P58

P32 = 58538086613548548979322909890333<32>

P41 = 27331887467833258552502650566280944366953<41>

P58 = 6541795177200537912720111371200600941834147753875171749613<58>

Mon Jan 30 00:27:51 2006  Msieve v. 1.03
Mon Jan 30 00:27:51 2006  random seeds: f48bdf24 eb4aed3e
Mon Jan 30 00:27:51 2006  factoring 178799609620859433102456092550449953189558502392026811425674771874894588929096911710737173707739189 (99 digits)
Mon Jan 30 00:27:52 2006  using multiplier of 1
Mon Jan 30 00:27:52 2006  sieve interval: 9 blocks of size 65536
Mon Jan 30 00:27:52 2006  processing polynomials in batches of 6
Mon Jan 30 00:27:52 2006  using a sieve bound of 2572489 (94118 primes)
Mon Jan 30 00:27:52 2006  using large prime bound of 385873350 (28 bits)
Mon Jan 30 00:27:52 2006  using double large prime bound of 2854963469885100 (43-52 bits)
Mon Jan 30 00:27:52 2006  using trial factoring cutoff of 56 bits
Mon Jan 30 00:27:52 2006  polynomial 'A' values have 13 factors
Mon Jan 30 00:28:08 2006  restarting with 15020 full and 918731 partial relations
Mon Jan 30 03:21:36 2006  94326 relations (22749 full + 71577 combined from 1400538 partial), need 94214
Mon Jan 30 03:21:37 2006  begin with 1400538 relations
Mon Jan 30 03:21:38 2006  reduce to 224123 relations in 10 passes
Mon Jan 30 03:21:38 2006  attempting to read 22749 full and 224123 partial relations
Mon Jan 30 03:21:43 2006  recovered 22749 full and 224123 partial relations
Mon Jan 30 03:21:43 2006  recovered 235484 polynomials
Mon Jan 30 03:21:43 2006  attempting to build 71577 cycles
Mon Jan 30 03:21:43 2006  found 71577 cycles in 6 passes
Mon Jan 30 03:21:45 2006  distribution of cycle lengths:
Mon Jan 30 03:21:45 2006     length 2 : 16449
Mon Jan 30 03:21:45 2006     length 3 : 15837
Mon Jan 30 03:21:45 2006     length 4 : 12749
Mon Jan 30 03:21:45 2006     length 5 : 9690
Mon Jan 30 03:21:45 2006     length 6 : 6646
Mon Jan 30 03:21:45 2006     length 7 : 4252
Mon Jan 30 03:21:45 2006     length 8 : 2620
Mon Jan 30 03:21:45 2006     length 9+: 3334
Mon Jan 30 03:21:45 2006  largest cycle: 21 relations
Mon Jan 30 03:21:45 2006  94118 x 94182 system, weight 6188121 (avg 65.70/col)
Mon Jan 30 03:21:45 2006  reduce to 92662 x 92726 in 3 passes
Mon Jan 30 03:25:00 2006  lanczos halted after 1467 iterations
Mon Jan 30 03:25:00 2006  recovered 64 nontrivial dependencies
Mon Jan 30 03:26:02 2006  prp41 factor: 27331887467833258552502650566280944366953
Mon Jan 30 03:26:02 2006  prp58 factor: 6541795177200537912720111371200600941834147753875171749613
Mon Jan 30 03:26:02 2006  elapsed time 02:58:11

(29·10184+7)/9 = 3(2)1833<185> = 3 · 1609 · 141209 · 51361763 · C168

C168 = P32 · C137

P32 = 40099719731363732494892431187567<32>

C137 = [22952740803469060968111049404977261126816846627377021815399203618706658891312214574568337698722128170320166788147251434819194627650881241<137>]

Jan 29, 2006 (3rd)

By Patrick Keller / GMP-ECM B1=1000000

(29·10200+7)/9 = 3(2)1993<201> = 19 · 31469 · 200361424120519799<18> · 58874401726386398612126252576411<32> · C146

C146 = P36 · P110

P36 = 606815175214790313738987778416739217<36>

P110 = 75287329942185691582016605126251222192589334987378940003905961066870448780390121188605939719076412292159168861<110>

Jan 29, 2006 (2nd)

By Patrick Keller / GMP-ECM B1=1000000, GGNFS-0.77.1-20050930-pentium4 gnfs

(29·10186+7)/9 = 3(2)1853<187> = 367 · 6869 · 24173692225247190029<20> · 817085648520860204729531<24> · C137

C137 = P33 · P34 · P71

P33 = 148875337781562336091206119274899<33>

P34 = 5595198805825978240661829971576263<34>

P71 = 77686768150478058338957220040145869488476905274432941974964154046333127<71>

Number: 32223_186
N=434672912384034472276489075857058056092971658726960112621499647289367910737488108932999434401951383764401
  ( 105 digits)
Divisors found:
 r1=5595198805825978240661829971576263 (pp34)
 r2=77686768150478058338957220040145869488476905274432941974964154046333127 (pp71)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 9.48 hours.
Scaled time: 4.83 units (timescale=%1.3lf).
Factorization parameters were as follows:
name: 1
n: 434672912384034472276489075857058056092971658726960112621499647289367910737488108932999434401951383764401
skew: 43423.78
# norm 3.55e+014
c5: 2700
c4: -32793540
c3: -22483127152441
c2: 82849481010709582
c1: 14402080289847793642392
c0: -46281243702985892444165040
# alpha -6.74
Y1: 17831828861
Y0: -174325078919840638189
# Murphy_E 2.18e-009
# M 75917951504007049919756011760453746537937058616496215661199923963867940747621339656342162085021060087616
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Sieved special-q in [1250000, 1950001)
Relations: rels:4463965, finalFF:492216
Initial matrix: 366964 x 492216 with sparse part having weight 33506857.
Pruned matrix : 311533 x 313431 with weight 13262973.
Total sieving time: 7.31 hours.
Total relation processing time: 0.23 hours.
Matrix solve time: 1.80 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 9.48 hours.
 --------- CPU info (if available) ----------

Jan 29, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(4·10153+23)/9 = (4)1527<153> = 3 · 17 · 19 · 81017 · 241784369429<12> · C134

C134 = P46 · P89

P46 = 1470703507530817065767950099767404004845089349<46>

P89 = 15920774731201487385655812078291835754560386012725533646207019291393849532640008894695559<89>

Number: 44447_153
N=23414739239786028749269162319365649597012527790011081766399867486328722607760076327047273100135171383472611229438026705790715508501091
  ( 134 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=1470703507530817065767950099767404004845089349 (pp46)
 r2=15920774731201487385655812078291835754560386012725533646207019291393849532640008894695559 (pp89)
Version: GGNFS-0.77.1
Total time: 41.25 hours.
Scaled time: 24.59 units (timescale=0.596).
Factorization parameters were as follows:
name: 44447_153
n: 23414739239786028749269162319365649597012527790011081766399867486328722607760076327047273100135171383472611229438026705790715508501091
m: 10000000000000000000000000000000
c5: 1
c0: 575
skew: 2
type: snfs
Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1500000, 2500001)
Relations: rels:5624531, finalFF:597924
Initial matrix: 433646 x 597924 with sparse part having weight 43829030.
Pruned matrix : 383560 x 385792 with weight 18604471.
Total sieving time: 36.47 hours.
Total relation processing time: 0.33 hours.
Matrix solve time: 4.29 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 41.25 hours.
 --------- CPU info (if available) ----------

Jan 28, 2006 (3rd)

By Patrick Keller / GMP-ECM B1=1000000

(29·10200+7)/9 = 3(2)1993<201> = 19 · 31469 · 200361424120519799<18> · C178

C178 = P32 · C146

P32 = 58874401726386398612126252576411<32>

C146 = [45685494310321139538690186388518699890739761704723675271383671232036884261792667410604433223602786884855278216669151772545738533720768128503921837<146>]

Jan 28, 2006 (2nd)

By Patrick Keller / GMP-ECM B1=1000000

(35·10171-53)/9 = 3(8)1703<172> = 11 · 257 · 313 · 14547037 · C159

C159 = P36 · P123

P36 = 451637800707841604043591937013618243<36>

P123 = 668945230356071257795118498826470672455372523944031278211962172797587051335478238590834313058838878619295303466223808615463<123>

Jan 28, 2006

By Cedric Vonck / GGNFS-0.77.1-20050930-pentium4 gnfs

(10166+11)/3 = (3)1657<166> = 2269 · 5764399 · 19537095989<11> · 87732744049<11> · 301816485953164436063353<24> · C111

C111 = P53 · P59

P53 = 11206452347884993130940717654027456951433829993441411<53>

P59 = 43959969732682098946597196186987599511353917863039376632629<59>

Divisors found:
 r1=11206452347884993130940717654027456951433829993441411 (pp53)
 r2=43959969732682098946597196186987599511353917863039376632629 (pp59)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 37.53 hours.
Scaled time: 20.19 units (timescale=0.538).
Factorization parameters were as follows:
name: c111
n: 492635306023768541594765890513052108909476061496811112954272759376577034953854526502589831415278876920382399519
skew: 25890.51
# norm 6.53e+014
c5: 14280
c4: -898725224
c3: -24028726065267
c2: 149970026802419081
c1: 8622273537997815680117
c0: 2369636294795826677063373
# alpha -5.25
Y1: 598043715709
Y0: -2030304024354184370578
# Murphy_E 9.11e-010
# M 344700207265714400774493844422343622305068913230711086885117440445706540058613325752159815816366332677658325980
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2400001)
Primes: RFBsize:230209, AFBsize:231093, largePrimes:7527070 encountered
Relations: rels:7440978, finalFF:621380
Max relations in full relation-set: 28
Initial matrix: 461385 x 621380 with sparse part having weight 53695434.
Pruned matrix : 332381 x 334751 with weight 28979305.
Total sieving time: 32.00 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 4.82 hours.
Time per square root: 0.30 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 37.53 hours.
 --------- CPU info (if available) ----------

Jan 27, 2006

A very improvised snfs poly file for GGNFS is available on each contribution pages. Default parameters are required and the skew is not adjusted.

Jan 27, 2006 (3rd)

By Patrick Keller / GMP-ECM

(35·10179-53)/9 = 3(8)1783<180> = 11 · 1453 · C176

C176 = P28 · C148

P28 = 4823708954837782458566048329<28>

C148 = [5044128471268801172062513142983485358949897775689870766059301754241680504722143167099125805317082288533122296651679099968127315184968035371550200469<148>]

Jan 27, 2006 (2nd)

By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs

(5·10177+31)/9 = (5)1769<177> = 13 · 56345207 · 3866383109<10> · 242143359684157<15> · 272242916096747<15> · 1691532864670216129<19> · C112

C112 = P46 · P66

P46 = 5590949666318516260855679354188427787135841331<46>

P66 = 314649542503316748079738255963456709156720035705251552887876749141<66>

Number: 7638
N=1759189754666192572326725349064953542205081951959080946286724157353603060805175015430135904517498852334266546671
  ( 112 digits)
Divisors found:
 r1=5590949666318516260855679354188427787135841331 (pp46)
 r2=314649542503316748079738255963456709156720035705251552887876749141 (pp66)
Version: GGNFS-0.77.1-20050930-athlon
Total time: 23.44 hours.
Scaled time: 15.47 units (timescale=%1.3lf).
Factorization parameters were as follows:
name: 7638
n: 1759189754666192572326725349064953542205081951959080946286724157353603060805175015430135904517498852334266546671
skew: 23920.37
# norm 1.64e+015
c5: 26760
c4: 2529054184
c3: -88766237821472
c2: -1536599333403767721
c1: 11040733049224213553472
c0: -20360395729652409608835548
# alpha -5.47
Y1: 739415148989
Y0: -2309737831355081448027
# Murphy_E 8.07e-010
# M 79677056783275846577819398475589618451768605930335261907244912079153872042265783015618928186592278468264372413
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2650001)
Relations: rels:7206433, finalFF:570022
Initial matrix: 499190 x 570022 with sparse part having weight 44320846.
Pruned matrix : 465373 x 467932 with weight 28459747.
Total sieving time: 20.25 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 2.65 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 23.44 hours.
 --------- CPU info (if available) ----------

Jan 27, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(8·10152+1)/9 = (8)1519<152> = 276553 · 96941219 · 17522761249341089058283<23> · C117

C117 = P52 · P65

P52 = 9275450587465013271141450209568903221034440958615769<52>

P65 = 20399666486620694433547638703203893366675685859664738168665270201<65>

Number: 88889_152
N=189216098497416263473135181856600180019937737923795853280762266113886314312612554827066663044652111065432137324399569
  ( 117 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=9275450587465013271141450209568903221034440958615769 (pp52)
 r2=20399666486620694433547638703203893366675685859664738168665270201 (pp65)
Version: GGNFS-0.77.1
Total time: 39.61 hours.
Scaled time: 23.61 units (timescale=0.596).
Factorization parameters were as follows:
name: 88889_152
n: 189216098497416263473135181856600180019937737923795853280762266113886314312612554827066663044652111065432137324399569
m: 1000000000000000000000000000000
c5: 800
c0: 1
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2200001)
Relations: rels:5656806, finalFF:560541
Initial matrix: 352461 x 560541 with sparse part having weight 49911832.
Pruned matrix : 311880 x 313706 with weight 17483011.
Total sieving time: 35.95 hours.
Total relation processing time: 0.37 hours.
Matrix solve time: 3.15 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 39.61 hours.
 --------- CPU info (if available) ----------

Jan 26, 2006 (2nd)

By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs

(8·10166+1)/9 = (8)1659<166> = 3 · 557461665979<12> · 1225671932987<13> · 1106648171488609<16> · 8449459157386939<16> · C111

C111 = P48 · P64

P48 = 333087075628896812713251964530979547595195984979<48>

P64 = 1392325284264560906132614928910781331907389357350433733048086539<64>

Number: 3254
N=463765557259855051917117131486710479266089943564208828987238225638693593801271651567757735109441644551336097681
  ( 111 digits)
Divisors found:
 r1=333087075628896812713251964530979547595195984979 (pp48)
 r2=1392325284264560906132614928910781331907389357350433733048086539 (pp64)
Version: GGNFS-0.77.1-20050930-athlon
Total time: 19.29 hours.
Scaled time: 11.85 units (timescale=%1.3lf).
Factorization parameters were as follows:
name: 3254
n: 463765557259855051917117131486710479266089943564208828987238225638693593801271651567757735109441644551336097681
skew: 36628.95
# norm 5.55e+015
c5: 16800
c4: -2384216080
c3: -58737157009298
c2: -3097661265535552497
c1: 9175246943003298098750
c0: 479467956148092230621982685
# alpha -6.74
Y1: 604398104101
Y0: -1941787400956269041544
# Murphy_E 9.07e-010
# M 391675059068029791990482987611213515275710334411496631346201367720880232500594510316273613195473518983785111212
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 50000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1600000, 2350001)
Relations: rels:7130922, finalFF:535065
Initial matrix: 460667 x 535065 with sparse part having weight 42098767.
Pruned matrix : 426581 x 428948 with weight 25847979.
Total sieving time: 16.52 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 2.21 hours.
Time per square root: 0.21 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 19.29 hours.
 --------- CPU info (if available) ----------

Jan 26, 2006

By Anton Korobeynikov / GGNFS-0.77.1-20050930-athlon

2·10155-1 = 1(9)155<156> = 5012795239<10> · C146

C146 = P72 · P75

P72 = 136754115856816167695867638454568058370179471864695591167031691027321981<72>

P75 = 291749166878241872177396255297205394204088421236507456460074010898849116061<75>

Number: snfs
N=39897899368396683078640308292073846665253745067243908623573443351652528969376480849310828991552990102095809942178250620541654244896237621885436841
  ( 146 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=136754115856816167695867638454568058370179471864695591167031691027321981 (pp72)
 r2=291749166878241872177396255297205394204088421236507456460074010898849116061 (pp75)
Version: GGNFS-0.77.1-20050930-athlon
Total time: 141.14 hours.
Scaled time: 66.90 units (timescale=0.474).
Factorization parameters were as follows:
n: 39897899368396683078640308292073846665253745067243908623573443351652528969376480849310828991552990102095809942178250620541654244896237621885436841
c5: 2
c0: -1
m: 10000000000000000000000000000000
skew: 100.0
type: snfs
lss: 1
qintsize: 50000Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 48/48
Sieved rational special-q in [1500000, 3550001)
Primes: RFBsize:216816, AFBsize:216491, largePrimes:5779940 encountered
Relations: rels:5731745, finalFF:497024
Max relations in full relation-set: 28
Initial matrix: 433372 x 497024 with sparse part having weight 47577503.
Pruned matrix : 403451 x 405681 with weight 35625976.
Total sieving time: 129.13 hours.
Total relation processing time: 0.88 hours.
Matrix solve time: 10.85 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 141.14 hours.
 --------- CPU info (if available) ----------

Jan 25, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1

(28·10151+17)/9 = 3(1)1503<152> = 3 · 11 · 19 · 47 · 53 · 743 · 5279 · 6760674071<10> · C129

C129 = P64 · P66

P64 = 1183424773474736884406097266107576876938774299229979351789940959<64>

P66 = 634750602886514005931448326915798097467522134045896246417437275273<66>

Number: 31113_151
N=751179588433925505819980439132160983509357836200324681542769367407649269891006424737915625504962455505240739186983603374500606807
  ( 129 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=1183424773474736884406097266107576876938774299229979351789940959 (pp64)
 r2=634750602886514005931448326915798097467522134045896246417437275273 (pp66)
Version: GGNFS-0.77.1
Total time: 36.25 hours.
Scaled time: 21.61 units (timescale=0.596).
Factorization parameters were as follows:
name: 31113_151
n:  751179588433925505819980439132160983509357836200324681542769367407649269891006424737915625504962455505240739186983603374500606807
m: 1000000000000000000000000000000
c5: 280
c0: 17
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2100001)
Relations: rels:5476607, finalFF:488877
Initial matrix: 352462 x 488877 with sparse part having weight 42762285.
Pruned matrix : 322831 x 324657 with weight 19033619.
Total sieving time: 32.22 hours.
Total relation processing time: 0.38 hours.
Matrix solve time: 3.50 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 36.25 hours.
 --------- CPU info (if available) ----------

Jan 25, 2006

By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs

(52·10177-7)/9 = 5(7)177<178> = 5209 · 687901 · 3591592130707531<16> · 20758583474340401<17> · 163882620580891776606591883<27> · C111

C111 = P55 · P56

P55 = 5990130956546303578954044839627845137546757129595421161<55>

P56 = 22030613574269288396243921906995869107155224693130054301<56>

Number: 7205
N=131966260362939672544609184922691216201854675825526623713085165777457266196327622856980876044228227484894463461
  ( 111 digits)
Divisors found:
 r1=5990130956546303578954044839627845137546757129595421161 (pp55)
 r2=22030613574269288396243921906995869107155224693130054301 (pp56)
Version: GGNFS-0.77.1-20050930-athlon
Total time: 19.89 hours.
Scaled time: 12.93 units (timescale=%1.3lf).
Factorization parameters were as follows:
name: 7205
n: 131966260362939672544609184922691216201854675825526623713085165777457266196327622856980876044228227484894463461
skew: 38293.48
# norm 4.68e+015
c5: 26460
c4: -1421202454
c3: -176948763340345
c2: -2446403972040051259
c1: 106057665132258845107595
c0: -6358896990066060629975025
# alpha -6.46
Y1: 616825309463
Y0: -1379039484047520995828
# Murphy_E 8.87e-010
# M 73243177485515507332517433451890715278931353287625047006678691986437432307082725942451292464863658852031109008
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1600000, 2400001)
Relations: rels:7208189, finalFF:557042
Initial matrix: 460412 x 557042 with sparse part having weight 47165794.
Pruned matrix : 419163 x 421529 with weight 26297790.
Total sieving time: 17.25 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 2.10 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 19.89 hours.
 --------- CPU info (if available) ----------

Jan 24, 2006

By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs

(13·10164-1)/3 = 4(3)164<165> = 17 · 23 · 121291 · 1720324112526590653<19> · 22830290549856975884476811953<29> · C111

C111 = P45 · P66

P45 = 250560538262323237800920263917376214890034701<45>

P66 = 928500998327696518716189155494288425648796690706977226894213494177<66>

Number: 2007
N=232645709918092128212963626281842374753128885585849987283506411402099491993298681298998317099407771797991436077
  ( 111 digits)
Divisors found:
 r1=250560538262323237800920263917376214890034701 (pp45)
 r2=928500998327696518716189155494288425648796690706977226894213494177 (pp66)
Version: GGNFS-0.77.1-20050930-athlon
Total time: 23.62 hours.
Scaled time: 15.31 units (timescale=%1.3lf).
Factorization parameters were as follows:
name: 2007
n: 232645709918092128212963626281842374753128885585849987283506411402099491993298681298998317099407771797991436077
skew: 14212.24
# norm 1.41e+014
c5: 17520
c4: -731536343
c3: -7203612784458
c2: 137854935490016143
c1: 757017358734400134189
c0: -3936459434010134648132846
# alpha -3.52
Y1: 140945592403
Y0: -1677383992046597419989
# Murphy_E 8.77e-010
# M 30919382169914387085751545851925427078681855413600291588789589589734820051013111462667174408849572806160572640
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1600000, 2500001)
Relations: rels:7297886, finalFF:584279
Initial matrix: 460506 x 584279 with sparse part having weight 46858369.
Pruned matrix : 409772 x 412138 with weight 22844098.
Total sieving time: 21.23 hours.
Total relation processing time: 0.28 hours.
Matrix solve time: 1.92 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 23.62 hours.
 --------- CPU info (if available) ----------

Jan 23, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1

(4·10152+41)/9 = (4)1519<152> = 7 · 227 · 971 · 674759 · C140

C140 = P67 · P74

P67 = 1749054437074730839738212413266980681168427109942203394836261055113<67>

P74 = 24407446290192717863936113799240790417381456561254089477520149077854868713<74>

Number: 44449_152
N=42689952231524751722138041230328646463026795672759687658152146679145117324025601300082106418039877056208737757403079020376978414617472379569
  ( 140 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=1749054437074730839738212413266980681168427109942203394836261055113 (pp67)
 r2=24407446290192717863936113799240790417381456561254089477520149077854868713 (pp74)
Version: GGNFS-0.77.1
Total time: 40.18 hours.
Scaled time: 23.99 units (timescale=0.597).
Factorization parameters were as follows:
name: 44449_152
n: 42689952231524751722138041230328646463026795672759687658152146679145117324025601300082106418039877056208737757403079020376978414617472379569
m: 1000000000000000000000000000000
c5: 400
c0: 41
skew: 2
type: snfs

Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2200001)
Relations: rels:5353614, finalFF:451285
Initial matrix: 352740 x 451285 with sparse part having weight 39087828.
Pruned matrix : 333599 x 335426 with weight 20667424.
Total sieving time: 35.74 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 4.00 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 40.18 hours.
 --------- CPU info (if available) ----------

Jan 23, 2006

By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs

(10167+11)/3 = (3)1667<167> = 37 · 1223 · 1659737 · 2908723 · 447435816063229601<18> · 1294695630404312613929<22> · C111

C111 = P49 · P62

P49 = 8084500782190389840478406072564528309399381768737<49>

P62 = 32580465758870391821055101253905389293574411343938722240893569<62>

Number: 3051
N=263396800911714895792509875297859568219343048500407357011345512027494719081492325733089149289256654778588552353
  ( 111 digits)
Divisors found:
 r1=8084500782190389840478406072564528309399381768737 (pp49)
 r2=32580465758870391821055101253905389293574411343938722240893569 (pp62)
Version: GGNFS-0.77.1-20050930-athlon
Total time: 19.92 hours.
Scaled time: 13.26 units (timescale=%1.3lf).
Factorization parameters were as follows:
name: 1
n: 263396800911714895792509875297859568219343048500407357011345512027494719081492325733089149289256654778588552353
skew: 44063.22
# norm 5.82e+015
c5: 31440
c4: -2042808076
c3: -259462411933762
c2: 3562919922588584576
c1: 78571915379339780403777
c0: -1247587394058679282894357380
# alpha -7.13
Y1: 449769722723
Y0: -1529773914367355424991
# Murphy_E 9.78e-010
# M 37620472442472730250295197130900633958251966432039131133767733126942109554102128164093057823374055476852748918
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1600000, 2300001)
Relations: rels:7226550, finalFF:590752
Initial matrix: 460667 x 590752 with sparse part having weight 46800960.
Pruned matrix : 405019 x 407386 with weight 21906508.
Total sieving time: 17.67 hours.
Total relation processing time: 0.25 hours.
Matrix solve time: 1.81 hours.
Time per square root: 0.19 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 19.92 hours.
 --------- CPU info (if available) ----------

Jan 22, 2006

By Cedric Vonck / GGNFS-0.77.1-20050930-pentium4 gnfs

2·10161-9 = 1(9)1601<162> = 11 · 8009 · 46649 · 5470052140709707519<19> · 21260817950106947166511<23> · C111

C111 = P44 · P68

P44 = 38623719592924262442438059227864671483234091<44>

P68 = 10834057799333342211229610150242910516634871944815694724812226195039<68>

Number: c111
N=418451610494985126825836635808849111611795791400042430454732256218470337626978790680198450889274838215059874549
  ( 111 digits)
Divisors found:
 r1=38623719592924262442438059227864671483234091 (pp44)
 r2=10834057799333342211229610150242910516634871944815694724812226195039 (pp68)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 38.14 hours.
Scaled time: 21.67 units (timescale=0.568).
Factorization parameters were as follows:
name: c111
n: 418451610494985126825836635808849111611795791400042430454732256218470337626978790680198450889274838215059874549
skew: 3675.70
# norm 1.93e+014
c5: 32760
c4: -178083787
c3: 21650278439078
c2: 8917979542614550
c1: -49383796745086078804
c0: 13429828240883863427696
# alpha -3.65
Y1: 795881887993
Y0: -1664410687743954876989
# Murphy_E 8.91e-010
# M 10948574208808051795460323832426812352113482816811172364528579270127779274130082656672732319498982550206267293
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2500001)
Primes: RFBsize:230209, AFBsize:230091, largePrimes:7793681 encountered
Relations: rels:7932693, finalFF:773618
Max relations in full relation-set: 28
Initial matrix: 460383 x 773618 with sparse part having weight 72578266.
Pruned matrix : 260552 x 262917 with weight 44454129.
Total sieving time: 33.38 hours.
Total relation processing time: 0.46 hours.
Matrix solve time: 4.05 hours.
Time per square root: 0.26 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 38.14 hours.
 --------- CPU info (if available) ----------

Jan 21, 2006 (3rd)

By Patrick Keller / GGNFS-0.77.1-20050930-athlon gnfs

(7·10158-1)/3 = 2(3)158<159> = 1567 · 6272477 · 94340496413<11> · 411102666467<12> · 48861300224203<14> · C113

C113 = P37 · P76

P37 = 1447531832598287194675337087588890669<37>

P76 = 8654203791135258006846208256907995285539701724907372088440732832849802487071<76>

Number: 1
N=12527235473461064690789740751463629224250685860494368593748060178562891242691247493191763713705069665306105040499
  ( 113 digits)
Divisors found:
 r1=1447531832598287194675337087588890669 (pp37)
 r2=8654203791135258006846208256907995285539701724907372088440732832849802487071 
(pp76)
Version: GGNFS-0.77.1-20050930-athlon
Total time: 26.10 hours.
Scaled time: 17.25 units (timescale=%1.3lf).
Factorization parameters were as follows:
name: 1
n: 
12527235473461064690789740751463629224250685860494368593748060178562891242691247493191763713705069665306105040499
skew: 89208.53
# norm 3.49e+015
c5: 2760
c4: -1034197276
c3: -28219325036870
c2: 7094204249441952635
c1: -225125126489700920174112
c0: -346886755808856710520625020
# alpha -6.18
Y1: 434919627923
Y0: -5387556766897775617289
# Murphy_E 7.50e-010
# M 
12155549874620238031766711571075608703631898509942543672223711551128349335307687833438143686070227069253819519139
type: gnfs
rlim: 3500000
alim: 3500000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 5000Factor base limits: 3500000/3500000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1750000, 2655001)
Relations: rels:7505319, finalFF:659459
Initial matrix: 501526 x 659459 with sparse part having weight 55260502.
Pruned matrix : 438001 x 440572 with weight 25312097.
Total sieving time: 22.64 hours.
Total relation processing time: 0.54 hours.
Matrix solve time: 2.73 hours.
Time per square root: 0.20 hours.
Prototype def-par.txt line would be:
gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000
total time: 26.10 hours.
 --------- CPU info (if available) ----------

Jan 21, 2006 (2nd)

By Makoto Kamada / GGNFS-0.77.1-20050930-pentium4 gnfs

By Torbjörn Granlund / GMP-ECM

10810+1 = 1(0)8091<811> = 61 · 101 · 109 · 181 · 541 · 1621 · 3541 · 8101 · 9901 · 19441 · 27541 · 27961 · 68041 · 119881 · 153469 · 329941 · 2925721 · 4188901 · 39526741 · 49229101 · 68189581 · 999999000001<12> · 29639179139212862101<20> · 4999437541453012143121<22> · 13029637224192121671301<23> · 1105097795002994798105101<25> · 67128593062302476037266041<26> · 7997499229153265919258822361<28> · 59779577156334533866654838281<29> · 292833529380862495499652402770042860551961<42> · 141849229571534821256183437819902857798933927761<48> · 902957305935680526667861848839993076071896366838581<51> · 341796090604674881849636380229010216626944264336893367139245334739710314141368913850637159182300704681<102> · C108 · [21431956757675468974876300755804900832277300719777308299609301048389700236714216988820459065467670651445681992662548793310029766116893035870982334672674080173615607829147502498184662701<185>]

C108 = P43 · P65

P43 = 2187911623791867750065408022595894263802921<43>

P65 = 79802900676249574386310013540996547368285959759708473463717727701<65>

Number: 10001_810a
N=174601694001874347255805749546028712001883150079648147890917445185989799312355477070999037232383781006414621
  ( 108 digits)
Divisors found:
 r1=2187911623791867750065408022595894263802921 (pp43)
 r2=79802900676249574386310013540996547368285959759708473463717727701 (pp65)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 18.72 hours.
Scaled time: 11.51 units (timescale=0.615).
Factorization parameters were as follows:
name: 10001_810a
n: 174601694001874347255805749546028712001883150079648147890917445185989799312355477070999037232383781006414621
skew: 5126.41
# norm 1.93e+14
c5: 103740
c4: 5489741268
c3: -13075289527817
c2: -139084549632406609
c1: 119742151420102586749
c0: 271623207935125340303085
# alpha -5.35
Y1: 259012632439
Y0: -278750831169188009758
# Murphy_E 1.45e-09
# M 134662390696672647263499356795199525153224044769487875113261803659845520946252776074226595599860047310328984
type: gnfs
rlim: 2500000
alim: 2500000
lpbr: 26
lpba: 26
mfbr: 49
mfba: 49
rlambda: 2.6
alambda: 2.6
qintsize: 150000
Factor base limits: 2500000/2500000
Large primes per side: 3
Large prime bits: 26/26
Max factor residue bits: 49/49
Sieved algebraic special-q in [1250000, 2600001)
Primes: RFBsize:183072, AFBsize:182575, largePrimes:4597622 encountered
Relations: rels:4798738, finalFF:516298
Max relations in full relation-set: 28
Initial matrix: 365731 x 516298 with sparse part having weight 45217492.
Pruned matrix : 265981 x 267873 with weight 25469744.
Total sieving time: 15.82 hours.
Total relation processing time: 0.35 hours.
Matrix solve time: 2.37 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000
total time: 18.72 hours.
 --------- CPU info (if available) ----------

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 21, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(34·10151-7)/9 = 3(7)151<152> = 37 · C151

C151 = P44 · P49 · P59

P44 = 36244743842331203919950327303612252533187707<44>

P49 = 1236569276238851873641077650635328609093214576107<49>

P59 = 22780916748875701195796464739236626157318164712696869631829<59>

Number: 37777_151
N=1021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021
  ( 151 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=36244743842331203919950327303612252533187707 (pp44)
 r2=1236569276238851873641077650635328609093214576107 (pp49)
 r3=22780916748875701195796464739236626157318164712696869631829 (pp59)
Version: GGNFS-0.77.1
Total time: 46.75 hours.
Scaled time: 31.09 units (timescale=0.665).
Factorization parameters were as follows:
name: 37777_151
n: 1021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021021
m: 1000000000000000000000000000000
c5: 340
c0: -7
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2400001)
Relations: rels:5359277, finalFF:399435
Initial matrix: 352217 x 399435 with sparse part having weight 36448166.
Pruned matrix : 346243 x 348068 with weight 26257292.
Total sieving time: 41.64 hours.
Total relation processing time: 0.43 hours.
Matrix solve time: 4.52 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 46.75 hours.
 --------- CPU info (if available) ----------

Jan 20, 2006 (2nd)

By Yousuke Koide / GMP-ECM

10810+1 = 1(0)8091<811> = 61 · 101 · 109 · 181 · 541 · 1621 · 3541 · 8101 · 9901 · 19441 · 27541 · 27961 · 68041 · 119881 · 153469 · 329941 · 2925721 · 4188901 · 39526741 · 49229101 · 68189581 · 999999000001<12> · 29639179139212862101<20> · 4999437541453012143121<22> · 13029637224192121671301<23> · 1105097795002994798105101<25> · 67128593062302476037266041<26> · 7997499229153265919258822361<28> · 59779577156334533866654838281<29> · 141849229571534821256183437819902857798933927761<48> · 902957305935680526667861848839993076071896366838581<51> · 341796090604674881849636380229010216626944264336893367139245334739710314141368913850637159182300704681<102> · C149 · [21431956757675468974876300755804900832277300719777308299609301048389700236714216988820459065467670651445681992662548793310029766116893035870982334672674080173615607829147502498184662701<185>]

C149 = P42 · C108

P42 = 292833529380862495499652402770042860551961<42>

C108 = [174601694001874347255805749546028712001883150079648147890917445185989799312355477070999037232383781006414621<108>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 20, 2006

By Cedric Vonck / GGNFS-0.77.1-20050930-pentium4 gnfs

(28·10159+17)/9 = 3(1)1583<160> = 11 · 31 · 60558053 · 7212362800961<13> · 33539753385806481216611969<26> · C111

C111 = P51 · P61

P51 = 462536132185574572774501768659198144654440616697393<51>

P61 = 1346499340514681298574411447231016501419631070503438624796113<61>

Number: c111
N=622804596952087616912505747405171660214728457594249079875162518181585744977322568358844642895637638988043633409
  ( 111 digits)
Divisors found:
 r1=462536132185574572774501768659198144654440616697393 (pp51)
 r2=1346499340514681298574411447231016501419631070503438624796113 (pp61)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 35.69 hours.
Scaled time: 21.20 units (timescale=0.594).
Factorization parameters were as follows:
name: c111
n: 622804596952087616912505747405171660214728457594249079875162518181585744977322568358844642895637638988043633409
skew: 40274.04
# norm 3.24e+015
c5: 24960
c4: 3358680112
c3: -154095379278068
c2: -5133738171144417744
c1: 97735448881250080837173
c0: 973118633560276453861668837
# alpha -6.68
Y1: 255538396069
Y0: -1902917132300748293272
# Murphy_E 9.18e-010
# M 204503118033941889104818766711331234716892044883651475030150490804811943446656433575566145287157210501727805036
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2400001)
Primes: RFBsize:230209, AFBsize:230053, largePrimes:7688165 encountered
Relations: rels:7775371, finalFF:751041
Max relations in full relation-set: 28
Initial matrix: 460347 x 751041 with sparse part having weight 67651935.
Pruned matrix : 260052 x 262417 with weight 38209459.
Total sieving time: 31.54 hours.
Total relation processing time: 0.46 hours.
Matrix solve time: 3.42 hours.
Time per square root: 0.27 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 35.69 hours.
 --------- CPU info (if available) ----------

Jan 19, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(85·10151+41)/9 = 9(4)1509<152> = 3 · 11 · 263 · C149

C149 = P34 · P56 · P60

P34 = 4943181161334121867022094443412343<34>

P56 = 15942446963562877289932971560669341883979707656772226419<56>

P60 = 138084591641348859848844692898664238439608537558881691144443<60>

Number: 94449_151
N=10881950045448144307459896813508980809361037497919627197193737117691490315064459551151566360691835977007079668676626851531794497573965254573619592631
  ( 149 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=4943181161334121867022094443412343 (pp34)
 r2=15942446963562877289932971560669341883979707656772226419 (pp56)
 r3=138084591641348859848844692898664238439608537558881691144443 (pp60)
Version: GGNFS-0.77.1
Total time: 45.03 hours.
Scaled time: 26.84 units (timescale=0.596).
Factorization parameters were as follows:
name: 94449_151
n: 10881950045448144307459896813508980809361037497919627197193737117691490315064459551151566360691835977007079668676626851531794497573965254573619592631
m: 1000000000000000000000000000000
c5: 850
c0: 41
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2300001)
Relations: rels:5470422, finalFF:459583
Initial matrix: 352868 x 459583 with sparse part having weight 41964979.
Pruned matrix : 334801 x 336629 with weight 21806643.
Total sieving time: 40.36 hours.
Total relation processing time: 0.41 hours.
Matrix solve time: 4.10 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 45.03 hours.
 --------- CPU info (if available) ----------

Jan 17, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(89·10151+1)/9 = 9(8)1509<152> = 3 · 112 · 683 · 106781 · C142

C142 = P61 · P81

P61 = 9592561240368708557394631004994331725705539077245555042315551<61>

P81 = 389396106087029426819397405054446679770014664080460923953210556844866305408789611<81>

Number: 98889_151
N=3735305994400940222977603340946986263067520786719671553018228690399643253656412142170867746660925810754124002709470582364123614636317632540661
  ( 142 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=9592561240368708557394631004994331725705539077245555042315551 (pp61)
 r2=389396106087029426819397405054446679770014664080460923953210556844866305408789611 (pp81)
Version: GGNFS-0.77.1
Total time: 40.47 hours.
Scaled time: 24.20 units (timescale=0.598).
Factorization parameters were as follows:
name: 98889_151
n: 3735305994400940222977603340946986263067520786719671553018228690399643253656412142170867746660925810754124002709470582364123614636317632540661
m: 1000000000000000000000000000000
c5: 890
c0: 1
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2200001)
Relations: rels:5400256, finalFF:457265
Initial matrix: 353142 x 457265 with sparse part having weight 41226568.
Pruned matrix : 332763 x 334592 with weight 21288107.
Total sieving time: 36.15 hours.
Total relation processing time: 0.31 hours.
Matrix solve time: 3.84 hours.
Time per square root: 0.17 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 40.47 hours.
 --------- CPU info (if available) ----------

Jan 15, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(4·10152-31)/9 = (4)1511<152> = 41 · 79 · 4231 · 19037823664438599021743461<26> · C120

C120 = P51 · P70

P51 = 166866328854011532118907641869784764648724705750463<51>

P70 = 1020886585728828363510597287873903676785706217228771834142475438673643<70>

Number: 44441_152
N=170351596736875709959179822326526166723291839274113159290765004032671542668674951513691570325256153664621191583653146709
  ( 120 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=166866328854011532118907641869784764648724705750463 (pp51)
 r2=1020886585728828363510597287873903676785706217228771834142475438673643 (pp70)
Version: GGNFS-0.77.1
Total time: 42.82 hours.
Scaled time: 25.60 units (timescale=0.598).
Factorization parameters were as follows:
name: 44441_152
n: 170351596736875709959179822326526166723291839274113159290765004032671542668674951513691570325256153664621191583653146709
m: 1000000000000000000000000000000
c5: 400
c0: -31
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2300001)
Relations: rels:5546011, finalFF:491989
Initial matrix: 352175 x 491989 with sparse part having weight 44706048.
Pruned matrix : 327635 x 329459 with weight 20162990.
Total sieving time: 38.40 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 3.86 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 42.82 hours.
 --------- CPU info (if available) ----------

Jan 13, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(5·10151+13)/9 = (5)1507<151> = 7 · 337 · 709 · C145

C145 = P66 · P80

P66 = 244675379719578289333919494527112794313295764375089268344563909567<66>

P80 = 13575725494988365411487737203669177049217503397028681709211591765872759556449241<80>

Number: 55557_151
N=3321645790455038235796858506990636081217959819910994508057282977448881698190081711822116035849592955559900268249470745567977846482699307549788647
  ( 145 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=244675379719578289333919494527112794313295764375089268344563909567 (pp66)
 r2=13575725494988365411487737203669177049217503397028681709211591765872759556449241 (pp80)
Version: GGNFS-0.77.1
Total time: 43.12 hours.
Scaled time: 25.78 units (timescale=0.598).
Factorization parameters were as follows:
name: 55557_151
n: 3321645790455038235796858506990636081217959819910994508057282977448881698190081711822116035849592955559900268249470745567977846482699307549788647
m: 1000000000000000000000000000000
c5: 50
c0: 13
skew: 2
type: snfs

 Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2300001)
Relations: rels:5749297, finalFF:559546
Initial matrix: 352970 x 559546 with sparse part having weight 51636734.
Pruned matrix : 313574 x 315402 with weight 18663720.
Total sieving time: 39.14 hours.
Total relation processing time: 0.42 hours.
Matrix solve time: 3.40 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 43.12 hours.
 --------- CPU info (if available) ----------

Jan 12, 2006

By Cedric Vonck / GGNFS-0.77.1-20050930-pentium4 gnfs

(13·10164-31)/9 = 1(4)1631<165> = 3 · 43 · 112428709734049<15> · 12667023571737990991217609155379403223<38> · C111

C111 = P40 · P72

P40 = 1676745044461232317729000675458505147939<40>

P72 = 468913024426091623245443201751896636676035669103202976763622771817695493<72>

Number: c111
N=786247589989777914636073830302682947375520031653629043043502213698140564149219934257068310767319486956018538927
  ( 111 digits)
Divisors found:
 r1=1676745044461232317729000675458505147939 (pp40)
 r2=468913024426091623245443201751896636676035669103202976763622771817695493 (pp72)
Version: GGNFS-0.77.1-20050930-pentium4
Total time: 34.26 hours.
Scaled time: 20.14 units (timescale=0.588).
Factorization parameters were as follows:
name: c111
n: 786247589989777914636073830302682947375520031653629043043502213698140564149219934257068310767319486956018538927
skew: 33636.57
# norm 3.04e+015
c5: 25920
c4: 3144008652
c3: -165915269317612
c2: -3366808236145090300
c1: 65987022536508996805519
c0: -83913059230236699400938539
# alpha -6.22
Y1: 168306501707
Y0: -1978718297937859459848
# Murphy_E 8.62e-010
# M 382289855528369169824421895336199655196115297917391454091611178216699183661511295281539641929425741668177499676
type: gnfs
rlim: 3200000
alim: 3200000
lpbr: 27
lpba: 27
mfbr: 50
mfba: 50
rlambda: 2.6
alambda: 2.6
qintsize: 100000
Factor base limits: 3200000/3200000
Large primes per side: 3
Large prime bits: 27/27
Max factor residue bits: 50/50
Sieved algebraic special-q in [1600000, 2400001)
Primes: RFBsize:230209, AFBsize:230419, largePrimes:7530904 encountered
Relations: rels:7451513, finalFF:629444
Max relations in full relation-set: 28
Initial matrix: 460708 x 629444 with sparse part having weight 52954694.
Pruned matrix : 325045 x 327412 with weight 28218188.
Total sieving time: 29.63 hours.
Total relation processing time: 0.40 hours.
Matrix solve time: 3.93 hours.
Time per square root: 0.29 hours.
Prototype def-par.txt line would be:
gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000
total time: 34.26 hours.
 --------- CPU info (if available) ----------

Jan 11, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(5·10151-41)/9 = (5)1501<151> = 8807 · 2090089 · C141

C141 = P41 · P101

P41 = 11985535893412477734546646139854999516751<41>

P101 = 25181248688759856231710588775652390270239456503420879894844818915001826111432510170224977191479409487<101>

Number: 55551_151
N=301810760000077146934882355719805754244522020140143157553847294497017706100796642885120166592755779952215374038834393599733412999151844816737
  ( 141 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=11985535893412477734546646139854999516751 (pp41)
 r2=25181248688759856231710588775652390270239456503420879894844818915001826111432510170224977191479409487 (pp101)
Version: GGNFS-0.77.1
Total time: 36.08 hours.
Scaled time: 21.54 units (timescale=0.597).
Factorization parameters were as follows:
name: 55551_151
n: 301810760000077146934882355719805754244522020140143157553847294497017706100796642885120166592755779952215374038834393599733412999151844816737
m: 1000000000000000000000000000000
c5: 50
c0: -41
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2100001)
Relations: rels:5700417, finalFF:582235
Initial matrix: 353156 x 582235 with sparse part having weight 52139676.
Pruned matrix : 306424 x 308253 with weight 17013977.
Total sieving time: 32.85 hours.
Total relation processing time: 0.30 hours.
Matrix solve time: 2.80 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 36.08 hours.
 --------- CPU info (if available) ----------

Jan 9, 2006 (2nd)

By Yousuke Koide / GMP-ECM

(10613-1)/9 = (1)613<613> = 116511326129882791<18> · 1338285489332902166657911<25> · 1167883827993965201733843631<28> · C544

C544 = P36(1578...) · P36(4178...) · C473

P36(1578...) = 157818501697366913685542354577959717<36>

P36(4178...) = 417832220121515364538149502380148831<36>

C473 = [92529686120873990343331646774569359605383200587531417818236454390368869356415580228140609613497955460838507350423994235002078982421038981440839145461968437684528151941016349039119710736708391988071730726458391973172748638236782424739028612908524572972797032173010469396535113785013391541941058401658302567269148785675157132157433612203464707174823357971319412397911253267576408572089565418449213549477068089648406765856499332638101600661504414922416754050898040460592701003<473>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 9, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(4·10151-13)/9 = (4)1503<151> = 32 · 569 · 739 · 296843 · 2093219419<10> · C130

C130 = P57 · P73

P57 = 608858606877851551008985766196261799773945455000342152507<57>

P73 = 3104275453960187109937984286123825972776995247295782410574851825856126963<73>

Number: 44443_151
N=1890064828263309725274083499046605546833450559934940425099723669089227887530971292896451763065906695772892072780173366261700746241
  ( 130 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=608858606877851551008985766196261799773945455000342152507 (pp57)
 r2=3104275453960187109937984286123825972776995247295782410574851825856126963 (pp73)
Version: GGNFS-0.77.1
Total time: 35.91 hours.
Scaled time: 23.92 units (timescale=0.666).
Factorization parameters were as follows:
name: 44443_151
n: 1890064828263309725274083499046605546833450559934940425099723669089227887530971292896451763065906695772892072780173366261700746241
m: 1000000000000000000000000000000
c5: 40
c0: -13
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2100001)
Relations: rels:5703153, finalFF:584406
Initial matrix: 352876 x 584406 with sparse part having weight 52535784.
Pruned matrix : 305996 x 307824 with weight 17082130.
Total sieving time: 32.57 hours.
Total relation processing time: 0.36 hours.
Matrix solve time: 2.85 hours.
Time per square root: 0.13 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 35.91 hours.
 --------- CPU info (if available) ----------

Jan 7, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(7·10151-43)/9 = (7)1503<151> = 33 · 29 · C148

C148 = P59 · P90

P59 = 45315988862875285213569229229556178268002361973050983850023<59>

P90 = 219200886965523354035724320238357087792206973888306661944263918310909301395050880685320197<90>

Number: 77773_151
N=9933304952462040584645948630622960124875833688094224492691925642117212998439052078898822193841350929473534837519511849013764722576983113381580814531
  ( 148 digits)
SNFS difficulty: 151 digits.
Divisors found:
 r1=45315988862875285213569229229556178268002361973050983850023 (pp59)
 r2=219200886965523354035724320238357087792206973888306661944263918310909301395050880685320197 (pp90)
Version: GGNFS-0.77.1
Total time: 45.55 hours.
Scaled time: 30.33 units (timescale=0.666).
Factorization parameters were as follows:
name: 77773_151
n: 9933304952462040584645948630622960124875833688094224492691925642117212998439052078898822193841350929473534837519511849013764722576983113381580814531
m: 1000000000000000000000000000000
c5: 70
c0: -43
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2300001)
Relations: rels:5323814, finalFF:394816
Initial matrix: 351642 x 394816 with sparse part having weight 35764287.
Pruned matrix : 344365 x 346187 with weight 26333968.
Total sieving time: 40.55 hours.
Total relation processing time: 0.29 hours.
Matrix solve time: 4.55 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 45.55 hours.
 --------- CPU info (if available) ----------

Jan 5, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1

(2·10153+61)/9 = (2)1529<153> = 47 · 45584453 · 28080199986351056858875439<26> · C118

C118 = P39 · P79

P39 = 671616835389977570079621109237856169919<39>

P79 = 5499853356503855968659112953597044134358448571426698521260112204765203148087759<79>

Number: 22229_153
N=3693794106404065858730314506980409104367505481133478480581009263807454409922295169004251243400306482394846724627921521
  ( 118 digits)
SNFS difficulty: 153 digits.
Divisors found:
 r1=671616835389977570079621109237856169919 (pp39)
 r2=5499853356503855968659112953597044134358448571426698521260112204765203148087759 (pp79)
Version: GGNFS-0.77.1
Total time: 56.97 hours.
Scaled time: 37.88 units (timescale=0.665).
Factorization parameters were as follows:
name: 22229_153
n: 3693794106404065858730314506980409104367505481133478480581009263807454409922295169004251243400306482394846724627921521
m: 1000000000000000000000000000000
c5: 2000
c0: 61
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2700001)
Relations: rels:5744016, finalFF:475866
Initial matrix: 352137 x 475866 with sparse part having weight 49699157.
Pruned matrix : 333291 x 335115 with weight 25753267.
Total sieving time: 51.98 hours.
Total relation processing time: 0.44 hours.
Matrix solve time: 4.41 hours.
Time per square root: 0.15 hours.
Prototype def-par.txt line would be:
snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 56.97 hours.
 --------- CPU info (if available) ----------

Jan 5, 2006

By Wataru Sakai / GMP-ECM 6.0.1

3·10162-1 = 2(9)162<163> = 1586308304691323221318531843777<31> · C133

C133 = P36 · P98

P36 = 152512406662190891155427973892329217<36>

P98 = 12400194079641198397538641885769926694273799859212033454948583982801438301040530455353496340235711<98>

3·10167-1 = 2(9)167<168> = 7 · 7643 · 5308447 · C157

C157 = P38 · C119

P38 = 22854213927330216399615920416772214007<38>

C119 = [46219535988371850084418374386615219342097027661120626172731378243865022947240172061060017102055950948979932685073852531<119>]

Jan 3, 2006

By Sinkiti Sibata / GGNFS-0.77.1

(2·10152+61)/9 = (2)1519<152> = 19 · 661 · 3110104741<10> · C138

C138 = P36 · P103

P36 = 212106865486264043300787031493682199<36>

P103 = 2682271187373818595628680353095781651261120492663158413594580075578341939139175919064741649056564506009<103>

Number: 22229_152
N=568928133937980278199098064552428646633330057246257057269990790106201631376496707972280571278537623830907316340729803882559809990871833791
  ( 138 digits)
SNFS difficulty: 152 digits.
Divisors found:
 r1=212106865486264043300787031493682199 (pp36)
 r2=2682271187373818595628680353095781651261120492663158413594580075578341939139175919064741649056564506009 (pp103)
Version: GGNFS-0.77.1
Total time: 40.24 hours.
Scaled time: 26.76 units (timescale=0.665).
Factorization parameters were as follows:
name: 22229_152
n: 568928133937980278199098064552428646633330057246257057269990790106201631376496707972280571278537623830907316340729803882559809990871833791
m: 1000000000000000000000000000000
c5: 200
c0: 61
skew: 2
type: snfs
Factor base limits: 2400000/2400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1200000, 2200001)
Relations: rels:5449459, finalFF:461888
Initial matrix: 352626 x 461888 with sparse part having weight 40268875.
Pruned matrix : 331996 x 333823 with weight 20373572.
Total sieving time: 35.71 hours.
Total relation processing time: 0.34 hours.
Matrix solve time: 4.04 hours.
Time per square root: 0.14 hours.
Prototype def-par.txt line would be:
snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000
total time: 40.24 hours.
 --------- CPU info (if available) ----------

Jan 1, 2006 (3rd)

By Yousuke Koide / GMP-ECM

(10867-1)/9 = (1)867<867> = 3 · 37 · 613 · 42773 · 210631 · 2071723 · 52986961 · 93101929 · 1112647111<10> · 5363222357<10> · 234771432523<12> · 6270681177984151<16> · 13168164561429877<17> · 93195753455238027770502373<26> · 74451201112778571232641337987561693<35> · 25086158646798685749029022942725879293529996353937930044688310225209792405267161387550045665503080767367139652501504645587640324255739525766942448322852994756555563269219516158897234150632016254115138596672215506548424356751044570760748443769<242> · C465

C465 = P35 · C431

P35 = 20086446755059947304637543254330027<35>

C431 = [43847928340273007036683492466629425347593144386187849570352692715343015468508233711269987298844088842010811958146922848088904584451385409058136753439089940818345804415994995588939268929792742826083627766997939694984246400007687684923922833991165782358300738461285079416521540204902744071543408565874874731448917358285646695823461539103120712047524782671709937412975148617883482385473395336582811704194633808078648898999907547620693<431>]

Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 1, 2006 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1

(10153+71)/9 = (1)1529<153> = 7 · 5113880010251<13> · C139

C139 = P51 · P89

P51 = 102810924599828884362050857164373075486103832573319<51>

P89 = 30190454557728793269250249717674139102743562662711596919033095611883027825428747426710493<89>

Number: 11119_153
N=3103908547169215253162254552873669619616617637161201595918077528854736573322626119479853392157234575315036994281948666107068847843409136267
  ( 139 digits)
SNFS difficulty: 155 digits.
Divisors found:
 r1=102810924599828884362050857164373075486103832573319 (pp51)
 r2=30190454557728793269250249717674139102743562662711596919033095611883027825428747426710493 (pp89)
Version: GGNFS-0.77.1
Total time: 53.43 hours.
Scaled time: 35.48 units (timescale=0.664).
Factorization parameters were as follows:
name: 11119_153
n: 3103908547169215253162254552873669619616617637161201595918077528854736573322626119479853392157234575315036994281948666107068847843409136267
m: 10000000000000000000000000000000
c5: 1
c0: 7100
skew: 2
type: snfs

Factor base limits: 3000000/3000000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [1500000, 2800001)
Relations: rels:5486477, finalFF:518137
Initial matrix: 434532 x 518137 with sparse part having weight 39785945.
Pruned matrix : 414550 x 416786 with weight 23920260.
Total sieving time: 47.55 hours.
Total relation processing time: 0.32 hours.
Matrix solve time: 5.41 hours.
Time per square root: 0.16 hours.
Prototype def-par.txt line would be:
snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000
total time: 53.43 hours.
 --------- CPU info (if available) ----------

Jan 1, 2006

By Kenichiro Yamaguchi / GGNFS-0.77.1

10179-3 = (9)1787<179> = C179

C179 = P44 · P62 · P74

P44 = 47527552610960667080491218952801922312569073<44>

P62 = 38918563279240249010933742596447312973214118388632853991466677<62>

P74 = 54062702222061890579230284912359478718122077297383163210696543917211696057<74>

Number: 99997_179
N=99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997
  ( 179 digits)
SNFS difficulty: 180 digits.
Divisors found:
 r1=47527552610960667080491218952801922312569073 (pp44)
 r2=38918563279240249010933742596447312973214118388632853991466677 (pp62)
 r3=54062702222061890579230284912359478718122077297383163210696543917211696057 (pp74)
Version: GGNFS-0.77.1
Total time: 623.03 hours.
Scaled time: 484.09 units (timescale=0.777).
Factorization parameters were as follows:
name: 99997_175
n: 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999997 
m: 1000000000000000000000000000000000000 
c5: 1
c0: -30
type: snfs
skew: 1
qintsize: 100000
Factor base limits: 7400000/7400000
Large primes per side: 3
Large prime bits: 27/27
Sieved special-q in [3700000, 8100001)
Relations: rels:6798472, finalFF:1134568
Initial matrix: 1002617 x 1134568 with sparse part having weight 56588036.
Pruned matrix : 947705 x 952782 with weight 39508237.
Total sieving time: 606.40 hours.
Total relation processing time: 0.97 hours.
Matrix solve time: 15.38 hours.
Time per square root: 0.28 hours.
Prototype def-par.txt line would be:
snfs,180,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000
total time: 623.03 hours.
 --------- CPU info (if available) ----------

Note: This is the second largest number factored by GGNFS in our tables. Congratulations!