Table of contents

  1. December 2004
  2. November 2004
  3. October 2004
  4. September 2004
  5. August 2004
  6. July 2004
  7. June 2004
  8. May 2004
  9. April 2004
  10. March 2004
  11. February 2004
  12. January 2004

December 2004

Dec 31, 2004

By Makoto Kamada / GMP-ECM 5.0.3

(35·10192-53)/9 = 3(8)1913<193> = 1637 · 3959391502285618111<19> · C171

C171 = P31 · P141

P31 = 1902831840384627321743557842401<31>

P141 = 315317445054668231466894928407418052176979857291002402769887593292955927140627717865032030003548506786533662654988210078682631168818914249769<141>

Dec 30, 2004 (2nd)

By Wataru Sakai / GMP-ECM

(2·10185-11)/9 = (2)1841<185> = 32 · 359 · 421 · 1087 · C176

C176 = P27 · C149

P27 = 993965187607299234770545369<27>

C149 = [15120554373554536809234562282082433804237632080329979107830133430786296738906060498222935854150096195649500877326258778496443087888428857652973202257<149>]

Dec 30, 2004

By Makoto Kamada / PPSIQS, PFGW

(101314+17)/9 = 11...113<1314> is prime.

Dec 28, 2004 (2nd)

By Makoto Kamada / GMP-ECM 5.0.3

(23·10188+1)/3 = 7(6)1877<189> = 13 · 41 · 929 · 1163 · 2371 · 357136939157939605250647<24> · C154

C154 = P28 · C126

P28 = 5115162052884287672659773391<28>

C126 = [307367694999875553737492429759713462809392993487376399203199693098476266926067270006622194260810515476294038695403330251569111<126>]

(71·10162-17)/9 = 7(8)1617<163> = 3 · 243502289 · 116444549857<12> · C143

C143 = P30 · C114

P30 = 128270027616314750452923569549<30>

C114 = [723014790938678651721147391990553557307168178882364588086043927423948319684735855253124973472587538762189468083777<114>]

Dec 28, 2004

By Shusuke Kubota / GGNFS-0.72.6

(8·10126-53)/9 = (8)1253<126> = 181650851122063<15> · C112

C112 = P41 · P72

P41 = 47779997009825364594464778334350093705527<41>

P72 = 102415083220217550609994342087264735608014189248540563036727476735646283<72>

Dec 26, 2004

By Makoto Kamada / GMP-ECM 5.0.3

(35·10196-53)/9 = 3(8)1953<197> = 33 · 13 · 84349 · 461651807 · 446380663993523863<18> · 18926803629417875634761866211<29> · C135

C135 = P24 · P111

P24 = 908799301214037157739831<24>

P111 = 370572601126933505818972951766246195700206529887515200446193569195537707291856741066535946708729578200520407957<111>

(4·10198-7)/3 = 1(3)1971<199> = C199

C199 = P26 · C173

P26 = 35433614694519093943915021<26>

C173 = [37629052097232818667461377267500258556528765122464137560967604709699561844372971913230440011564750950923381136673132384892693048327207884015141809874584076051079951831846111<173>]

(13·10155-31)/9 = 1(4)1541<156> = 3 · 11 · 3467296306805827<16> · C139

C139 = P26 · P113

P26 = 53176083389660692023025181<26>

P113 = 23739939025715336414882807123530767717941537308874831499933776828542756367871245825790200233389506764457581381871<113>

Dec 25, 2004

By Makoto Kamada / GMP-ECM 5.0.3

10191-3 = (9)1907<191> = 113 · 2454455881<10> · C180

C180 = P26 · C155

P26 = 13778267355178489115141197<26>

C155 = [26168071567655827784668613095752679469186561174274715129360764348641252465542696852075271284487059377732452739736751363821922726151257160699482936406081017<155>]

Dec 24, 2004 (2nd)

msieve 0.88 was released.

Quadratic Sieve Source Code (jasonp)

Dec 24, 2004

By Makoto Kamada / GMP-ECM 5.0.3

(89·10187+1)/9 = 9(8)1869<188> = 3 · 11 · 2113 · C184

C184 = P26 · P158

P26 = 53436670079527513453372141<26>

P158 = 26539618343392390368380352055345120368680743940244939749660016224269777920657790101145291847422912050143063087742829198697524309000191824413799439858404431901<158>

(17·10183-71)/9 = 1(8)1821<184>= 34 · 11 · 19 · 404051 · 1262581 · C168

C168 = P34 · C134

P34 = 8226908102544685947546600578514601<34>

C134 = [26585389367622980285597634026808282856915211378205220420001757511984116964702632958717990400249729741198964996462743818335851565740519<134>]

Dec 23, 2004 (3rd)

By Makoto Kamada / GMP-ECM 5.0.3

(65·10186+43)/9 = 7(2)1857<187> = 3 · 89 · 4679 · 597347347464359<15> · 1063097615099489<16> · 48686557186389825347<20> · C132

C132 = P29 · C104

P29 = 14690759029212971209960298983<29>

C104 = [12727794571503673891861633135672096636151861671189328309590168102650816980079545459487050908766251834789<104>]

Dec 23, 2004 (2nd)

By Wataru Sakai / GMP-ECM

(10169+53)/9 = (1)1687<169> = 7 · 423599701769<12> · 1052364121297714227371<22> · C135

C135 = P35 · C101

P35 = 18307918306050479551975785178628311<35>

C101 = [19449068501458045327500024953679334708298737317275986294768751101310893283329289738705475713907062479<101>]

(10195+71)/9 = (1)1949<195> = 7 · 17 · 23 · 2389 · 12658232542072891<17> · C172

C172 = P32 · C140

P32 = 54775119319789267517672726665291<32>

C140 = [24508128083609856106882937213433754990235080308233947248497274818116540519436837105107908460599060015366174127469342984467972328959407611243<140>]

Dec 23, 2004

By Makoto Kamada / GMP-ECM 5.0.3

(7·10135+11)/9 = (7)1349<135> = 311557 · 638558070133433464879<21> · C109

C109 = P26 · P83

P26 = 57239702533873135368356933<26>

P83 = 68299928839346941052777163320649254834472709556110044073808899477677543549258602821<83>

Dec 22, 2004

By Makoto Kamada / GMP-ECM 5.0.3

(34·10192-43)/9 = 3(7)1913<193> = 31 · 383 · 2817168331182533<16> · C174

C174 = P30 · C144

P30 = 303858227491837508671753047587<30>

C144 = [371699641301045371715009397719700819194689634622987190169463978076986750813314250294469112308304309717672733098887774670224422497803703559243331<144>]

Dec 21, 2004 (3rd)

By Shusuke Kubota / GGNFS-0.72.6 / 9.27 hours on Celeron 2.5GHz

(7·10129+11)/9 = (7)1289<129> = 19 · 292 · 2511503 · 108933706067<12> · C108

C108 = P43 · P65

P43 = 2283988048706725299301369546639948434838543<43>

P65 = 77896173863502176571577678368953373896208627033496246039633699907<65>

Dec 21, 2004 (2nd)

711...117, 311...113, 199...991 and 177...771 (n≤150) were completed.

Factorizations of the Plateau and Depression numbers were completed up to n=150. Many sequences of them were finished by Greg Childers and GGNFS.

Dec 21, 2004

By Greg Childers / GGNFS

(64·10149+53)/9 = 7(1)1487<150> = 34 · 11 · 239 · 3140489951628443<16> · 92248545285620965837<20> · C110

C110 = P45 · P65

P45 = 227609230400940542986888598100153182950382309<45>

P65 = 50642490439835718189428667246630220888405040722636658823591995707<65>

(28·10142+17)/9 = 3(1)1413<143> = 3 · 61 · 397 · 929 · 445940406966740321<18> · C118

C118 = P42 · P76

P42 = 106540935181710634812146198229680364269369<42>

P76 = 9702080662448933987065740048827096886400601223981574208001722106465596982803<76>

(28·10144+17)/9 = 3(1)1433<145> = 31 · 43 · 283 · 511487 · 38231297339<11> · 14125658889973<14> · C110

C110 = P46 · P64

P46 = 5863383766003845426545406587677594940597698973<46>

P64 = 5091998492558949370668423992575290217029909268874571443087414611<64>

(28·10146+17)/9 = 3(1)1453<147> = C147

C147 = P45 · P103

P45 = 215042343423248601224429232591047426278759019<45>

P103 = 1446743493204865942525593959923268509919858672928989291036331355757624848206979381830636837666024790427<103>

(28·10147+17)/9 = 3(1)1463<148> = 11 · 29 · 379 · 362767017637<12> · 4490115412771<13> · C119

C119 = P55 · P64

P55 = 3379960048529008835409795832584003030196599486272692489<55>

P64 = 4674000593576153338391447008543295421946203065781538473141212771<64>

2·10138-9 = 1(9)1371<139> = 7 · 1361 · C135

C135 = P65 · P70

P65 = 28067396514726202523860938206489746457258001501485978553895083833<65>

P70 = 7479485083314129370275849920397548796557371512278764262868303993853001<70>

2·10140-9 = 1(9)1391<141> = 17 · 59113 · C135

C135 = P47 · P89

P47 = 11920269538992421121435956097648950019099811559<47>

P89 = 16695983163826097420159437859577435460952586279369215627290094387500562238589852030582969<89>

2·10144-9 = 1(9)1431<145> = 7 · 47 · 1697 · 4751 · 15421121 · 324513125593<12> · C117

C117 = P57 · P60

P57 = 573979583578236121980436103332418434430645159014685375809<57>

P60 = 262495926279377751706900324634363777228196866952780943282841<60>

2·10146-9 = 1(9)1451<147> = 1471 · 958054117111388133836953<24> · C120

C120 = P48 · P72

P48 = 248481397786006983813082785705803914377145937759<48>

P72 = 571127931149896369612391508288727305834841885540092677990337631749027823<72>

2·10148-9 = 1(9)1471<149> = 57431787553239244660626976882036073<35> · C114

C114 = P45 · P70

P45 = 252248599228180796094726301293542573587723903<45>

P70 = 1380539695291779642420640847677458347322068680428219755758017617145889<70>

2·10150-9 = 1(9)1491<151> = 72 · 313 · 5857 · 19249 · 48073 · C134

C134 = P58 · P77

P58 = 2145366910370960233318195778943906318667242154816224697409<58>

P77 = 11215105892080335130809942373623305706116017816514634296425819268673685145143<77>

(16·10142-61)/9 = 1(7)1411<143> = 13 · 14011 · 168481 · C132

C132 = P49 · P84

P49 = 3563479047113386761119623011481295788624826790313<49>

P84 = 162569790755232174632253038467971580277889280486954183359029125576276166458052487149<84>

(16·10143-61)/9 = 1(7)1421<144> = 3 · 11 · 541 · 3777559 · 41314201 · 585278303828958603403<21> · C105

C105 = P46 · P59

P46 = 6781373468336971839816239803424973990462518899<46>

P59 = 16075909995899462039765753864202879468478273494535100080009<59>

Dec 20, 2004

GGNFS-0.72.6 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 19, 2004 (4th)

By Wataru Sakai / GMP-ECM

(10179+71)/9 = (1)1789<179> = 17 · 43 · C176

C176 = P28 · C148

P28 = 9049402502510222344057348417<28>

C148 = [1679655468607621721991622154551885402806533022303409245104185450719565742097648958717415511161217486545435460473818370679440714209715530546103064797<148>]

(10193+71)/9 = (1)1929<193> = 3 · 83 · 1431244686853<13> · 4508363445277<13> · C165

C165 = P31 · C135

P31 = 1413521664942116360011121415991<31>

C135 = [489241024496907354315699990163522497568807868639472158427158410636880445374402685926600142762794996201973895068523081010022271307068961<135>]

Dec 19, 2004 (3rd)

GGNFS-0.72.5 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 19, 2004 (2nd)

By Makoto Kamada / GMP-ECM 5.0.3

(65·10169+43)/9 = 7(2)1687<170> = 7 · 11 · 23 · 68659 · 4321029614939<13> · C150

C150 = P27 · P123

P27 = 530897822686884962677615417<27>

P123 = 258914650400347979772352997931146995187006701423208429518294066462041557386591671044316656361151981352276780780439601952161<123>

Dec 19, 2004

By Sinkiti Sibata / GGNFS-0.70.1 / 56.62 hours

(16·10141-7)/9 = 1(7)141<142> = 2700157891<10> · 723675947437300258661473<24> · C108

C108 = P40 · P69

P40 = 2059716706349518931454333178468365050321<40>

P69 = 441709442271126037425440816784629391989083973497442626102237114143659<69>

Dec 18, 2004 (4th)

GGNFS-0.72.4 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 18, 2004 (3rd)

344...443 and 322...223 (n≤150) were completed.

Dec 18, 2004 (2nd)

By Greg Childers / GGNFS

(31·10149-13)/9 = 3(4)1483<150> = 11 · 109 · C147

C147 = P57 · P90

P57 = 460950251520524706530553225277879860588205486095525504899<57>

P90 = 623226548022901662551202045361712347011223958350429685982315610317292019855843356086236743<90>

(29·10140+7)/9 = 3(2)1393<141> = 778202447329343<15> · 255634545372895486257701<24> · C103

C103 = P47 · P57

P47 = 14599358663108219697910971266419485362482734451<47>

P57 = 110945470430273774745793119192113514201471215817716782511<57>

(29·10142+7)/9 = 3(2)1413<143> = 32 · C142

C142 = P47 · P95

P47 = 72676809139323704052905476303361918607632886971<47>

P95 = 49262577099619249943533650691225341348077300300841245943490622038640278667808424840167507319957<95>

(29·10146+7)/9 = 3(2)1453<147> = 17 · 19 · 31 · 251 · 1546424377213905874648018232119<31> · C110

C110 = P40 · P71

P40 = 4848526173866663057910655329664036964087<40>

P71 = 17099331001716948283396379468311539628698618084906876523024979878696657<71>

(29·10149+7)/9 = 3(2)1483<150> = 11 · 281 · 293 · 1732331 · C138

C138 = P62 · P76

P62 = 42837029641825804525955562286559217176950686548923355753737357<62>

P76 = 4794448269214011981143749845644741116116001253418507462237430283225763744863<76>

(29·10150+7)/9 = 3(2)1493<151> = 97 · 605486638403<12> · C137

C137 = P43 · P95

P43 = 4679166340772318350732117004005241862927997<43>

P95 = 11724942082485353843533433020987100707385825600287806825634979780638923301536053795840228051849<95>

(64·10148+53)/9 = 7(1)1477<149> = 19 · 29 · 739 · 1396523 · 1479913 · 51349048391867140770561613<26> · C106

C106 = P43 · P63

P43 = 9967543258841904417522097714798246109082401<43>

P63 = 165096026422179072094658317382771330545919884412110764726758719<63>

Dec 18, 2004

By Makoto Kamada / GMP-ECM 5.0.3

(65·10154+43)/9 = 7(2)1537<155> = 2903 · C152

C152 = P29 · P123

P29 = 39403853043503858648144059421<29>

P123 = 631371713196639185248714562919354903977906977865731980463798981070349227815458512741230212303393723150149371924035521455529<123>

Dec 17, 2004 (4th)

By Makoto Kamada / PFGW v1.2 RC1d

(13·103883+23)/9 = 144...447<3884> and (13·103883+41)/9 = 144...449<3884> are quasi-repdigit twin PRPs. These twin PRPs are the new record of the largest known quasi-repdigit twin PRPs in our tables.

Dec 17, 2004 (3rd)

355...553 (n≤150) was completed.

Dec 17, 2004 (2nd)

By Greg Childers / GGNFS

(32·10144-23)/9 = 3(5)1433<145> = 383 · 1867 · 32069 · 491186890889<12> · 601542130669492044017<21> · C102

C102 = P49 · P54

P49 = 2823771980123860179925775653461357305045257981711<49>

P54 = 185838853516964345350674982007227448082307037218837519<54>

Dec 17, 2004

By Makoto Kamada / GMP-ECM 5.0.3

(67·10199+23)/9 = 7(4)1987<200> = 7 · 11 · 107 · 127 · 28019 · 31477349 · C182

C182 = P30 · P153

P30 = 392167369159626686630550297457<30>

P153 = 205698836039776681355251012909841390282900437647629545411809050461810170629288834346279937426562252492963093662881506361037147935518256982678931785012097<153>

(14·10178-41)/9 = 1(5)1771<179> = 18077 · 970583 · 1735406205257<13> · 1745824177303<13> · C144

C144 = P27 · C117

P27 = 390328319148709270682251559<27>

C117 = [749712543163762808092051180657424884788820203073702176064721437535025801283241160904783569650296980815170595794069349<117>]

Dec 16, 2004 (3rd)

GGNFS-0.72.3 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 16, 2004 (2nd)

By Greg Childers / GGNFS

(31·10138-13)/9 = 3(4)1373<139> = 401 · 12893 · 12796260241<11> · 32929379212201443533<20> · C103

C103 = P48 · P55

P48 = 554633079933542031591579522742284342348517448827<48>

P55 = 2850679897768946559674743117034328399343889356271523721<55>

(31·10139-13)/9 = 3(4)1383<140> = 32 · 11 · 6701 · 21661 · 544650650153<12> · C118

C118 = P52 · P67

P52 = 2811507313834452114978909949105462027192928332606231<52>

P67 = 1565339792198947156697525257721137106919198765964637815049851256959<67>

(31·10145-13)/9 = 3(4)1443<146> = 3 · 11 · 487 · C142

C142 = P46 · P96

P46 = 6393603290665443480881234946610729026930442627<46>

P96 = 335220521651667107218263786787058988531447285220162861949338018864065764032755852659552020024879<96>

(31·10147-13)/9 = 3(4)1463<148> = 11 · 71 · 479 · 158838667231<12> · C131

C131 = P55 · P77

P55 = 3725073438097583761450446773397119494749844316356871593<55>

P77 = 15561145506225560175962989989424633757984940983855470418315679653575452991279<77>

(32·10150-23)/9 = 3(5)1493<151> = 2503 · 870363835261<12> · C136

C136 = P45 · P91

P45 = 194933845780761498493769886876022080930190049<45>

P91 = 8372565063096327905371943814043884867748842695140487878773556389068879437910468067490768259<91>

(64·10138+53)/9 = 7(1)1377<139> = 13 · 23 · 419 · 97673 · C129

C129 = P61 · P69

P61 = 1052353020314591008868541069764109032283018939271285517954081<61>

P69 = 552225267501012347389213738145076502574147575051856567905610514951589<69>

(64·10144+53)/9 = 7(1)1437<145> = 132 · C143

C143 = P64 · P80

P64 = 3246208754910879163055187223222904457641401288132318036614219281<64>

P80 = 12962068590155777291886746877946054984585085319160237158221903879170639247980853<80>

(64·10150+53)/9 = 7(1)1497<151> = 13 · 172 · 1637 · 2909 · 146161 · 1680823 · C130

C130 = P59 · P71

P59 = 51282266809016720519204373549550234146821081068719639373219<59>

P71 = 31548823397773504003120507136102584888224633364181214122391057893172301<71>

Dec 16, 2004

By Wataru Sakai / GMP-ECM

(10160+53)/9 = (1)1597<160> = 19 · 197753 · C153

C153 = P29 · P124

P29 = 32153282272391582463785808433<29>

P124 = 9197197143541566352036992011167749604031684102841422515193498657056297262146411381413519532306022893669673640065317970473607<124>

Dec 15, 2004 (5th)

By Makoto Kamada / GMP-ECM 5.0.3

(83·10195+61)/9 = 9(2)1949<196> = 11 · 307 · 311 · C190

C190 = P31 · C160

P31 = 4833547434892721567340970805149<31>

C160 = [1816678800589205850678424867940972226068049860751790110242961033905951362648474454003602444521902168474105268092631266292494058628857653685711600584129938854943<160>]

Dec 15, 2004 (4th)

By Greg Childers / GGNFS-0.70.0, GGNFS-0.71.7 / 303 hours (12 days and 15 hours)

(16·10175-1)/3 = 5(3)175<176> = C176

C176 = P43 · P134

P43 = 3809865316728652188521021727126618149052923<43>

P134 = 13998745073520892175014741138026536702111802636628910125487741607654260812520248593507784157795562918507819534511398477530470887314671<134>

Even though the factor was unfortunately smaller than our hopes, this is the new record of the largest number factored by GGNFS in our tables. Congratulations!
ggnfs.log (edited because of GGNFS problems)

Dec 15, 2004 (3rd)

By Makoto Kamada / GMP-ECM 5.0.3

(34·10196-43)/9 = 3(7)1953<197> = 3 · 3049 · 220117579995449<15> · 6082933562488974875094137<25> · C154

C154 = P24 · C130

P24 = 637323208774495304079671<24>

C130 = [4839830943105633696299301741374201570992839784033415334780269648603480365146737448838678293254973474826576076504959048705689662033<130>]

Dec 15, 2004 (2nd)

GGNFS-0.72.2 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 15, 2004

By Makoto Kamada / GMP-ECM 5.0.3, msieve 0.87

(10154+71)/9 = (1)1539<154> = 35 · 854869 · 2970437718965177<16> · 50125992759858511<17> · C113

C113 = P26 · P42 · P46

P26 = 10284751290915106911292019<26>

P42 = 428115055933763296537972075861137296953451<42>

P46 = 8158567576053432819049447894238169488585549399<46>

Dec 14, 2004 (6th)

By Sinkiti Sibata / GGNFS-0.70.1 / 34.26 hours

(16·10140-7)/9 = 1(7)140<141> = 32 · 4283 · C136

C136 = P46 · P91

P46 = 1255732917140267214235755887825512553979909037<46>

P91 = 3672735143054920858870024280177506909993855314539893398136327244475556479693338563201319543<91>

Dec 14, 2004 (5th)

11...117, 11...119, 755...557, 755...557, 788...887, 799...997, (n≤200) is available. These composite numbers passed GMP-ECM B1=74700...95290+alpha, over 100 times.

Dec 14, 2004 (4th)

755...557 (n≤150) was completed.

Dec 14, 2004 (3rd)

By Greg Childers / GGNFS

(68·10144+13)/9 = 7(5)1437<145> = 35 · 23 · 13945404136120024546427<23> · C119

C119 = P44 · P76

P44 = 23211451151738845633925222558021475575706593<44>

P76 = 4176369314833240238377846678742353391606662434841524592045050920015716823683<76>

(68·10145+13)/9 = 7(5)1447<146> = 7 · 11 · C144

C144 = P64 · P81

P64 = 3924112290854612071698252065274700350541910266881493019700289331<64>

P81 = 250054256481860730548134214414765998644899272453962050170910893493868726358200611<81>

(68·10148+13)/9 = 7(5)1477<149> = 22469 · 34809824759<11> · C134

C132 = P58 · P77

P58 = 3471085524687375963317592208635711331114334690023841311771<58>

P77 = 27830147468737212631279231922913712354156722622633589702232018214118020162277<77>

(32·10142-23)/9 = 3(5)1413<143> = 32 · 7 · 163 · C139

C139 = P62 · P77

P62 = 37052386610194089858497157707817016361529223865041303681128493<62>

P77 = 93446519026618071246939147177137029587740773266947403638405006224304646112009<77>

(32·10146-23)/9 = 3(5)1453<147> = 199 · 1004013187382899<16> · C130

C130 = P57 · P73

P57 = 620232911534784175359515185436256508463118883004253873169<57>

P73 = 2869195676553103553611261011625813130057391138589500599594406300755325437<73>

(32·10147-23)/9 = 3(5)1463<148> = 11 · 17 · 19 · 269 · C142

C142 = P32 · P45 · P66

P32 = 19807720402464734386066888634009<32>

P45 = 307825839486242903383200941887027385926143823<45>

P66 = 610127235327811591990564716338073902112550108597058390517294034147<66>

(32·10148-23)/9 = 3(5)1473<149> = 3 · 74 · C145

C145 = P64 · P82

P64 = 2336600842212296595339738075465078869491766404430005313162342671<64>

P82 = 2112562299719826137213358170247400044085579867209545258021531756610672011142726181<82>

Dec 14, 2004 (2nd)

By Anton Korobeynikov / GGNFS-0.71.9

(68·10143+13)/9 = 7(5)1427<144> = 11 · 167 · 1733 · C138

C138 = P48 · P90

P48 = 696668753191122752626885118291333116963574293177<48>

P90 = 340668793268167583982152596103912829483677946852078596397114775594959634036933728303335021<90>

(68·10146+13)/9 = 7(5)1457<147> = 883316111 · C138

C138 = P50 · P89

P50 = 60219299227531140351493841994138016855672231869409<50>

P89 = 14204127246749615447126583868720585230285770174675273371735992145641241202515285142665643<89>

Dec 14, 2004

By Makoto Kamada / msieve 0.87 / 5.9 hours

(8·10170-17)/9 = (8)1697<170> = 33 · 29 · 12289 · 20047 · 839916478644411211<18> · 31528405303865506514741<23> · 20073120811434752849076139<26> · C93

C93 = P44 · P50

P44 = 26154423033817308400292740294424628345830003<44>

P50 = 33145275390848276684510115292036240442121498596449<50>

Dec 13, 2004 (7th)

By Makoto Kamada / msieve 0.87 / 4.9 hours

(34·10165-43)/9 = 3(7)1643<166> = 7 · 11 · 151 · 521 · 197551 · 974989 · 2923190689<10> · 395209137409964686843<21> · 5921549992603136653212469<25> · C93

C93 = P40 · P54

P40 = 2483082289701751110405794664423845525849<40>

P54 = 190608132858769839835092587114608953328792302604968283<54>

Dec 13, 2004 (6th)

By Makoto Kamada / GMP-ECM 5.0.3

(83·10178+61)/9 = 9(2)1779<179> = 3 · 53 · 580639028849827970531<21> · C156

C156 = P27 · P130

P27 = 451940302079296897849001351<27>

P130 = 2210299689009418095104358190470413704614975776514014390656867590105814388845964997621074189972097637164793795116092662237699844351<130>

Dec 13, 2004 (5th)

11...117 (n≤150) was completed.

Dec 13, 2004 (4th)

By Greg Childers / GGNFS

(10149+53)/9 = (1)1487<149> = 1013 · 5227 · C142

C142 = P65 · P77

P65 = 23430958549178212402707250428155549302593049861696641748046787997<65>

P77 = 89558227449013240886491994775259054330327008822547351840698641976896740449511<77>

(10150+53)/9 = (1)1497<150> = 3 · 67 · 83 · 14503 · 2161417 · 69806218615185630871<20> · C115

C115 = P40 · P76

P40 = 1550861962896362912059273139971142622091<40>

P76 = 1962545224781331986129612684018787936117517536125682255077567793742609038509<76>

Dec 13, 2004 (3rd)

By Makoto Kamada / GGNFS-0.72.0 / 1.66 hours

(8·10168+1)/9 = (8)1679<168> = 1753 · 34897 · 83516827 · 80165767057<11> · 4834032192520903818107<22> · 94198351040254255401851<23> · C97

C97 = P35 · P63

P35 = 30169491546237451126417322718589489<35>

P63 = 157976940889535480798393803341491245339384466696501354253146107<63>

Dec 13, 2004 (2nd)

By Makoto Kamada / msieve 0.87

(8·10174+1)/9 = (8)1739<174> = 19 · 97 · 16124164670147<14> · 221098473172853592548251<24> · 4262454753021520624390749153398250693570713<43> · C92

C92 = P25 · P68

P25 = 2366083081249221177484393<25>

P68 = 13414342849447855126321989865167738040587090052732205552308327988851<68>

This factoring took over 3 hours. It may be faster to use GGNFS for SNFS of 4·10116-2·1058+1.

Dec 13, 2004

By Sinkiti Sibata / GGNFS-0.70.1

(16·10138-7)/9 = 1(7)138<139> = 5323 · C135

C135 = P57 · P78

P57 = 649934656190487760276914498985166053925743092100945933373<57>

P78 = 513867689954309299765783673109096251362712759990535028034435498581446456796463<78>

Dec 12, 2004

By Makoto Kamada / msieve 0.87

(8·10158-17)/9 = (8)1577<158> = 3 · 1220340659<10> · 32286752089<11> · 72827732377<11> · 8301373285666551053<19> · 139473270822343305961<21> · C88

C88 = P31 · P58

P31 = 1169902647640413773391556110703<31>

P58 = 7623130284963374144087381380873323320095760613859702563373<58>

Dec 11, 2004 (4th)

By Makoto Kamada / msieve 0.87

(89·10153+1)/9 = 9(8)1529<154> = 11 · 31 · 61 · 563 · 617 · 1117 · 2633 · 30170927 · 13269024345448025737931<23> · 95346673734407302484957<23> · C86

C86 = P27 · P59

P27 = 199359831203703219591466201<27>

P59 = 61149772131444053967584347436622464995185610376773276810391<59>

Dec 11, 2004 (3rd)

msieve 0.87 was released.

Quadratic Sieve Source Code (jasonp)

Dec 11, 2004 (2nd)

By Makoto Kamada / GMP-ECM 5.0.3

(14·10156-41)/9 = 1(5)1551<157> = 3 · 19 · 1093 · 56633 · C147

C147 = P31 · P117

P31 = 1919321978500255112680979149073<31>

P117 = 229706404554227575881050953912992750721970586230677319515972406160550922439917765063028600524700241223343578439937939<117>

Dec 11, 2004

GGNFS-0.72.0 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 10, 2004 (4th)

By Anton Korobeynikov / GGNFS-0.71.4 / 58.05 hours

(86·10152+31)/9 = 9(5)1519<153> = 7 · 834108229 · C144

C144 = P46 · P49 · P49

P46 = 5916645523928895560960823067319451365163322579<46>

P49 = 2783345759919546350694624569529505710407778741641<49>

P49 = 9937857967881569744716675196424141346528220723527<49>

Dec 10, 2004 (3rd)

By Greg Childers / GGNFS

(10140+53)/9 = (1)1397<140> = 15859 · C135

C135 = P63 · P73

P63 = 161691650409957190061302716209501924724287055024494821243134517<63>

P73 = 4333053960970062840083114465588607914859544329042298986285990197655880739<73>

(10147+53)/9 = (1)1467<147> = 32 · 13 · 151 · C142

C142 = P44 · P99

P44 = 10392908444136833280614366847742405653164693<44>

P99 = 605142395504852185677280557529678463437111016154847913971417589537210607510736253010560300340667507<99>

(10148+53)/9 = (1)1477<148> = 31 · 1007701577<10> · 77394931309<11> · C126

C126 = P53 · P74

P53 = 26898408626574685411475228622320332544226431162701931<53>

P74 = 17085384328576636444339757093579807788530852090805211367408163306648009429<74>

Dec 10, 2004 (2nd)

GGNFS-0.71.9 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 10, 2004

GGNFS-0.71.8 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 9, 2004 (5th)

By Makoto Kamada / GMP-ECM 5.0.3

(82·10152+71)/9 = 9(1)1519<153> = 29 · 18500819251420504507<20> · C133

C133 = P29 · P104

P29 = 20320825861690147373696604259<29>

P104 = 83568196683319286258285200016862573476781318049153265408827931610734633480187591296569782940670468893547<104>

Dec 9, 2004 (4th)

By Shusuke Kubota / GGNFS-0.71.5

(10139+53)/9 = (1)1387<139> = 7 · 89603 · 494555401 · C124

C124 = P36 · P89

P36 = 176827799542399848274317146465458063<36>

P89 = 20256826497809082138672188977645433308832908147433208461196189192626007022311405140270879<89>

Dec 9, 2004 (3rd)

GGNFS-0.71.7 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 9, 2004 (2nd)

By Makoto Kamada / GMP-ECM 5.0.3

10190-3 = (9)1897<190> = 13 · 83 · 4643 · 60176382186443<14> · 24247727135706472746493<23> · C148

C148 = P26 · C122

P26 = 15856958895942670619463887<26>

C122 = [86270608381892148012698739631845419861639079433916728783296259834586875917761568164414847996201372303949473085717528423177<122>]

(13·10179-31)/9 = 1(4)1781<180> = 3 · 11 · C178

C178 = P29 · P149

P29 = 47555107054099220811823592857<29>

P149 = 92042782537003529143002241535802764554347167753625910240795469084669493153549273134827856152661551725168206897218757398977607257927676929695429419361<149>

Dec 9, 2004

By Sinkiti Sibata / GGNFS-0.70.1

(16·10136-7)/9 = 1(7)136<137> = 6673 · 18341 · 3019273298751951641903953<25> · C104

C104 = P42 · P62

P42 = 487032858873040250970401605234600730199253<42>

P62 = 98780824831805079961323248153464809705702148164960536849302921<62>

Dec 8, 2004 (4th)

By Makoto Kamada / GMP-ECM 5.0.3

(7·10141-43)/9 = (7)1403<141> = 17 · 53 · 282601199 · C130

C130 = P31 · P100

P31 = 1574316101332138785462689892739<31>

P100 = 1940281765520387244103496867893092651817906432972400795380473345512195790910670994377350923737040493<100>

Dec 8, 2004 (3rd)

By Sinkiti Sibata / GGNFS-0.70.1

(16·10132-7)/9 = 1(7)132<133> = 4091 · C129

C129 = P56 · P74

P56 = 39734988745756660736484277534239281808586565334587909561<56>

P74 = 10936412922253554084536350258014871846461387346020142817387129265559878427<74>

Dec 8, 2004 (2nd)

By Anton Korobeynikov / GGNFS-0.71.4 / 21.42 hours

(17·10155-71)/9 = 1(8)1541<156> = 72 · 11 · 2273 · 77509 · 477951899 · 856409645357881<15> · 27828450109337756621<20> · C102

C102 = P48 · P54

P48 = 463334366860167086975713144840516592702801361011<48>

P54 = 376891898680072906895465671777956457460775907782569723<54>

Dec 8, 2004

By Wataru Sakai / GMP-ECM

(5·10152-23)/9 = (5)1513<152> = 62809181451689<14> · C138

C138 = P32 · P107

P32 = 12548544045884127597307664939741<32>

P107 = 70487323789881755639863584147362798330937168877631959339433595235900542310291872512913681437975703092766797<107>

(5·10176-23)/9 = (5)1753<176> = 19 · 911 · C172

C172 = P34 · C138

P34 = 9838025667759598362012006539421529<34>

C138 = [326247780390063490080526567389407287772607756850489421386244699258972286197300264888556697435749420641611080508391884903615843955966802973<138>]

(5·10185-23)/9 = (5)1843<185> = 79 · 76231583 · 1164328700579194207<19> · C157

C157 = P32 · C126

P32 = 44029950759275554233180522078377<32>

C126 = [179945778510708836080589448871146949371246104317066383335530794551793683889740159757425063640639714889836321930337300962902711<126>]

(5·10199-23)/9 = (5)1983<199> = 3 · 31277 · 34583 · 36830777 · 6174445327<10> · 6305736184704221383<19> · C154

C154 = P36 · C118

P36 = 724344547984221899382886622270430893<36>

C118 = [1648271169388862731941891235732784535672931381905839004531566345519986740360582709947982611814951380175473284494571461<118>]

(5·10163+13)/9 = (5)1627<163> = 7 · 491 · 1046680382986660661<19> · C142

C142 = P26 · C116

P26 = 26988494111082482595723749<26>

C116 = [57220971289632372895013854360486568742682462018091052842231747397803851776811199836976065406658831179664130202209649<116>]

(5·10186+13)/9 = (5)1857<186> = 607 · 6829 · 182167813054452217<18> · 10476133674495648057887<23> · C140

C140 = P27 · C114

P27 = 190677856249892933027003657<27>

C114 = [368305966614359849878248308076574802324713112212101126609697090992222639256078430962020706404288947139555620813273<114>]

Dec 7, 2004 (4th)

By Makoto Kamada / GMP-ECM 5.0.3

(35·10196-53)/9 = 3(8)1953<197> = 33 · 13 · 84349 · 461651807 · 446380663993523863<18> · C163

C163 = P29 · C135

P29 = 18926803629417875634761866211<29>

C135 = [336776120953225288643226992880947527845758942085320941973414384306598461989585511719956906492874857738494126576871114666265672188235267<135>]

(85·10161+41)/9 = 9(4)1609<162> = 11 · 83 · 209449 · 1091088610187<13> · C142

C142 = P26 · P117

P26 = 33021332476616799373620007<26>

P117 = 137079569356035158482487428813303734714433035006722204903992526651466396669052463171631042443137570267364740891961453<117>

(4·10155-1)/3 = 1(3)155<156> = 151 · 641 · 7424986690579144283<19> · C132

C132 = P29 · P103

P29 = 32537224823637510391509266027<29>

P103 = 5702004715141250324592893927739745126640887028125912343545134331965464704909840526351019937949019814043<103>

Dec 7, 2004 (3rd)

Julien Peter Benney found that (4·10412+11)/3 = 133...337<413> and (4·10412+17)/3 = 133...339<413> were both known quasi-repdigit PRP. Since he certified them, they are largest known quasi-repdigit twin primes in our tables.

Dec 7, 2004 (2nd)

GGNFS-0.71.5 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 7, 2004

By Sinkiti Sibata / GGNFS-0.70.1

(16·10131-7)/9 = 1(7)131<132> = 33 · 139721 · 1392379 · 64448238772141583<17> · C102

C102 = P48 · P55

P48 = 126773620565632621474342903723317695123985413047<48>

P55 = 4142424598295145863695670107132026586654598300541319289<55>

Dec 6, 2004 (4th)

By Anton Korobeynikov / GGNFS 0.70.5 / 37.46 hours

(82·10137-1)/9 = 9(1)137<138> = 44349101 · 528962167 · 1588131761408045295839<22> · C101

C101 = P42 · P59

P42 = 281370009777220690515530704122601367281633<42>

P59 = 86915568294721639240260955391551243599117252530367574753259<59>

Dec 6, 2004 (3rd)

By Sinkiti Sibata / GGNFS-0.70.1

(16·10130-7)/9 = 1(7)130<131> = 12497 · 33461 · C122

C122 = P49 · P74

P49 = 2112089921820679781744198782415549997699574508339<49>

P74 = 20128915799688648372177091556396761859688862753096460181357741600342796879<74>

Dec 6, 2004 (2nd)

By Makoto Kamada / GMP-ECM 5.0.3

(5·10197-17)/3 = 1(6)1961<198> = 11 · 1571 · 1858081 · 1178143418903287<16> · C172

C172 = P31 · C142

P31 = 3522029825882670138039041087429<31>

C142 = [1250904186313340025450120284311952830351894795982674479551805374307412050854432355660691881603971802205820203665609456742869350344170229044487<142>]

(89·10180+1)/9 = 9(8)1799<181> = 17 · 711962455993260516463<21> · 37287164971883204362343<23> · 178087690675076789660107777<27> · C111

C111 = P28 · P83

P28 = 1836752405977035142322213813<28>

P83 = 66988090653869154796356914160027099834175680263483228734044444225891821948368819613<83>

Dec 6, 2004

By Sinkiti Sibata / GGNFS-0.70.1

(16·10127-7)/9 = 1(7)127<128> = 114693613537<12> · C117

C117 = P52 · P66

P52 = 1432526224890454290005732653421985323921177043437903<52>

P66 = 108202091642690612080696186218659713612499366409534224544829733407<66>

Dec 5, 2004 (4th)

GGNFS-0.71.4 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 5, 2004 (3rd)

GGNFS-0.71.3 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 5, 2004 (2nd)

By Sinkiti Sibata / GGNFS-0.70.1

(16·10124-7)/9 = 1(7)124<125> = 19 · 201650400703<12> · C112

C112 = P49 · P63

P49 = 8061265009413844533245712365503543115208628772099<49>

P63 = 575601059094305216400883552872914415011012773679268369924032839<63>

Dec 5, 2004

By Makoto Kamada / GMP-ECM 5.0.3

(67·10192+23)/9 = 7(4)1917<193> = 588388657 · 473571759119<12> · C173

C173 = P27 · C147

P27 = 247113343178195423532631009<27>

C147 = [108115014113743706097313938559946532660489082228120055398223454136003589755006326987813757811102399272584414115207438615275324259808578167084402401<147>]

(19·10157-1)/9 = 2(1)157<158> = 3 · 7 · 4129 · 4139 · C149

C149 = P27 · C123

P27 = 136082245808735331544874467<27>

C123 = [432264947155761060829306720543648014786687216349608237446155217915853935721724780996199161863813705702775908099453240301483<123>]

Dec 4, 2004 (3rd)

GGNFS-0.71.1 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 4, 2004 (2nd)

By Sinkiti Sibata / GGNFS-0.70.1

(16·10123-7)/9 = 1(7)123<124> = 199 · 5600480939<10> · C112

C112 = P55 · P57

P55 = 3711635947520139376607971042276914863160805160094937273<55>

P57 = 429767629665384154819713549254016469779176647072708834109<57>

Dec 4, 2004

By Makoto Kamada / GMP-ECM 5.0.3

(67·10173+23)/9 = 7(4)1727<174> = 33 · 11 · 31 · C170

C170 = P31 · P140

P31 = 1766929502237122321235840283331<31>

P140 = 45760939050151198083124362442251491469266489532022812113975671545539418763484593578723515297321205480338552739180121531079776092367024738291<140>

(82·10165+71)/9 = 9(1)1649<166> = 11 · 29201 · 302966291 · 364565927850011<15> · 745566723451344502621<21> · C117

C117 = P25 · P93

P25 = 1727465953459239178198193<25>

P93 = 199395123722108219762101258306495643568878017823261529174109326165560747503185844363920385393<93>

(89·10175+1)/9 = 9(8)1749<176> = 3 · 11 · 2377 · 83045563 · 21545311091948629<17> · 127739194355601203<18> · C130

C130 = P27 · C104

P27 = 141537670211263258844233207<27>

C104 = [38970767349783144219279011210910131816536940309633342017981904856586050373395627747411366558141016535387<104>]

10197-3 = (9)1967<197> = 310081 · 7705783 · C185

C185 = P26 · P160

P26 = 19800200290640756281384783<26>

P160 = 2113676338782529383631911341697070869314713846244158628386025817812523873083823305465977453836754943580723873981756958063209332596570098946045694781651672856933<160>

Dec 3, 2004 (2nd)

By Shusuke Kubota / GGNFS-0.70.5

(7·10124+11)/9 = (7)1239<124> = 3 · 172 · 258238199 · C113

C113 = P50 · P64

P50 = 19868732321027394216451642651070948350251914069663<50>

P64 = 1748420098107193426676503120668847937109279362577915086064334601<64>

By Shusuke Kubota / GGNFS-0.70.8

(7·10126+11)/9 = (7)1259<126> = 22271 · 80747 · 901095332672663<15> · C102

C102 = P37 · P66

P37 = 1537394659614008849872667637402373837<37>

P66 = 312200294478902060785162453270293641028258099510397454756653037557<66>

Dec 3, 2004

By Makoto Kamada / GMP-ECM 5.0.3

(89·10197+1)/9 = 9(8)1969<198> = 11 · 1097 · 34754543550863119<17> · 647278217121651105541<21> · 19529714814982986435712937<26> · C132

C132 = P26 · P106

P26 = 99429846509411749958422469<26>

P106 = 1876000427359727953324536228737013368523167019576875931142646854395957088873360379620808498186817858813341<106>

(13·10159-31)/9 = 1(4)1581<160> = 11 · 523 · 104233 · C151

C151 = P26 · C125

P26 = 42526728145464632871517871<26>

C125 = [56642088762451993788216439528213975846550803193188960613596424777252377675643954980444537446717541555381340504538287254009879<125>]

(13·10185-31)/9 = 1(4)1841<186> = 32 · 11 · 432 · 145650497 · C172

C172 = P24 · C148

P24 = 616424391175458370238527<24>

C148 = [8788949140262138501748897593892201010008266230539906431857259336313619515107342349987432858956812504209471310423515168067698813237717931981034195989<148>]

Dec 2, 2004 (2nd)

GGNFS-0.70.8 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 2, 2004

GGNFS-0.70.7 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 1, 2004

By Sander Hoogendoorn / GMP-ECM

(10167-7)/3 = (3)1661<167> = 31 · 14423429872606091<17> · C149

C149 = P28 · P122

P28 = 5664959712306389776211251367<28>

P122 = 13159872405639673476085451592514711254830025807888333907677621446969621966794316849249920344102308883420682926710686585633<122>

(10168-7)/3 = (3)1671<168> = 131 · C166

C166 = P35 · C131

P35 = 49129598861427367631541486362214571<35>

C131 = [51792184773653319969285271375059174848183340563143297361801486678007691346322178986782793210838274087534397894208901070916797560531<131>]

(10172-7)/3 = (3)1711<172> = 19609 · 3691043 · 157129729 · 39201016808809<14> · 4609274485532784321203087<25> · C115

C115 = P30 · P35 · P52

P30 = 570122674955008147531767848417<30>

P35 = 11333195299738113424648260115996519<35>

P52 = 251052899844665539831518869295788289023081792664233<51>

(2·10163+43)/9 = (2)1627<163> = 7 · 665141705436521827<18> · C144

C144 = P26 · C119

P26 = 16929455156593115948878553<26>

C119 = [28192415356793158638192183338666628496972623324831542589743436403638771282467070408328673563565546545108383620701535231<119>]

November 2004

Dec 1, 2004 (2nd)

322...221, 322...227, 322...229, 344...447, 344...449, 355...557, 355...559, 366...661, 366...667, 377...771, 377...779, 388...881, 388...887, 388...889, 399...997, 400...007, 400...009, 411...113, 411...117, 411...119 and 933...337 (n≤100) are available.

Nov 30, 2004 (7th)

By Makoto Kamada / GMP-ECM 5.0.3

10192-3 = (9)1917<192> = 3373 · 1103279 · C183

C183 = P26 · C157

P26 = 30864312787215673925304239<26>

C157 = [8706461730553172977813938282972806864367872281670324568896027694773613506445164070346157989738792353402973884613674914181525210628797616969415943359190918769<157>]

Nov 30, 2004 (6th)

GGNFS-0.70.5 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Nov 30, 2004 (5th)

msieve 0.86 was released.

Quadratic Sieve Source Code (jasonp)

Nov 30, 2004 (4th)

44...441 (n≤150) was completed.

Nov 30, 2004 (3rd)

By Greg Childers / GGNFS

(4·10130-31)/9 = (4)1291<130> = 75527 · 220937753 · 576740377 · C108

C108 = P50 · P58

P50 = 82316388271718992535493854854902462632193974477977<50>

P58 = 5610203963132911588641032634751981165774474014979257829159<58>

(4·10131-31)/9 = (4)1301<131> = 19 · 59 · 29663681603<11> · C118

C118 = P32 · P86

P32 = 19898201668653412909642060123783<32>

P86 = 67169635286000088005844876733316178067015095264586514159340939544920440830653975497429<86>

(4·10132-31)/9 = (4)1311<132> = 3 · 41 · 60631 · 5836027724826491<16> · C110

C110 = P45 · P65

P45 = 265065681903452574231618672879301887100401451<45>

P65 = 38525367449329849902508906228617759067605667618693350206245274677<65>

(4·10133-31)/9 = (4)1321<133> = 5721928315993231<16> · C117

C117 = P58 · P60

P58 = 1735452327903854190023457957435424681329865983947155036639<58>

P60 = 447571455406096696043129588706088166397164260457243328029449<60>

(4·10136-31)/9 = (4)1351<136> = 83 · C134

C134 = P56 · P78

P56 = 79451228100693916255143231337984876222044824965114646033<56>

P78 = 673967221238885072947092435754689304476836110066757345212331509269592690413619<78>

(4·10137-31)/9 = (4)1361<137> = 41 · C136

C136 = P46 · P90

P46 = 6869123999252418154919315865684516827094541121<46>

P90 = 157809182106244750209852121177286389343708081076801048075413388076705668185445417312005681<90>

(4·10140-31)/9 = (4)1391<140> = 23 · C139

C139 = P65 · P74

P65 = 24518156032205797056772046449083639191754617378818170209503581971<65>

P74 = 78813722664143068054142655919643641120799630958057702523852687920859278677<74>

(4·10142-31)/9 = (4)1411<142> = 41 · 97 · 170353 · 823811777 · 43558364561<11> · 2022943313791<13> · C101

C101 = P39 · P63

P39 = 236820510953045757591589885882927684211<39>

P63 = 381601010506268970060209410967573719387449808922893251533526613<63>

Nov 30, 2004 (2nd)

By Shusuke Kubota / GGNFS-0.70.3

(5·10130+31)/9 = (5)1299<130> = 3 · 23 · 51427 · 26450620557023929943<20> · C104

C104 = P52 · P53

P52 = 4635144405734630957124292278499961746134157093520999<52>

P53 = 12769917141727375254462396830140380254077895120501449<53>

Nov 30, 2004

By Wataru Sakai / GMP-ECM

(5·10156+13)/9 = (5)1557<156> = 61 · 35883949 · C147

C147 = P42 · C106

P42 = 141949580829913622469021786349231378104071<42>

C106 = [1787982709613837304766056524502437988069122805088687283861386909168481258575131304571383347300968369897803<106>]

Nov 29, 2004 (5th)

522...227 and 522...229 (n≤100) are available.

Nov 29, 2004 (4th)

By Makoto Kamada / GMP-ECM 5.0.3

(65·10178+43)/9 = 7(2)1777<179> = 47 · 113 · 526853 · 117345719 · 331998677 · 125870285644374589<18> · C136

C136 = P32 · C105

P32 = 34925085627768598997827271895379<32>

C105 = [150709555076264278185583346205721159950525735347533468788839353587238178965623321225618403977229020577573<105>]

(82·10168+71)/9 = 9(1)1679<169> = 47 · 20771 · 2738014493<10> · 8340066325362023339<19> · C135

C135 = P28 · P107

P28 = 7262015406780976497651635071<28>

P107 = 56279945247362475178321704744702295910960579330789100156703457165720974711163852864758122202783987702363211<107>

(89·10180+1)/9 = 9(8)1799<181> = 17 · 711962455993260516463<21> · 37287164971883204362343<23> · C137

C137 = P27 · C111

P27 = 178087690675076789660107777<27>

C111 = [123040536680301911313422257942859732764642569947211890294501585759146536824001134870642602879460846543813914369<111>]

Nov 29, 2004 (3rd)

By Makoto Kamada

Quasi-repdigit
(47·1074+43)/9 = 522222222222222222222222222222222222222222222222222222222222222222222222227<75>
and
(47·1074+61)/9 = 522222222222222222222222222222222222222222222222222222222222222222222222229<75>
are twin primes.

Nov 29, 2004 (2nd)

By Sander Hoogendoorn / msieve

(7·10143-43)/9 = (7)1423<143> = 59 · 35869 · 191783 · 3444401 · 44469666660757781600487511<26> · C100

C100 = P47 · P53

P47 = 24948940438712878811224813097421187454482816577<47>

P53 = 50146942064568647740731181087923885752797750645042963<53>

Nov 29, 2004

311...117, 311...119, 622...227, 755...559, 799...991, 877...773, 899...993 and 955...553 (n≤100) are available.

Nov 28, 2004 (5th)

By Shusuke Kubota / GGNFS-0.70.1

(5·10126+31)/9 = (5)1259<126> = 521 · 792151 · 156296359 · C109

C109 = P52 · P58

P52 = 4788555075836757340511905624313572115822592076397359<52>

P58 = 1798574571163878516629102891778727258723642619099647230209<58>

Nov 28, 2004 (4th)

By Makoto Kamada / GMP-ECM 5.0.3

10168-3 = (9)1677<168> = 757 · 24733 · 13293083 · 869228495029187<15> · C139

C139 = P28 · C112

P28 = 3574884941983036986718429117<28>

C112 = [1293021014233451367860042934501894795317867498820089424677269278083402029329064783389164520002782265317692374641<112>]

(17·10187-71)/9 = 1(8)1861<188> = 11 · 38049998170671837090688817<26> · C161

C161 = P30 · P131

P30 = 500583471801384822334086674083<30>

P131 = 90153497646641310326944319538203642791563401319391629531885316013320146569086840682444563959288491745885439016303429741998231221761<131>

(34·10185-43)/9 = 3(7)1843<186> = 11 · 61 · 83 · 1316321 · 623003279 · 18576467372337956163671<23> · C144

C144 = P27 · P117

P27 = 943456638254876301560541259<27>

P117 = 471952813067679536412424737894219140870046369285479378119371881739921957018989451689975654750562766644831308181474011<117>

Nov 28, 2004 (3rd)

GGNFS-0.70.3 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Nov 28, 2004 (2nd)

GGNFS-0.70.2 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Nov 28, 2004

By Chris Monico / GGNFS

(8·10123-71)/9 = (8)1221<123> = 59 · 2371 · 39675256449581<14> · C105

C105 = P41 · P65

P41 = 13743112145606138592276235346147400975883<41>

P65 = 11653572407563622678749471750669621137543866870846033463628735823<65>

Nov 27, 2004 (4th)

msieve 0.85 was released.

Quadratic Sieve Source Code (jasonp)

Nov 27, 2004 (3rd)

By Makoto Kamada / GMP-ECM

(85·10164+41)/9 = 9(4)1639<165> = 13 · C164

C164 = P25 · C139

P25 = 9275757052376397976700267<25>

C139 = [7832198734760978711300895023427036398367349101003456204899634720632547083923743972218242866754462014563820003748123331699889049038309233519<139>]

Nov 27, 2004 (2nd)

By Chris Monico / GGNFS

(79·10124-7)/9 = 8(7)124<125> = 3 · 17 · 558451843 · 2197459741159<13> · C103

C103 = P45 · P58

P45 = 978064542225600247365749793689829702362300081<45>

P58 = 1433970560180904882402161060064805652850063739099545014191<58>

Nov 27, 2004

By Tyler Cadigan / msieve

(61·10129-7)/9 = 6(7)129<130> = 32 · 159503 · 1686796403<10> · 1845746771074187<16> · C100

C100 = P38 · P63

P38 = 15011723137161761012900283660230077453<38>

P63 = 101020759799138908138104413379091516200230288773064326782116947<63>

Nov 26, 2004

msieve 0.84 was released.

Quadratic Sieve Source Code (jasonp)

Nov 25, 2004 (3rd)

By Makoto Kamada / GMP-ECM 5.0.3, msieve 0.83

(4·10180-7)/3 = 1(3)1791<181> = 439 · 523 · 468246781 · 7005540497<10> · C157

C157 = P26 · P131

P26 = 49126811938877552796360949<26>

P131 = 36036076265445438586478714042933026041107308690559018523356664426584143141830063618501543233862519218295082853384877539172172913311<131>

(17·10158-71)/9 = 1(8)1571<159> = 47 · 239 · 557 · 3046148953<10> · 31515879309500237<17> · 160815156612194113<18> · C109

C109 = P26 · P28 · P56

P26 = 19929262765951023340195939<26>

P28 = 4471053250096044906331280357<28>

P56 = 21945568692107157846002081502727353184117153310937384959<56>

Nov 25, 2004 (2nd)

By Wataru Sakai / GMP-ECM

(5·10190-23)/9 = (5)1893<190> = 3 · 17 · 30130033 · 779004426475729<15> · 46962959609138895677063<23> · C143

C143 = P38 · C106

P38 = 61642877659009561805910411419732303873<38>

C106 = [1603169430525280273237360004572538062979242075276083440879876329917685791614748633736351381778420177694221<106>]

(5·10167+13)/9 = (5)1667<167> = 32 · 4027 · 10463 · 12941 · 44897457148379489<17> · C138

C138 = P28 · C111

P28 = 1519650041086432620438421693<28>

C111 = [165925816166136783147225072078845728669837032683683114399003933918276111210507446722985872485375711425173815489<111>]

(5·10194+13)/9 = (5)1937<194> = 32 · 29 · C192

C192 = P32 · C160

P32 = 72183554542030111065458816494591<32>

C160 = [2948823122470032866495397931641631076837872862146515937374630399399691716360185120348712377301754173916545728370837830033590887336640616636222383068117446587807<160>]

Nov 25, 2004

By Makoto Kamada / GMP-ECM 5.0.3

(13·10176-31)/9 = 1(4)1751<177> = 33 · 13789411323683<14> · 20108993600248507<17> · C146

C146 = P27 · P119

P27 = 919274982543929146287864137<27>

P119 = 20987251902277439315835412886692413430000160319885037281360957482093961933965137116493522296638638966863414764101433939<119>

Nov 24, 2004 (4th)

By Tyler Cadigan / msieve

(67·10156+23)/9 = 7(4)1557<157> = 374537 · 4814221 · 227689867 · 338290097399<12> · 413613060941<12> · 72510490965281<14> · C100

C100 = P38 · P63

P38 = 14917762329505675779775661725272770447<38>

P63 = 119806334369687274043260690713148583532971512794600312831270741<63>

Nov 24, 2004 (3rd)

msieve 0.83 was released.

Quadratic Sieve Source Code (jasonp)

Nov 24, 2004 (2nd)

266...663, 266...669, 277...771, 277...773, 277...779, 288...881, 288...883, 288...887, 288...889, 299...993, 300...007, 355...551, 399...991, 400...003 and 799...993 (n≤100) are available. Informations of prime numbers of these sequences will be added later.

Nov 24, 2004

By Chris Monico / GGNFS using GNFS

(8·10148-53)/9 = (8)1473<148> = 32 · 7 · 431 · 248738599 · 134896475509<12> · 81297467634174116800523<23> · C102

C102 = P41 · P61

P41 = 33362022211327796044904182030601554515509<41>

P61 = 3597132922037104807822989294234113281590924432430024026595303<61>

Nov 23, 2004 (3rd)

By Makoto Kamada / GMP-ECM 5.0.3

(89·10198+1)/9 = 9(8)1979<199> = 31 · 83 · 431 · 12487 · 83813 · 1079213 · C178

C178 = P28 · C151

P28 = 2166408303061502899372383833<28>

C151 = [3644294481802054702074482416107025751122026723203262487883027906121152932420037231524191511230107502368223926430246726131550570211348197102339570924797<151>]

Nov 23, 2004 (2nd)

799...997, 788...887 and 11...119 (n≤150) were completed.

Nov 23, 2004

By Greg Childers / GGNFS

8·10139-3 = 7(9)1387<140> = 7 · 112 · 43 · 75504318159299399<17> · C119

C119 = P56 · P63

P56 = 53181657984068063389700004228999618220712448404117930933<56>

P63 = 547021578430613077164648426239735659338966913240144796636418371<63>

8·10141-3 = 7(9)1407<142> = 11 · 17 · 61 · 6959 · 302847772207<12> · C123

C123 = P58 · P66

P58 = 1185232496324771611590117896185458422554822208631466121153<58>

P66 = 280765521984314571728757275616961371379255644747798552859870702739<66>

8·10145-3 = 7(9)1447<146> = 7 · 11 · 526853 · 17889769 · 4083062647<10> · C122

C122 = P49 · P73

P49 = 5432017963480199442613897882981427399940756907141<49>

P73 = 4970016502471565136207973969627421842489501711999009641490689905361979799<73>

8·10146-3 = 7(9)1457<147> = 1754323 · C141

C141 = P41 · P101

P41 = 18351387702450182134423448389687445402087<41>

P101 = 24849148948365694342391056763061445659228526938352956792115566893567105171128030431206393684524186297<101>

8·10149-3 = 7(9)1487<150> = 11 · C149

C149 = P49 · P101

P49 = 1608596188928145380118735290506229512519831269403<49>

P101 = 45211640576951157081593994501104368226546751365593910539229359833369471085265494438783448596836822709<101>

(71·10147-17)/9 = 7(8)1467<148> = 3 · 11 · 7866941 · C140

C140 = P49 · P92

P49 = 2411716854538498351434879565592026270255766655401<49>

P92 = 12599975127327249106637760921991198006549550241223232357269921755064764788764675455843046379<92>

(10133+71)/9 = (1)1329<133> = 3 · 221133233 · 402697969 · C115

C115 = P57 · P58

P57 = 611251062157160116053505645645324711651025064485264201597<57>

P58 = 6804295316508357009360057256130556002704534027000187849417<58>

(10134+71)/9 = (1)1339<134> = 66930601 · 2577926833<10> · C116

C116 = P54 · P63

P54 = 152520855991614307365754769680642555850200904536277789<54>

P63 = 422214306274309203634349912768473401465731860766384413693202387<63>

(10140+71)/9 = (1)1399<140> = 3019 · 88311091476456073451058821<26> · C110

C110 = P50 · P60

P50 = 52078789742353988905206507892145138499461319382907<50>

P60 = 800236289305257565863023061393908386883691754499093142776683<60>

(10146+71)/9 = (1)1459<146> = 19 · C144

C144 = P66 · P79

P66 = 184646504480794719922073218304967625981702798346467821334085569801<66>

P79 = 3167107459097619074471329268330657548194777692213070386010929467909308160277101<79>

(10148+71)/9 = (1)1479<148> = 3 · 8597 · 3852160831<10> · 9995876197<10> · C124

C124 = P32 · P92

P32 = 12476283869625123042297542871211<32>

P92 = 89676527294667108544580024600501584617379940687367211028857390036651681323077608208888583017<92>

(4·10129-31)/9 = (4)1281<129> = 33 · 72 · 29 · 47 · 69491 · 2910329 · C112

C112 = P40 · P72

P40 = 6644217187391228553272246466613438348297<40>

P72 = 183420263630950549926230025403996103660765791705539480901333728354630323<72>

Nov 22, 2004 (3rd)

By Sander Hoogendoorn / msieve

(5·10153-41)/9 = (5)1521<153> = 77487647 · 2204792656187868734453<22> · 774566864323827238548139<24> · C100

C100 = P34 · P66

P34 = 4868018463265120432019152903104101<34>

P66 = 862414673433490031047050515436939614937611480649348290013333269899<66>

Nov 22, 2004 (2nd)

By Makoto Kamada / GMP-ECM 5.0.3

(10166-7)/3 = (3)1651<166> = 73417 · 183263 · 290970679 · 49453772833844866271629206734839<32> · C116

C116 = P28 · P89

P28 = 1113136581588381763569732661<28>

P89 = 15467146780696512880245699179255829824832237755447208093092936733693117638812275194175521<89>

(65·10190+43)/9 = 7(2)1897<191> = 97 · 151 · 153349398479784413<18> · C170

C170 = P27 · C144

P27 = 183068228936534766174026813<27>

C144 = [175641488448662568292346598460069514633018298245744830567434504238051771414505754718431128038197886273870786613292219718333171634534692608363389<144>]

Nov 22, 2004

The condition of 744...447 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=92980+alpha) 100 times.

(67·10153+23)/9, (67·10154+23)/9, (67·10155+23)/9, (67·10156+23)/9, (67·10157+23)/9, (67·10158+23)/9, (67·10160+23)/9, (67·10161+23)/9, (67·10163+23)/9, (67·10165+23)/9, (67·10166+23)/9, (67·10167+23)/9, (67·10169+23)/9, (67·10170+23)/9, (67·10172+23)/9, (67·10173+23)/9, (67·10175+23)/9, (67·10177+23)/9, (67·10178+23)/9, (67·10179+23)/9, (67·10180+23)/9, (67·10182+23)/9, (67·10185+23)/9, (67·10186+23)/9, (67·10187+23)/9, (67·10189+23)/9, (67·10191+23)/9, (67·10192+23)/9, (67·10193+23)/9, (67·10194+23)/9, (67·10195+23)/9, (67·10196+23)/9, (67·10198+23)/9, (67·10199+23)/9, (67·10200+23)/9, (35/200)

The condition of 88...887 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=97260+alpha) 100 times.

(8·10153-17)/9, (8·10156-17)/9, (8·10157-17)/9, (8·10158-17)/9, (8·10159-17)/9, (8·10160-17)/9, (8·10164-17)/9, (8·10166-17)/9, (8·10168-17)/9, (8·10169-17)/9, (8·10170-17)/9, (8·10173-17)/9, (8·10176-17)/9, (8·10179-17)/9, (8·10180-17)/9, (8·10181-17)/9, (8·10182-17)/9, (8·10183-17)/9, (8·10184-17)/9, (8·10186-17)/9, (8·10187-17)/9, (8·10188-17)/9, (8·10189-17)/9, (8·10194-17)/9, (8·10196-17)/9, (8·10198-17)/9, (8·10199-17)/9, (8·10200-17)/9, (28/200)

The condition of 88...889 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=97540+alpha) 100 times.

(8·10152+1)/9, (8·10154+1)/9, (8·10157+1)/9, (8·10158+1)/9, (8·10160+1)/9, (8·10161+1)/9, (8·10163+1)/9, (8·10164+1)/9, (8·10166+1)/9, (8·10168+1)/9, (8·10169+1)/9, (8·10170+1)/9, (8·10172+1)/9, (8·10174+1)/9, (8·10175+1)/9, (8·10177+1)/9, (8·10181+1)/9, (8·10182+1)/9, (8·10183+1)/9, (8·10184+1)/9, (8·10185+1)/9, (8·10187+1)/9, (8·10188+1)/9, (8·10191+1)/9, (8·10193+1)/9, (8·10194+1)/9, (8·10196+1)/9, (8·10197+1)/9, (8·10199+1)/9, (29/200)

The condition of 944...449 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=99040+alpha) 100 times.

(85·10151+41)/9, (85·10152+41)/9, (85·10153+41)/9, (85·10155+41)/9, (85·10156+41)/9, (85·10157+41)/9, (85·10160+41)/9, (85·10161+41)/9, (85·10163+41)/9, (85·10164+41)/9, (85·10167+41)/9, (85·10168+41)/9, (85·10169+41)/9, (85·10171+41)/9, (85·10172+41)/9, (85·10173+41)/9, (85·10174+41)/9, (85·10175+41)/9, (85·10176+41)/9, (85·10178+41)/9, (85·10180+41)/9, (85·10181+41)/9, (85·10182+41)/9, (85·10183+41)/9, (85·10184+41)/9, (85·10185+41)/9, (85·10186+41)/9, (85·10187+41)/9, (85·10188+41)/9, (85·10190+41)/9, (85·10191+41)/9, (85·10193+41)/9, (85·10194+41)/9, (85·10195+41)/9, (85·10196+41)/9, (85·10197+41)/9, (85·10198+41)/9, (85·10199+41)/9, (38/200)

The condition of 988...889 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=100190+alpha) 100 times.

(89·10151+1)/9, (89·10152+1)/9, (89·10153+1)/9, (89·10156+1)/9, (89·10157+1)/9, (89·10158+1)/9, (89·10159+1)/9, (89·10161+1)/9, (89·10163+1)/9, (89·10164+1)/9, (89·10166+1)/9, (89·10167+1)/9, (89·10168+1)/9, (89·10169+1)/9, (89·10171+1)/9, (89·10173+1)/9, (89·10175+1)/9, (89·10176+1)/9, (89·10180+1)/9, (89·10181+1)/9, (89·10182+1)/9, (89·10183+1)/9, (89·10184+1)/9, (89·10185+1)/9, (89·10187+1)/9, (89·10188+1)/9, (89·10192+1)/9, (89·10194+1)/9, (89·10195+1)/9, (89·10196+1)/9, (89·10197+1)/9, (89·10198+1)/9, (89·10199+1)/9, (89·10200+1)/9, (34/200)

The condition of 99...997 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=100710+alpha) 100 times.

10153-3, 10154-3, 10156-3, 10160-3, 10161-3, 10163-3, 10164-3, 10165-3, 10167-3, 10168-3, 10170-3, 10173-3, 10175-3, 10176-3, 10178-3, 10179-3, 10181-3, 10182-3, 10183-3, 10184-3, 10185-3, 10186-3, 10188-3, 10189-3, 10190-3, 10191-3, 10192-3, 10193-3, 10194-3, 10195-3, 10196-3, 10197-3, 10198-3, 10199-3, (34/200)

Nov 20, 2004 (3rd)

By Shusuke Kubota / GGNFS-0.61.4

(10134+53)/9 = (1)1337<134> = 857 · C131

C131 = P36 · P95

P36 = 383340872454506628075311185389987877<36>

P95 = 33821396956493599820008975386545402390305808392843410894208806796427045074415792788778035519153<95>

Nov 20, 2004 (2nd)

GGNFS-0.70.1 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Nov 20, 2004

By Makoto Kamada / GGNFS-0.70.0

(52·10122-7)/9 = 5(7)122<123> = 727 · 411119 · C115

C115 = P53 · P62

P53 = 34326541091370501393491790752141817728023093828339547<53>

P62 = 56315614972351838954498824575900740272205844808950807812632507<62>

Nov 19, 2004 (6th)

By Makoto Kamada / GMP-ECM 5.0.3

10159-9 = (9)1581<159> = 557 · 787 · 66522203560881529<17> · 463502940459739711<18> · C119

C119 = P31 · P89

P31 = 5179103681557614987753607571009<31>

P89 = 14285529639955355530391178145824057096420000669920946451104886135613114248058746965615319<89>

Nov 19, 2004 (5th)

744...447 (n≤150) was completed.

Nov 19, 2004 (4th)

By Greg Childers / GGNFS

(67·10148+23)/9 = 7(4)1477<149> = 6661 · 141269 · 600751 · 36847794477555463628357<23> · C112

C112 = P53 · P59

P53 = 77114685180950478136168944173445251467824251338942361<53>

P59 = 46345001232140831568843313936274842864739135107245044052829<59>

(71·10138-17)/9 = 7(8)1377<139> = 3 · C139

C139 = P57 · P82

P57 = 497589033115324640626102330769306515629359267339105914379<57>

P82 = 5284741934857251295549603541307186208907336416374025172372021148916822046895889751<82>

(71·10139-17)/9 = 7(8)1387<140> = 72 · 11 · 79 · 255160033657<12> · C124

C124 = P38 · P86

P38 = 74683163719405354510140581375543030633<38>

P86 = 97222016550347459714234634927812482067585583291822069595377195849699467194412554310267<86>

(71·10140-17)/9 = 7(8)1397<141> = 67 · 11329115051407<14> · C127

C127 = P39 · P88

P39 = 438645112216249819274995785373443797591<39>

P88 = 2369363833052043505260160173273515243743938145451689220954572120377577758305105168418053<88>

Nov 19, 2004 (3rd)

By Tyler Cadigan / PPSIQS

(5·10172+13)/9 = (5)1717<172> = 101461595881<12> · 1613209310291<13> · 12790834324951<14> · 651617447839102781<18> · 25668188216953676600419<23> · C96

C96 = P46 · P50

P46 = 2256579594291633882026679617922701519986197101<46>

P50 = 70306849294485634326719382660244586464933649247803<50>

Nov 19, 2004 (2nd)

By Michael Peterson / GGNFS-0.61.5

(4·10127-13)/9 = (4)1263<127> = 3 · 47 · 53323 · C120

C120 = P46 · P75

P46 = 2846737118714661285060545448478612165177077451<46>

P75 = 207652148919543248026448953901026153521235458496800922573702157980311356351<75>

Nov 19, 2004

By Makoto Kamada / GGNFS-0.70.0

(7·10122+11)/9 = (7)1219<122> = 124247 · C117

C117 = P49 · P69

P49 = 3465222210340721307172630045672830146253255208019<49>

P69 = 180650234614923349183890268209847021508615869190124760161480053008903<69>

Nov 18, 2004 (3rd)

By Makoto Kamada / GGNFS-0.70.0

The first try of version 0.70.0 on Pentium 4, Windows XP and Cygwin completed all right.

3·10122-1 = 2(9)122<123> = 13 · C122

C122 = P52 · P71

P52 = 2294796717664213509541276266917758467689777187014509<52>

P71 = 10056194912293669804719011098323636255061719884507348567986171070655047<71>

Nov 18, 2004 (2nd)

The condition of 377...773 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=84110+alpha) 100 times.

(34·10153-43)/9, (34·10155-43)/9, (34·10157-43)/9, (34·10161-43)/9, (34·10163-43)/9, (34·10165-43)/9, (34·10166-43)/9, (34·10167-43)/9, (34·10170-43)/9, (34·10173-43)/9, (34·10174-43)/9, (34·10175-43)/9, (34·10177-43)/9, (34·10178-43)/9, (34·10181-43)/9, (34·10183-43)/9, (34·10185-43)/9, (34·10186-43)/9, (34·10187-43)/9, (34·10188-43)/9, (34·10189-43)/9, (34·10190-43)/9, (34·10192-43)/9, (34·10193-43)/9, (34·10194-43)/9, (34·10195-43)/9, (34·10196-43)/9, (34·10197-43)/9, (34·10198-43)/9, (34·10199-43)/9, (34·10200-43)/9, (31/200)

The condition of 911...119 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=98340+alpha) 100 times.

(82·10151+71)/9, (82·10152+71)/9, (82·10153+71)/9, (82·10154+71)/9, (82·10161+71)/9, (82·10163+71)/9, (82·10164+71)/9, (82·10165+71)/9, (82·10166+71)/9, (82·10167+71)/9, (82·10168+71)/9, (82·10172+71)/9, (82·10173+71)/9, (82·10174+71)/9, (82·10175+71)/9, (82·10177+71)/9, (82·10179+71)/9, (82·10180+71)/9, (82·10181+71)/9, (82·10183+71)/9, (82·10187+71)/9, (82·10188+71)/9, (82·10189+71)/9, (82·10190+71)/9, (82·10192+71)/9, (82·10194+71)/9, (82·10195+71)/9, (82·10196+71)/9, (82·10197+71)/9, (82·10198+71)/9, (82·10200+71)/9, (31/200)

The condition of 922...229 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=98660+alpha) 100 times.

(83·10151+61)/9, (83·10152+61)/9, (83·10153+61)/9, (83·10154+61)/9, (83·10155+61)/9, (83·10156+61)/9, (83·10158+61)/9, (83·10159+61)/9, (83·10160+61)/9, (83·10161+61)/9, (83·10162+61)/9, (83·10163+61)/9, (83·10165+61)/9, (83·10166+61)/9, (83·10167+61)/9, (83·10168+61)/9, (83·10169+61)/9, (83·10170+61)/9, (83·10171+61)/9, (83·10173+61)/9, (83·10175+61)/9, (83·10176+61)/9, (83·10177+61)/9, (83·10178+61)/9, (83·10179+61)/9, (83·10181+61)/9, (83·10182+61)/9, (83·10184+61)/9, (83·10187+61)/9, (83·10188+61)/9, (83·10191+61)/9, (83·10192+61)/9, (83·10193+61)/9, (83·10195+61)/9, (83·10196+61)/9, (83·10197+61)/9, (83·10199+61)/9, (83·10200+61)/9, (38/200)

The condition of 955...559 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=99430+alpha) 100 times.

(86·10151+31)/9, (86·10152+31)/9, (86·10153+31)/9, (86·10155+31)/9, (86·10156+31)/9, (86·10158+31)/9, (86·10159+31)/9, (86·10160+31)/9, (86·10161+31)/9, (86·10162+31)/9, (86·10165+31)/9, (86·10166+31)/9, (86·10170+31)/9, (86·10171+31)/9, (86·10172+31)/9, (86·10175+31)/9, (86·10179+31)/9, (86·10180+31)/9, (86·10181+31)/9, (86·10182+31)/9, (86·10183+31)/9, (86·10184+31)/9, (86·10185+31)/9, (86·10186+31)/9, (86·10187+31)/9, (86·10188+31)/9, (86·10190+31)/9, (86·10191+31)/9, (86·10192+31)/9, (86·10193+31)/9, (86·10196+31)/9, (86·10197+31)/9, (86·10198+31)/9, (86·10199+31)/9, (86·10200+31)/9, (35/200)

Nov 18, 2004

GGNFS-0.70.0 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Nov 17, 2004 (2nd)

377...773 and 944...449 (n≤150) were completed.

Nov 17, 2004

By Greg Childers / GGNFS

(34·10143-43)/9 = 3(7)1423<144> = 11 · C143

C143 = P40 · P103

P40 = 5303478323193975489275062193344653297859<40>

P103 = 6475643389214664909180905822993338651255997991637410391579885045738572199800323634627385095230925268877<103>

(34·10148-43)/9 = 3(7)1473<149> = 32 · 59 · 12421837 · 26327682121623217<17> · C123

C123 = P51 · P72

P51 = 339435016372168216277854822656985814339270594209291<51>

P72 = 640894865533744949021678034578262702800166230434500370652136337415752097<72>

(34·10150-43)/9 = 3(7)1493<151> = C151

C151 = P73 · P79

P73 = 2980537215871294317759980094532234409121960036227028511662295660263806351<73>

P79 = 1267482169879038992405294059376824542448418727805469492688123456470418239686723<79>

(67·10137+23)/9 = 7(4)1367<138> = 32 · 11 · 1571 · 50551 · 18269750344649<14> · C115

C115 = P47 · P69

P47 = 10156287015730778196999211751735183709270977147<47>

P69 = 510297668541113733518710301264640286143970176338167928025785941705931<69>

(67·10139+23)/9 = 7(4)1387<140> = 7 · 11 · 85911567017072873<17> · C122

C122 = P48 · P74

P48 = 920695274837121657898248118589298971174940825079<48>

P74 = 12222893092295961385055314244926886249835620193256574809182425146437055733<74>

(67·10143+23)/9 = 7(4)1427<144> = 3 · 11 · 31 · 13159 · 19841047 · 692381464768111<15> · C115

C115 = P58(1222...) · P58(3291...)

P58(1222...) = 1222987365207941762906051930348745347286644687421923020447<58>

P58(3291...) = 3291560054791071269844285142364452516591255150663218276529<58>

(85·10140+41)/9 = 9(4)1399<141> = 13 · 4643 · 4721 · 1445976434080537<16> · C118

C118 = P58 · P60

P58 = 7185202977372406738124895286507377353093766528786744142337<58>

P60 = 319006934401805449392521138728439368368844964268262905327839<60>

(85·10141+41)/9 = 9(4)1409<142> = 11 · 96749 · 179260417013026587193<21> · C116

C116 = P56 · P60

P56 = 78170189665155358092653238692237726604017262558070041689<56>

P60 = 633303193781516226270814722927272081726934528151469064377983<60>

(85·10143+41)/9 = 9(4)1429<144> = 11 · 227 · 1717310435311<13> · 7404568870433460660757<22> · C107

C107 = P53 · P54

P53 = 44729239939864587872517849482291434765564572455327231<53>

P54 = 664994065478731545703654437614496956118976190588081741<54>

(85·10146+41)/9 = 9(4)1459<147> = 13 · 73 · 131 · 78707 · 259788940891979<15> · C123

C123 = P61 · P63

P61 = 3612692399145289099027331849131992047083677728881360569817507<61>

P63 = 102842802859636437430118761940559312808050476371919719919781701<63>

Nov 16, 2004 (7th)

By Makoto Kamada / GGNFS-0.61.4

(61·10121-7)/9 = 6(7)121<122> = 223 · 315354798404287<15> · C105

C105 = P50 · P56

P50 = 18423527972719656968229812631186321366924817348451<50>

P56 = 52313071622735468570280541636546647612790890086478437627<56>

Nov 16, 2004 (6th)

By Shusuke Kubota / GGNFS-0.54.3

(10123+53)/9 = (1)1227<123> = 3 · 13 · 16067 · 959380519 · C108

C108 = P39 · P69

P39 = 368917856829460329650573295334531396279<39>

P69 = 500999759426416448871186438136088238949059695719088812453886753474009<69>

Nov 16, 2004 (5th)

GGNFS-0.61.4 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Nov 16, 2004 (4th)

By Wataru Sakai / GMP-ECM

(5·10175-41)/9 = (5)1741<175> = 489133 · 1403517697<10> · 2435964161<10> · C151

C151 = P35 · C116

P35 = 64249247182044594022865768916254657<35>

C116 = [51706328378056163380057929616176601960754010322432217032605771561958673172388892161904595921026362579749982059360763<116>]

(5·10174+13)/9 = (5)1737<174> = 31 · 739 · 11221210807<11> · C160

C160 = P30 · C130

P30 = 221346161669387451500036308199<30>

C130 = [9763592520336947007359034884938306233546605251950183851573132162119148768617416230383434152961326133795560572245272063951466393961<130>]

Nov 16, 2004 (3rd)

Factor Table Search was a little updated.

Nov 16, 2004 (2nd)

By Makoto Kamada / GGNFS-0.61.3

(43·10121-7)/9 = 4(7)121<122> = 61961 · 335824030006567<15> · C103

C103 = P45 · P58

P45 = 498556064068364905575377137019233347351998029<45>

P58 = 4605552695693333047245432826706557295713424427607537947499<58>

Nov 16, 2004

By Makoto Kamada / GGNFS-0.61.3

(22·10118-1)/3 = 7(3)118<119> = 13 · 683 · 46122677 · C108

C108 = P46 · P63

P46 = 1645278806247524322110275736013255813925797763<46>

P63 = 108838703703268525047206477794831273530117068085894281825039077<63>

Nov 15, 2004 (4th)

By Makoto Kamada / GGNFS-0.61.3

(43·10118-7)/9 = 4(7)118<119> = 19 · 73 · 98807 · 29833059967<11> · C101

C101 = P49 · P52

P49 = 4147371827027709956210621807528024586954927823123<49>

P52 = 2817675640632456793753470954967503987056023729336633<52>

Nov 15, 2004 (3rd)

By Makoto Kamada / GGNFS-0.61.3

(8·10117-53)/9 = (8)1163<117> = 89 · 69447271 · C108

C108 = P32 · P76

P32 = 35555281959278360488127292667277<32>

P76 = 4044810312396143794463348184833709654782980882148838408537911465131339725841<76>

Nov 15, 2004 (2nd)

By Tyler Cadigan / PPSIQS

(5·10173-23)/9 = (5)1723<173> = 73 · 577 · 751 · 209427319 · 8783707168871028931<19> · 3704223193820463194057<22> · 33330086533252283656753<23> · C94

C94 = P41 · P54

P41 = 13288553992830918869852640666681150366227<41>

P54 = 581924161406619836031991292764923727221002266889607761<54>

Nov 15, 2004

By Makoto Kamada / GGNFS-0.61.3

8·10177-1 = 7(9)177<178> = 31 · 136541 · 3253850111311<13> · 8440450795922006821<19> · 53333947698860662675169<23> · C118

C118 = P34 · P38 · P46

P34 = 9968872192820575739845949794271179<34>

P38 = 32415706285123016616200393430316452541<38>

P46 = 3992976744065553378877586365261068883948677889<46>

Nov 14, 2004 (3rd)

By Makoto Kamada / GMP-ECM 5.0.3

(25·10189-1)/3 = 8(3)189<190> = 13 · 69481 · 14970782913227<14> · C171

C171 = P26 · C145

P26 = 86676545786512496411372249<26>

C145 = [7109895749786147500037053236349479036870422351297426331907172161150490762823519055732095429805711272517938685442758987053038644233257005201690907<145>]

Nov 14, 2004 (2nd)

By Makoto Kamada / GGNFS-0.61.3

8·10174-1 = 7(9)174<175> = 7 · 23 · 727 · 991 · 350002054657009<15> · 3160024442975017<16> · 39310962534049663193199913018639770440327<41> · C97

C97 = P41 · P57

P41 = 13703043947707774181309400489721470123919<41>

P57 = 115761536241975308742677535865950439003423498765891054183<57>

Nov 14, 2004

By Makoto Kamada / GGNFS-0.61.3

8·10162-1 = 7(9)162<163> = 72 · 17 · 31 · 6271 · 37951 · 795079 · 62702211983<11> · 9651608955277596810279846533429791009<37> · C97

C97 = P29 · P68

P29 = 78743575385006325299358447097<29>

P68 = 34357003118610299424339551498938680210668232190655460506174192679073<68>

Nov 13, 2004 (2nd)

By Makoto Kamada / GGNFS-0.61.3

8·10153-1 = 7(9)153<154> = 109 · 5431 · 242491 · 1442849 · 1708950029029<13> · 5716279930669628639686312159912662372461<40> · C85

C85 = P39 · P46

P39 = 545504243838876787482318238398405996241<39>

P46 = 7248133656376375468073798954069159761372067671<46>

Nov 13, 2004

The condition of 133...331 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=75660+alpha) 100 times.

(4·10151-7)/3, (4·10152-7)/3, (4·10153-7)/3, (4·10156-7)/3, (4·10157-7)/3, (4·10158-7)/3, (4·10159-7)/3, (4·10161-7)/3, (4·10164-7)/3, (4·10165-7)/3, (4·10166-7)/3, (4·10167-7)/3, (4·10168-7)/3, (4·10169-7)/3, (4·10170-7)/3, (4·10171-7)/3, (4·10172-7)/3, (4·10173-7)/3, (4·10174-7)/3, (4·10175-7)/3, (4·10176-7)/3, (4·10180-7)/3, (4·10181-7)/3, (4·10182-7)/3, (4·10184-7)/3, (4·10186-7)/3, (4·10188-7)/3, (4·10189-7)/3, (4·10191-7)/3, (4·10192-7)/3, (4·10194-7)/3, (4·10195-7)/3, (4·10198-7)/3, (4·10199-7)/3, (4·10200-7)/3, (35/200)

The condition of 155...551 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=76480+alpha) 100 times.

(14·10152-41)/9, (14·10153-41)/9, (14·10154-41)/9, (14·10156-41)/9, (14·10157-41)/9, (14·10158-41)/9, (14·10159-41)/9, (14·10161-41)/9, (14·10162-41)/9, (14·10163-41)/9, (14·10164-41)/9, (14·10165-41)/9, (14·10166-41)/9, (14·10167-41)/9, (14·10168-41)/9, (14·10170-41)/9, (14·10171-41)/9, (14·10173-41)/9, (14·10174-41)/9, (14·10175-41)/9, (14·10176-41)/9, (14·10177-41)/9, (14·10178-41)/9, (14·10179-41)/9, (14·10180-41)/9, (14·10181-41)/9, (14·10182-41)/9, (14·10186-41)/9, (14·10187-41)/9, (14·10188-41)/9, (14·10189-41)/9, (14·10190-41)/9, (14·10191-41)/9, (14·10192-41)/9, (14·10193-41)/9, (14·10194-41)/9, (14·10195-41)/9, (14·10196-41)/9, (14·10197-41)/9, (14·10198-41)/9, (14·10199-41)/9, (14·10200-41)/9, (42/200)

The condition of 722...227 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=92290+alpha) 100 times.

(65·10152+43)/9, (65·10154+43)/9, (65·10155+43)/9, (65·10158+43)/9, (65·10159+43)/9, (65·10160+43)/9, (65·10161+43)/9, (65·10162+43)/9, (65·10164+43)/9, (65·10165+43)/9, (65·10166+43)/9, (65·10167+43)/9, (65·10169+43)/9, (65·10172+43)/9, (65·10176+43)/9, (65·10177+43)/9, (65·10178+43)/9, (65·10179+43)/9, (65·10182+43)/9, (65·10183+43)/9, (65·10184+43)/9, (65·10185+43)/9, (65·10186+43)/9, (65·10187+43)/9, (65·10189+43)/9, (65·10190+43)/9, (65·10191+43)/9, (65·10192+43)/9, (65·10194+43)/9, (65·10196+43)/9, (65·10197+43)/9, (65·10199+43)/9, (65·10200+43)/9, (33/200)

The condition of 766...667 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=93690+alpha) 100 times.

(23·10153+1)/3, (23·10157+1)/3, (23·10158+1)/3, (23·10160+1)/3, (23·10164+1)/3, (23·10169+1)/3, (23·10170+1)/3, (23·10172+1)/3, (23·10173+1)/3, (23·10174+1)/3, (23·10176+1)/3, (23·10177+1)/3, (23·10178+1)/3, (23·10180+1)/3, (23·10181+1)/3, (23·10184+1)/3, (23·10185+1)/3, (23·10186+1)/3, (23·10188+1)/3, (23·10189+1)/3, (23·10190+1)/3, (23·10191+1)/3, (23·10192+1)/3, (23·10193+1)/3, (23·10194+1)/3, (23·10197+1)/3, (23·10198+1)/3, (23·10199+1)/3, (28/200)

The condition of 799...99 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=95600+alpha) 100 times.

8·10152-1, 8·10153-1, 8·10155-1, 8·10158-1, 8·10160-1, 8·10161-1, 8·10162-1, 8·10164-1, 8·10166-1, 8·10167-1, 8·10169-1, 8·10170-1, 8·10173-1, 8·10174-1, 8·10177-1, 8·10178-1, 8·10181-1, 8·10182-1, 8·10184-1, 8·10185-1, 8·10186-1, 8·10187-1, 8·10190-1, 8·10194-1, (24/200)

Nov 12, 2004

By Wataru Sakai / GMP-ECM

(10181+17)/9 = (1)1803<181> = 3 · 157 · 1217 · 158606909 · 387812569 · C158

C158 = P34 · C125

P34 = 1081691731937760857100887471929643<34>

C125 = [29133892481734837183602135697334988973490703807163310757974571749978078052900604926957726939876253751243046373693076558774153<125>]

(5·10188-41)/9 = (5)1871<188> = 32 · 67 · 157 · 1793435534795269<16> · C168

C168 = P36 · P133

P36 = 267134885878370005277119281985794223<36>

P133 = 1224881717314040900003966370392762445148337572297326038461150343979893110447980944688343141490583702371013296142048512794374120985363<133>

(5·10164-41)/9 = (5)1631<164> = 3 · 117526809611<12> · C153

C153 = P38 · C115

P38 = 54250638606310858569979433501919015383<38>

C115 = [2904453570756846986973383368766510254862338723725138737049038603407688954012735912987940359365696468744723414038809<115>]

Nov 11, 2004 (2nd)

By Shusuke Kubota / GMP-ECM 5.0.3

5·10166-1 = 4(9)166<167> = 612 · 7951 · 18959 · 41274509 · C148

C148 = P31 · C118

P31 = 1036244557985917323855656628571<31>

C118 = [2084150015239379466226403787131225346381006673209676738496589056569037295167669261491044464939395894913070594199352569<118>]

Nov 11, 2004

By Wataru Sakai / GMP-ECM

(5·10176-41)/9 = (5)1751<176> = 3 · 631 · 6034033529<10> · 10013849773<11> · 98325221251437639817<20> · C133

C133 = P28 · P105

P28 = 8172399203041353880379167139<28>

P105 = 604440540003181334214627528981518639548131252892792355509643671843685185995458137125142862269356354234517<105>

Nov 10, 2004 (3rd)

155...551 (n≤150) was completed.

Nov 10, 2004 (2nd)

By Greg Childers / GGNFS

(14·10140-41)/9 = 1(5)1391<141> = 262957 · 185149963951<12> · 293696979540157<15> · C110

C110 = P45 · P65

P45 = 611167735359721131651023938164092454793426939<45>

P65 = 17799887559676111000753968199524325003033331268272810906175016891<65>

(14·10146-41)/9 = 1(5)1451<147> = 462781533101<12> · C135

C135 = P42 · P93

P42 = 493231383009790687144135213331307371354879<42>

P93 = 681488927382207827202832096409483809732888791409873843538464019986605749494194438375808835269<93>

(34·10141-43)/9 = 3(7)1403<142> = 7 · 11 · 79 · 30323 · 1070654677<10> · C125

C125 = P55 · P71

P55 = 1150467406789084646317263815788298645922128786669413151<55>

P71 = 16627336548404451230259421219086560971123953205611549150942066216686911<71>

Nov 10, 2004

From Tetsuya Kobayashi

The script files which had been used in the factoring of 10165-9 on Nov 5, 2004 (2nd) are here. A rough explanation of the mechanism is as follows. NFS (Network File System) is used for sharing a disk and ssh (Secure SHell) is used for distributing sieve. A control machine assigns sections of sieve and instructs remote machines to do it. Then, control machine gathers up the output of remote machines and run getdeps. Subsequent processes are usual. ``This method will be unfit for larger networks and makes waste results toward the end of sieving. I want to improve those points.'', Tetsuya said. Even though his work is based on an old version of GGNFS, I think that it is very informative as an example of ``distributed GGNFS''.

Nov 9, 2004 (7th)

Factor tables of 255...551, 255...557 and 255...559 (n≤100) are available. All numbers in these tables were already factored.

Nov 9, 2004 (6th)

From Tetsuya Kobayashi

The polynomial file, ggnfs.log and summary.txt in the factoring 10165-9 on Nov 5, 2004 (2nd) are as follows. Four computers were used to do it.

991.165.poly
ggnfs.log
summary.txt

Nov 9, 2004 (5th)

By Tyler Cadigan / PPSIQS

(5·10196+13)/9 = (5)1957<196> = 432 · 1303 · 95311 · 16645471 · 305975203 · 17456327041<11> · 467993930323<12> · 348239323090133<15> · 10869928941544246112083<23> · 15920968338005800540769<23> · C88

C88 = P43 · P46

P43 = 1314729888815890011093442548195842498866843<43>

P46 = 7338667339699725942422357211608308067654167063<46>

Nov 9, 2004 (4th)

133...331 (n≤150) was completed.

Nov 9, 2004 (3rd)

By Greg Childers / GGNFS

(4·10146-7)/3 = 1(3)1451<147> = 1281109731533<13> · 2234563696977490535633<22> · C113

C113 = P56 · P57

P56 = 98439010663907932205417984632078554317280747667922950079<56>

P57 = 473143008752484838804350645547273469784832370360525259601<57>

(4·10150-7)/3 = 1(3)1491<151> = 103 · 433943 · C143

C143 = P56 · P88

P56 = 12058263342574662438959655691436592978350691488471507041<56>

P88 = 2473910936766159973199719902466729409132239356434370646909254385804633819505535105310579<88>

(14·10137-41)/9 = 1(5)1361<138> = 11 · 163 · C134

C134 = P53 · P81

P53 = 88920796317638411687463231951204881856777214882567741<53>

P81 = 975667622925422126960632146695785317083089191200444881132941766852849468937342027<81>

(14·10139-41)/9 = 1(5)1381<140> = 11 · 2099 · C135

C135 = P40 · P96

P40 = 2741898126287923955302448597913250770643<40>

P96 = 245713539354369828297831585227405025854316047634215987451649126813861768951334373772077456329813<96>

Nov 9, 2004 (2nd)

By Tyler Cadigan / PPSIQS

(4·10175-1)/3 = 1(3)175<176> = 13 · 10235547982337443<17> · 132373637436174277711<21> · 1446827710291087147427<22> · 2909691937810300783183627<25> · C93

C93 = P32 · P61

P32 = 45300429502669183472430760826609<32>

P61 = 3969324772814128024854248303482597305276455455985027092405597<61>

Nov 9, 2004

By Wataru Sakai / GMP-ECM

(5·10192-17)/3 = 1(6)1911<193> = 2267 · 2940263 · C183

C183 = P27 · P157

P27 = 243116320964027224524719021<27>

P157 = 1028482569210646198463262943523919512285451094438068047692482435826458280758245850867391209810067116107639173738835019545155224537244343341801897782308906221<157>

Nov 8, 2004 (3rd)

The condition of 533...33 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=88310+alpha) 100 times.

(16·10151-1)/3, (16·10155-1)/3, (16·10157-1)/3, (16·10161-1)/3, (16·10163-1)/3, (16·10165-1)/3, (16·10167-1)/3, (16·10169-1)/3, (16·10173-1)/3, (16·10175-1)/3, (16·10179-1)/3, (16·10181-1)/3, (16·10183-1)/3, (16·10185-1)/3, (16·10187-1)/3, (16·10189-1)/3, (16·10191-1)/3, (16·10193-1)/3, (16·10195-1)/3, (16·10197-1)/3, (16·10199-1)/3, (21/200)

The condition of 55...551 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=88530+alpha) 100 times.

(5·10151-41)/9, (5·10153-41)/9, (5·10155-41)/9, (5·10156-41)/9, (5·10157-41)/9, (5·10158-41)/9, (5·10159-41)/9, (5·10160-41)/9, (5·10161-41)/9, (5·10162-41)/9, (5·10163-41)/9, (5·10164-41)/9, (5·10165-41)/9, (5·10169-41)/9, (5·10170-41)/9, (5·10171-41)/9, (5·10172-41)/9, (5·10173-41)/9, (5·10175-41)/9, (5·10176-41)/9, (5·10177-41)/9, (5·10180-41)/9, (5·10181-41)/9, (5·10183-41)/9, (5·10184-41)/9, (5·10187-41)/9, (5·10188-41)/9, (5·10189-41)/9, (5·10190-41)/9, (5·10192-41)/9, (5·10196-41)/9, (5·10197-41)/9, (5·10198-41)/9, (5·10199-41)/9, (5·10200-41)/9, (35/200)

The condition of 55...553 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=88880+alpha) 100 times.

(5·10152-23)/9, (5·10155-23)/9, (5·10156-23)/9, (5·10159-23)/9, (5·10160-23)/9, (5·10161-23)/9, (5·10162-23)/9, (5·10163-23)/9, (5·10166-23)/9, (5·10168-23)/9, (5·10169-23)/9, (5·10170-23)/9, (5·10171-23)/9, (5·10173-23)/9, (5·10174-23)/9, (5·10176-23)/9, (5·10178-23)/9, (5·10179-23)/9, (5·10180-23)/9, (5·10182-23)/9, (5·10185-23)/9, (5·10187-23)/9, (5·10188-23)/9, (5·10190-23)/9, (5·10192-23)/9, (5·10193-23)/9, (5·10195-23)/9, (5·10196-23)/9, (5·10198-23)/9, (5·10199-23)/9, (5·10200-23)/9, (31/200)

The condition of 55...557 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=89190+alpha) 100 times.

(5·10151+13)/9, (5·10153+13)/9, (5·10155+13)/9, (5·10156+13)/9, (5·10157+13)/9, (5·10158+13)/9, (5·10159+13)/9, (5·10160+13)/9, (5·10163+13)/9, (5·10165+13)/9, (5·10167+13)/9, (5·10168+13)/9, (5·10169+13)/9, (5·10170+13)/9, (5·10172+13)/9, (5·10174+13)/9, (5·10175+13)/9, (5·10176+13)/9, (5·10178+13)/9, (5·10179+13)/9, (5·10180+13)/9, (5·10181+13)/9, (5·10182+13)/9, (5·10183+13)/9, (5·10185+13)/9, (5·10186+13)/9, (5·10187+13)/9, (5·10188+13)/9, (5·10190+13)/9, (5·10191+13)/9, (5·10192+13)/9, (5·10193+13)/9, (5·10194+13)/9, (5·10195+13)/9, (5·10196+13)/9, (5·10197+13)/9, (5·10198+13)/9, (5·10200+13)/9, (38/200)

The condition of 599...99 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=90170+alpha) 100 times.

6·10151-1, 6·10152-1, 6·10153-1, 6·10154-1, 6·10155-1, 6·10160-1, 6·10161-1, 6·10162-1, 6·10164-1, 6·10166-1, 6·10167-1, 6·10168-1, 6·10172-1, 6·10173-1, 6·10174-1, 6·10175-1, 6·10176-1, 6·10177-1, 6·10179-1, 6·10180-1, 6·10181-1, 6·10183-1, 6·10184-1, 6·10188-1, 6·10190-1, 6·10191-1, 6·10192-1, 6·10193-1, 6·10194-1, 6·10195-1, 6·10196-1, 6·10197-1, 6·10199-1, (33/200)

The condition of 66...667 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=91190+alpha) 100 times.

(2·10153+1)/3, (2·10155+1)/3, (2·10157+1)/3, (2·10158+1)/3, (2·10160+1)/3, (2·10162+1)/3, (2·10163+1)/3, (2·10164+1)/3, (2·10165+1)/3, (2·10166+1)/3, (2·10167+1)/3, (2·10169+1)/3, (2·10172+1)/3, (2·10173+1)/3, (2·10175+1)/3, (2·10176+1)/3, (2·10178+1)/3, (2·10180+1)/3, (2·10181+1)/3, (2·10182+1)/3, (2·10183+1)/3, (2·10185+1)/3, (2·10186+1)/3, (2·10187+1)/3, (2·10189+1)/3, (2·10191+1)/3, (2·10192+1)/3, (2·10195+1)/3, (2·10197+1)/3, (2·10198+1)/3, (2·10200+1)/3, (31/200)

Nov 8, 2004 (2nd)

By Tyler Cadigan / PPSIQS

(4·10153-1)/3 = 1(3)153<154> = 31 · 222741917 · 335176930366717<15> · 1763475447409625933<19> · 18447244184490294562889<23> · C89

C89 = P42 · P48

P49 = 124585402003739430907913473646625029133311<42>

P48 = 142145429023645149221440361683207313284739049241<48>

Nov 8, 2004

GGNFS 0.61.3 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Nov 7, 2004 (3rd)

By Tyler Cadigan / PPSIQS

(7·10138-61)/9 = (7)1371<138> = 3 · 43 · 89 · 15307 · 33744218117<11> · 51318452866693933259<20> · C100

C100 = P49 · P51

P49 = 3234184052598571652156704509502554289915810649389<49>

P51 = 790220106174916455599425329679987605916895550080539<51>

Nov 7, 2004 (2nd)

The condition of 133...33 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=76010+alpha) 100 times.

(4·10151-1)/3, (4·10153-1)/3, (4·10155-1)/3, (4·10157-1)/3, (4·10159-1)/3, (4·10163-1)/3, (4·10165-1)/3, (4·10167-1)/3, (4·10171-1)/3, (4·10175-1)/3, (4·10177-1)/3, (4·10179-1)/3, (4·10181-1)/3, (4·10183-1)/3, (4·10187-1)/3, (4·10189-1)/3, (4·10191-1)/3, (4·10195-1)/3, (4·10199-1)/3, (19/200)

The condition of 144...441 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=76200+alpha) 100 times.

(13·10152-31)/9, (13·10154-31)/9, (13·10155-31)/9, (13·10156-31)/9, (13·10158-31)/9, (13·10159-31)/9, (13·10162-31)/9, (13·10164-31)/9, (13·10165-31)/9, (13·10167-31)/9, (13·10169-31)/9, (13·10170-31)/9, (13·10171-31)/9, (13·10172-31)/9, (13·10173-31)/9, (13·10176-31)/9, (13·10177-31)/9, (13·10179-31)/9, (13·10180-31)/9, (13·10184-31)/9, (13·10185-31)/9, (13·10188-31)/9, (13·10190-31)/9, (13·10195-31)/9, (13·10197-31)/9, (13·10199-31)/9, (13·10200-31)/9, (27/200)

The condition of 22...223 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=79560+alpha) 100 times.

(2·10154+7)/9, (2·10155+7)/9, (2·10156+7)/9, (2·10157+7)/9, (2·10158+7)/9, (2·10159+7)/9, (2·10160+7)/9, (2·10161+7)/9, (2·10164+7)/9, (2·10165+7)/9, (2·10166+7)/9, (2·10167+7)/9, (2·10170+7)/9, (2·10171+7)/9, (2·10173+7)/9, (2·10174+7)/9, (2·10175+7)/9, (2·10176+7)/9, (2·10179+7)/9, (2·10180+7)/9, (2·10182+7)/9, (2·10183+7)/9, (2·10184+7)/9, (2·10186+7)/9, (2·10187+7)/9, (2·10188+7)/9, (2·10189+7)/9, (2·10193+7)/9, (2·10195+7)/9, (2·10196+7)/9, (2·10197+7)/9, (2·10198+7)/9, (2·10199+7)/9, (2·10200+7)/9, (34/200)

The condition of 499...99 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=87590+alpha) 100 times.

5·10152-1, 5·10156-1, 5·10157-1, 5·10158-1, 5·10160-1, 5·10161-1, 5·10162-1, 5·10163-1, 5·10164-1, 5·10165-1, 5·10166-1, 5·10168-1, 5·10169-1, 5·10170-1, 5·10172-1, 5·10173-1, 5·10174-1, 5·10175-1, 5·10176-1, 5·10177-1, 5·10179-1, 5·10180-1, 5·10181-1, 5·10182-1, 5·10183-1, 5·10184-1, 5·10185-1, 5·10186-1, 5·10187-1, 5·10189-1, 5·10190-1, 5·10191-1, 5·10193-1, 5·10194-1, 5·10196-1, 5·10197-1, 5·10198-1, 5·10199-1, 5·10200-1, (39/200)

Nov 7, 2004

By Wataru Sakai / GMP-ECM

(5·10162-17)/3 = 1(6)1611<163> = 164076642253592773<18> · C146

C146 = P28 · C118

P28 = 3467585771022759954025112257<28>

C118 = [2929373696380120915420844504125371244948839260830283456490946306945700548601185908936173210016579452797771199580868001<118>]

(10184+17)/9 = (1)1833<184> = 3 · 7 · 64542410159<11> · 433652311171<12> · C160

C160 = P28 · C133

P28 = 1688331714766061786380254203<28>

C133 = [1119679103226195952706671836219380541737724281816806432671745918941447425776987886165832562887561828879602297806261423269671804791259<133>]

Nov 6, 2004 (3rd)

144...441 (n≤150) was completed.

Nov 6, 2004 (2nd)

By Greg Childers / GGNFS

(13·10150-31)/9 = 1(4)1491<151> = 169751 · 6201733453<10> · C106

277424951607330545854241920211<30> · C106

C106 = P52 · P54

P52 = 7643203904427353004994376929256076336477323488058431<52>

P54 = 647074730566969724397780835465271843040203812266897367<54>

(4·10138-7)/3 = 1(3)1371<139> = 29 · 2857 · 21787 · C129

C129 = P42 · P88

P42 = 382932842861808317695433494904109585660143<42>

P88 = 1928903268506673934070107918549410566795740917933291209938848739593287198825685159518747<88>

(4·10142-7)/3 = 1(3)1411<143> = 2269 · 2801 · C136

C136 = P38 · P98

P38 = 89155954196849014324852853285161365719<38>

P98 = 23531021436195067102073279326523153267327728233174127236609298724412750456986803395729059934212921<98>

Nov 6, 2004

GGNFS 0.61.2 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Nov 5, 2004 (2nd)

By Tetsuya Kobayashi / GGNFS 0.54.4

10165-9 = (9)1641<165> = C165

C165 = P56 · P110

P56 = 56290473873165148381086844809790940629420103915155210253<56>

P110 = 17764995232643102887053101422297754638281216307353274409711866004077365678936425580088372114246263483737897747<110>

Nov 5, 2004

GGNFS 0.61.0 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Nov 4, 2004 (5th)

By Wataru Sakai / GMP-ECM

(5·10185-17)/3 = 1(6)1841<186> = 11 · 29 · 593 · 1033 · 1499 · 2882608259<10> · 3543071821004207029<19> · C146

C146 = P28 · C119

P28 = 1137427574791532814978635687<28>

C119 = [48979244692501259904533934318356529766121780019559339790576785973107299044147705538529594775240417601599059313944047857<119>]

(10170+17)/9 = (1)1693<170> = 13 · 46908733 · 49085863 · 317108850568469<15> · C139

C139 = P32 · P107

P32 = 23853351811645992189197990153699<32>

P107 = 49073408899896705750094374454189075664684293081586466829640514872636418882737156159115520956026323753326649<107>

Nov 4, 2004 (4th)

By Tyler Cadigan / PPSIQS

(10183+11)/3 = (3)1827<183> = 13859 · 141311 · 237857296739<12> · 492901867654387891957<21> · 9197990985038655821103413<25> · 23642196101363874691629911<26> · C91

C91 = P36 · P56

P36 = 111682434878115772842130175404571063<36>

P56 = 59776195362090066441427036679528098290966897427726454359<56>

Nov 4, 2004 (3rd)

133...33 (n≤150), 22...223 (n≤150) and 499...99 (n≤150) were completed.

Nov 4, 2004 (2nd)

By Greg Childers / GGNFS

(4·10139-1)/3 = 1(3)139<140> = 13 · 198347009088738161<18> · 7103905809983654359<19> · C139

C139 = P44 · P58

P44 = 93056477699817010118546054131289978954079037<44>

P58 = 7822146107956844303170723452387164481976821239051337106907<58>

(4·10143-1)/3 = 1(3)143<144> = 2243 · 881588849 · 9137732886173<13> · C118

C118 = P43 · P76

P43 = 1294098057730306146836411472921332043694387<43>

P76 = 5702138093159461528300041737131394665384546532724411445645938980376291125969<76>

(4·10145-1)/3 = 1(3)145<146> = 13 · 6067 · 869625401 · C132

C132 = P56 · P77

P56 = 18118019927333320870772343694119034872525813783531501521<56>

P77 = 10729474198605473759007978378665736227686878303045291450893504798797794382363<77>

(4·10147-1)/3 = 1(3)147<148> = C148

C148 = P66 · P82

P66 = 274164219895048137833082808225798287222829493125852842203567981453<66>

P82 = 4863265286198695370722014341939420965729914743888572766841772667924482793599369961<82>

(2·10143+7)/9 = (2)1423<143> = 149 · 1051 · 307423981 · 312160750988286806021859139<27> · C103

C103 = P42 · P61

P42 = 167309047980263602956732412676837060292367<42>

P61 = 8838183917468631024530100824665388670542398785290684942817409<61>

5·10145-1 = 4(9)145<146> = 7 · 191 · 200407 · 30320577358085873<17> · 3742689245540972587559<22> · C100

C100 = P32 · P69

P32 = 10770666850886758816127596408319<32>

P69 = 152672874066731926396057308274042971603911517666371368472643836198617<69>

Nov 4, 2004

By Tyler Cadigan / PPSIQS

(10144+71)/9 = (1)1439<144> = 1511 · 290183 · 11149616353<11> · 3676356032446416657105451<25> · C100

C100 = P44 · P57

P44 = 30544160959549048329568294296428368601133191<44>

P57 = 202402267134456416354294445204134193826917234103168515931<57>

Nov 3, 2004 (2nd)

The condition of 388...883 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=84770+alpha) 100 times.

(35·10153-53)/9, (35·10154-53)/9, (35·10158-53)/9, (35·10166-53)/9, (35·10167-53)/9, (35·10168-53)/9, (35·10169-53)/9, (35·10171-53)/9, (35·10172-53)/9, (35·10173-53)/9, (35·10176-53)/9, (35·10179-53)/9, (35·10181-53)/9, (35·10183-53)/9, (35·10184-53)/9, (35·10185-53)/9, (35·10187-53)/9, (35·10188-53)/9, (35·10189-53)/9, (35·10190-53)/9, (35·10191-53)/9, (35·10192-53)/9, (35·10194-53)/9, (35·10195-53)/9, (35·10196-53)/9, (35·10197-53)/9, (35·10200-53)/9, (27/200)

The condition of 433...33 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=85520+alpha) 100 times.

(13·10151-1)/3, (13·10153-1)/3, (13·10155-1)/3, (13·10156-1)/3, (13·10160-1)/3, (13·10161-1)/3, (13·10162-1)/3, (13·10163-1)/3, (13·10164-1)/3, (13·10165-1)/3, (13·10168-1)/3, (13·10171-1)/3, (13·10173-1)/3, (13·10175-1)/3, (13·10176-1)/3, (13·10177-1)/3, (13·10179-1)/3, (13·10180-1)/3, (13·10181-1)/3, (13·10182-1)/3, (13·10184-1)/3, (13·10187-1)/3, (13·10188-1)/3, (13·10189-1)/3, (13·10190-1)/3, (13·10192-1)/3, (13·10193-1)/3, (13·10194-1)/3, (13·10195-1)/3, (13·10196-1)/3, (13·10198-1)/3, (13·10199-1)/3, (13·10200-1)/3, (33/200)

The condition of 44...447 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=86620+alpha) 100 times.

(4·10151+23)/9, (4·10152+23)/9, (4·10153+23)/9, (4·10155+23)/9, (4·10156+23)/9, (4·10161+23)/9, (4·10162+23)/9, (4·10163+23)/9, (4·10164+23)/9, (4·10166+23)/9, (4·10168+23)/9, (4·10169+23)/9, (4·10170+23)/9, (4·10173+23)/9, (4·10174+23)/9, (4·10175+23)/9, (4·10177+23)/9, (4·10178+23)/9, (4·10179+23)/9, (4·10180+23)/9, (4·10181+23)/9, (4·10183+23)/9, (4·10184+23)/9, (4·10185+23)/9, (4·10186+23)/9, (4·10188+23)/9, (4·10190+23)/9, (4·10192+23)/9, (4·10193+23)/9, (4·10195+23)/9, (4·10196+23)/9, (4·10197+23)/9, (4·10199+23)/9, (4·10200+23)/9, (34/200)

Nov 3, 2004

GGNFS 0.60.10-unstable was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Nov 2, 2004

The condition of 33...337 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=100000) 100 times.

(10151+11)/3, (10152+11)/3, (10153+11)/3, (10154+11)/3, (10155+11)/3, (10157+11)/3, (10160+11)/3, (10162+11)/3, (10164+11)/3, (10165+11)/3, (10166+11)/3, (10167+11)/3, (10170+11)/3, (10171+11)/3, (10172+11)/3, (10173+11)/3, (10174+11)/3, (10175+11)/3, (10176+11)/3, (10177+11)/3, (10178+11)/3, (10179+11)/3, (10180+11)/3, (10181+11)/3, (10183+11)/3, (10184+11)/3, (10185+11)/3, (10186+11)/3, (10187+11)/3, (10191+11)/3, (10192+11)/3, (10193+11)/3, (10194+11)/3, (10196+11)/3, (10197+11)/3, (10198+11)/3, (10199+11)/3, (10200+11)/3, (38/200)

Nov 1, 2004

By Wataru Sakai / GMP-ECM

(5·10158-17)/3 = 1(6)1571<159> = 72 · 227 · 587117 · 28302487 · C141

C141 = P25 · C117

P25 = 4405758911640887447737379<25>

C117 = [204671243833471872423458363170935132549848443077825215001952886645519860774092659259664652641538107318116138813539527<117>]

(5·10165-17)/3 = 1(6)1641<166> = 11 · 147978871 · 6277820213076323022317<22> · C135

C135 = P31 · P104

P31 = 3475850552474898581672415558079<31>

P104 = 46923066431055131596850377334570935587835316961883534280229387652167397777381279528524667787672360491667<104>

(5·10178-17)/3 = 1(6)1771<179> = 23 · 281 · 607 · 69197 · 568081406548091538959<21> · C147

C147 = P26 · P121

P26 = 94260089305481863747511783<26>

P121 = 1146569050266090042828199836790859300199833117737340928358634815662751628743134117313969594764698562259165009594440249169<121>

(10199+17)/9 = (1)1983<199> = 3 · 53 · 61 · 5261569 · 14429307007535652733<20> · C169

C169 = P29 · C140

P29 = 28953978442052238625370216321<29>

C140 = [52114855818627273784665905718435775931825142980549134209824658135179401498225871520825691993065270825222298463381748305188842776996682367711<140>]

October 2004

Oct 31, 2004 (4th)

99...997 (n≤150) was completed.

Oct 31, 2004 (3rd)

By Greg Childers / GGNFS

10148-3 = (9)1477<148> = 13 · 59 · 8902981 · 2092098327453367265488153<25> · C114

C114 = P49 · P66

P49 = 1313437274082906131865018524905745892254428247173<49>

P66 = 532939316067522452437009431855311310168767228534802154162283932019<66>

Oct 31, 2004 (2nd)

By Tyler Cadigan / PPSIQS

(43·10128-7)/9 = 4(7)128<129> = 32 · 154937 · 738616566413580841092563<24> · C99

C99 = P40 · P60

P40 = 1954973229374376044259837704014211718857<40>

P60 = 237283989262243286151858068264136304653121566371862021029459<60>

Oct 31, 2004

By Sander Hoogendoorn / GGNFS

(2·10130+61)/9 = (2)1299<130> = 3 · 1013 · 1297927 · 4119130853<10> · 82383989539<11> · C100

C100 = P44 · P57

P44 = 12893334001210030724132713775348201750269021<44>

P57 = 128763531207327046074262161561454733351447087377845111599<57>

Oct 30, 2004 (4th)

By Shusuke Kubota / GMP-ECM 5.0c

(10177+17)/9 = (1)1763<177> = 79 · 199 · 337 · C170

C170 = P31 · C140

P31 = 1892299672990464278460298053559<31>

C140 = [11083004451549544720109865787472537752249266606417007670255378526710604506596194032710063538973026910205000830114341184301551035751303036791<140>]

Oct 30, 2004 (3rd)

By Makoto Kamada / GMP-ECM 5.0.3

(10180-7)/3 = (3)1791<180> = C180

C180 = P32 · P148

P32 = 49177191501454157350182747447299<32>

P148 = 6778210043236746233828300268523246840277702850524567595358247821792960480246500354171003532043608637885168961086829129013098596280247355631530720369<148>

Oct 30, 2004 (2nd)

GGNFS 0.60.9-unstable was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Oct 30, 2004

By Sander Hoogendoorn / GMP-ECM

(10154+17)/9 = (1)1533<154> = 3 · 7 · 4175881 · 117171638757881<15> · 4829596115648201347913864129<28> · C104

C104 = P30 · P74

P30 = 788762691872479934761930966381<30>

P74 = 28386405587527475548491315882496594361400361139034948208375826137519369177<74>

Oct 29, 2004 (2nd)

The condition of 188...881 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=77970+alpha) 100 times.

(17·10152-71)/9, (17·10153-71)/9, (17·10155-71)/9, (17·10157-71)/9, (17·10158-71)/9, (17·10161-71)/9, (17·10162-71)/9, (17·10164-71)/9, (17·10165-71)/9, (17·10166-71)/9, (17·10174-71)/9, (17·10179-71)/9, (17·10180-71)/9, (17·10181-71)/9, (17·10182-71)/9, (17·10183-71)/9, (17·10184-71)/9, (17·10185-71)/9, (17·10186-71)/9, (17·10187-71)/9, (17·10188-71)/9, (17·10189-71)/9, (17·10191-71)/9, (17·10192-71)/9, (17·10193-71)/9, (17·10195-71)/9, (17·10197-71)/9, (17·10198-71)/9, (17·10199-71)/9, (17·10200-71)/9, (30/200)

The condition of 211...11 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=78950+alpha) 100 times.

(19·10152-1)/9, (19·10155-1)/9, (19·10156-1)/9, (19·10157-1)/9, (19·10158-1)/9, (19·10160-1)/9, (19·10161-1)/9, (19·10164-1)/9, (19·10165-1)/9, (19·10166-1)/9, (19·10167-1)/9, (19·10169-1)/9, (19·10170-1)/9, (19·10176-1)/9, (19·10178-1)/9, (19·10179-1)/9, (19·10183-1)/9, (19·10184-1)/9, (19·10185-1)/9, (19·10187-1)/9, (19·10188-1)/9, (19·10189-1)/9, (19·10192-1)/9, (19·10193-1)/9, (19·10194-1)/9, (19·10195-1)/9, (19·10196-1)/9, (19·10197-1)/9, (19·10199-1)/9, (19·10200-1)/9, (30/200)

Oct 29, 2004

By Philippe Strohl / newpgen, pfgw, primo 2.2.0 beta 5

(28·10554-1)/9 = 3(1)554<555>, (28·10580-1)/9 = 3(1)580<581> and (28·101310-1)/9 = 3(1)1310<1311> are definitely prime.

(28·108537-1)/9 = 3(1)8537<8538> is a strong-tested near-repdigit prp for bases 2, 3, 5, 7, 11, 13, 101.

Oct 28, 2004

By Tyler Cadigan / PPSIQS

(73·10134-1)/9 = 8(1)134<135> = 13881683 · 269001190545339915526867145161<30> · C99

C99 = P47 · P53

P47 = 18432819128434097282510480246554333039481218741<47>

P53 = 11783987259061293732004233277125153540987549016928417<53>

Oct 27, 2004 (3rd)

By Makoto Kamada / GMP-ECM 5.0.3

(2·10187-11)/9 = (2)1861<187> = 19 · 4649532960488279<16> · C170

C170 = P26 · C144

P26 = 66702983608994124414569333<26>

C144 = [377119764747833718003946378619475660102486646646917939582436513454949109037981126041578149847338179007647070268403253033533084661810688970509237<144>]

(2·10198-11)/9 = (2)1971<198> = C198

C198 = P28 · P171

P28 = 1544037026288694228448962803<28>

P171 = 143922858350336298007015876592048703111776471944979409246319942874278590726370537456210410833733045044256670966248552842007007774259251774964473490039868315319739946574207<171>

(2·10199-11)/9 = (2)1981<199> = C199

C199 = P22 · C177

P22 = 6963796279053002235013<22>

C177 = [319110745514861526794711378703572343995428106001193557079701797757226211580497488909530035973009966646124859139500542679842644131385590979909709371867619340587830262001201479017<177>]

(2·10200-11)/9 = (2)1991<200> = 3 · 7 · C199

C199 = P26 · C173

P26 = 14001880603763633983098127<26>

C173 = [75575637883715360494127604153948330408332570614645220164868186345149960834182522442943792947391780510225177833932663779244341727897146410091059638069084001256139164641000663<173>]

(2·10187+43)/9 = (2)1867<187> = 7 · 239 · 2089 · 2719 · 3599899 · C170

C170 = P31 · C140

P31 = 1454013060523477510672955511551<31>

C140 = [44677130729451804862805296406299145317435763417023166693374258901454414212791155339352971120916809652830021667465704793500230882435827163161<140>]

(2·10200+43)/9 = (2)1997<200> = 32 · 31 · 359 · 17737 · C191

C191 = P26 · C165

P26 = 38777212649318798402557141<26>

C165 = [322576020641972706302877554164604660713708913064209859124760804918641746437488561431324513986094863871011370553215853295417573007065639808150520269489150069649253071<165>]

Oct 27, 2004 (2nd)

By Greg Childers / GGNFS

10147-3 = (9)1467<147> = 87257 · 2581475893243546379399562049<28> · C115

C115 = P34 · P35 · P47

P34 = 2978486598601309977385667600190257<34>

P35 = 76939696440259536071166115723477303<35>

P47 = 19372493773537840831076728862163526175658084499<47>

Oct 27, 2004

By Shusuke Kubota / GMP-ECM 5.0c

(10155+17)/9 = (1)1543<155> = 166099 · C149

C149 = P27 · P123

P27 = 273317524842305270518823897<27>

P123 = 244750165230574200547682049835258201594816962750328193064042361804148517538105347084808386128960345614953858844611763145771<123>

(10160+17)/9 = (1)1593<160> = 33 · 7 · 232 · 53 · 107881 · C148

C148 = P27 · C121

P27 = 301787558315959860024628403<27>

C121 = [6440474276189063029469896370990258701549175964742824120735650981327705765751244667703443710331099759156990377210821915787<121>]

Oct 26, 2004 (2nd)

By Greg Childers / GGNFS

(2·10148+7)/9 = (2)1473<148> = 34 · 13 · 19 · 101567257305949471<18> · C127

C127 = P48 · P79

P48 = 141303761410777573245254533260661267574419385131<48>

P79 = 7739235575743774151398238877945382293130861185697207152777976673706588113101589<79>

(2·10149+7)/9 = (2)1483<149> = 8821 · C145

C145 = P43 · P103

P43 = 1840443781568006396865580669535155839494213<43>

P103 = 1368822414508331612887738891689191177896334116203834760359254573437015084565780181118874791758026980951<103>

10146-3 = (9)1457<146> = 786435493 · 33687902299127<14> · 739507611188227323791<21> · C103

C103 = P51 · P53

P51 = 147774458556369431910404840981974982225732968722011<51>

P53 = 34539886053501171347512504592110662553160109081260627<53>

Oct 26, 2004

By Sander Hoogendoorn / GGNFS-0.60.6-unstable

(8·10122-53)/9 = (8)1213<122> = 4657 · 15971 · 9148829 · 297320813 · C99

C99 = P34 · P65

P34 = 4827809083534124843321592349710763<34>

P65 = 91005621608334442248646511271192948866304220688718076292235913339<65>

(10126+53)/9 = (1)1257<126> = 3 · 4969 · 17471 · C117

C117 = P30 · P88

P30 = 425870593031226135936543563393<30>

P88 = 1001778768087818674719079587739198460979731073535208269904425228780987895998402881908777<88>

10141-3 = (9)1407<141> = 757 · 21395260840097<14> · 1998567824579494876129<22> · C104

C104 = P47 · P58

P47 = 12839483153589083628646788780690801027737944337<47>

P58 = 2406135617024184285708011017528134490384412631178837377241<58>

Oct 25, 2004

By Tyler Cadigan / PPSIQS

(52·10134-7)/9 = 5(7)134<135> = 113 · 21401 · 97117666918073<14> · 2950265320624201<16> · C99

C99 = P34 · P65

P34 = 9827130435253045429747763011768723<34>

P65 = 84852040039259635923938051822061659838632591751201421054543493651<65>

Oct 24, 2004 (5th)

By Wataru Sakai / GMP-ECM

(10180+17)/9 = (1)1793<180> = 6949 · 135862068644287<15> · 21633659135200744087543<23> · C139

C139 = P23 · C116

P23 = 57990409560719099220689<23>

C116 = [93810358881996442890482228144067883749540447348259571159075789651402467670223973413339539712829879169409153603718813<116>]

Oct 24, 2004 (4th)

By Sander Hoogendoorn / GGNFS-0.60.6-unstable

(8·10118-53)/9 = (8)1173<118> = 3 · 7 · 19 · 228233 · 241565141 · C102

C102 = P45 · P57

P45 = 578704942589176822629197761530448010148528217<45>

P57 = 698239940722979733212883687994620092969422992590640558217<57>

Oct 24, 2004 (3rd)

By Shusuke Kubota / GMP-ECM 5.0c

(10156+17)/9 = (1)1553<156> = 17477 · 2390473 · 37402307 · 1264206703<10> · 47444143291487343389<20> · 48680022488359635652849<23> · C86

C86 = P28 · P58

P28 = 3167489193406668807814739101<28>

P58 = 7688502524564656969822416010021474832000147918615571810313<58>

Oct 24, 2004 (2nd)

The condition of 166...661 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=76900+alpha) 100 times.

(5·10155-17)/3, (5·10156-17)/3, (5·10157-17)/3, (5·10158-17)/3, (5·10159-17)/3, (5·10160-17)/3, (5·10162-17)/3, (5·10163-17)/3, (5·10164-17)/3, (5·10165-17)/3, (5·10166-17)/3, (5·10167-17)/3, (5·10171-17)/3, (5·10172-17)/3, (5·10174-17)/3, (5·10175-17)/3, (5·10176-17)/3, (5·10177-17)/3, (5·10178-17)/3, (5·10179-17)/3, (5·10180-17)/3, (5·10181-17)/3, (5·10183-17)/3, (5·10184-17)/3, (5·10185-17)/3, (5·10186-17)/3, (5·10187-17)/3, (5·10189-17)/3, (5·10190-17)/3, (5·10192-17)/3, (5·10194-17)/3, (5·10195-17)/3, (5·10196-17)/3, (5·10197-17)/3, (5·10198-17)/3, (5·10199-17)/3, (5·10200-17)/3, (37/200)

Oct 24, 2004

By Sander Hoogendoorn / GGNFS-0.60.6-unstable

(22·10125-1)/3 = 7(3)125<126> = 1303 · C123

C123 = P62 · P62

P62 = 13076611503468354728659845656356098066371387730347509283020637<62>

P62 = 43038962041908707110557819970297770102457906275634967258060303<62>

Oct 23, 2004 (2nd)

By Wataru Sakai / GMP-ECM

2·10159-1 = 1(9)159<160> = 31 · 269 · 1069 · 624521 · 972779112004724071<18> · C129

C129 = P30 · P100

P30 = 198218330943890143039085853511<30>

P100 = 1863087356568022561958848459430622336906208220440978054782168211919375375101660488520582074357218689<100>

Oct 23, 2004

By Tyler Cadigan / PPSIQS

(88·10130-7)/9 = 9(7)130<131> = 2267 · 287735621603<12> · 1724181776773381577<19> · C98

C98 = P39 · P60

P39 = 480171920602619344674066954688017245953<39>

P60 = 181056950467383564559423822136384214704873049423423083461817<60>

Oct 22, 2004 (2nd)

GGNFS 0.60.6-unstable was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Oct 22, 2004

The condition of 11...113 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=74360+alpha) 100 times.

(10151+17)/9, (10152+17)/9, (10153+17)/9, (10154+17)/9, (10155+17)/9, (10156+17)/9, (10157+17)/9, (10159+17)/9, (10160+17)/9, (10162+17)/9, (10165+17)/9, (10169+17)/9, (10170+17)/9, (10172+17)/9, (10173+17)/9, (10174+17)/9, (10176+17)/9, (10177+17)/9, (10178+17)/9, (10179+17)/9, (10180+17)/9, (10181+17)/9, (10183+17)/9, (10184+17)/9, (10185+17)/9, (10187+17)/9, (10188+17)/9, (10189+17)/9, (10192+17)/9, (10193+17)/9, (10195+17)/9, (10198+17)/9, (10199+17)/9, (33/200)

Oct 20, 2004 (4th)

The condition of 33...331 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=54860+alpha) 100 times.

(10152-7)/3, (10154-7)/3, (10159-7)/3, (10161-7)/3, (10163-7)/3, (10166-7)/3, (10167-7)/3, (10168-7)/3, (10169-7)/3, (10170-7)/3, (10172-7)/3, (10174-7)/3, (10175-7)/3, (10180-7)/3, (10182-7)/3, (10183-7)/3, (10185-7)/3, (10187-7)/3, (10189-7)/3, (10190-7)/3, (10191-7)/3, (10193-7)/3, (10195-7)/3, (10196-7)/3, (10198-7)/3, (10199-7)/3, (10200-7)/3, (27/200)

Oct 20, 2004 (3rd)

The condition of 833...33 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=68230+alpha) 100 times.

(25·10151-1)/3, (25·10153-1)/3, (25·10155-1)/3, (25·10159-1)/3, (25·10161-1)/3, (25·10163-1)/3, (25·10165-1)/3, (25·10169-1)/3, (25·10171-1)/3, (25·10179-1)/3, (25·10181-1)/3, (25·10183-1)/3, (25·10185-1)/3, (25·10189-1)/3, (25·10193-1)/3, (25·10195-1)/3, (25·10197-1)/3, (17/200)

Oct 20, 2004 (2nd)

By Tyler Cadigan / PPSIQS

(73·10142-1)/9 = 8(1)142<143> = 3 · 89 · 110879 · 316896856426336397<18> · 128431369081220952707<21> · C98

C98 = P47 · P52

P47 = 29112024575477100392322967162534860141551931511<47>

P52 = 2312375378201714336124580223199023275409487476004683<52>

Oct 20, 2004

By Sander Hoogendoorn / GGNFS-0.60.3-unstable, GGNFS-0.54.5b

(7·10119+11)/9 = (7)1189<119> = 13 · 79 · C116

C116 = P47 · P70

P47 = 21200188520689563589776797426334823576191297367<47>

P70 = 3572278947023668975795230555579869684684367732959994202489268058449431<70>

Oct 19, 2004 (3rd)

211...11 (n≤150) was completed.

Oct 19, 2004 (2nd)

By Greg Childers / GGNFS

(7·10117+11)/9 = (7)1169<117> = 65843 · C113

C113 = P32 · P81

P32 = 17618579928725054681087090473267<32>

P81 = 670463313689757794025465783085063598471823980469840546178141528091016173914592059<81>

(19·10141-1)/9 = 2(1)141<142> = 808001147 · 14451177179<11> · C123

C123 = P61 · P62

P61 = 1967526606641874254902868696224753606009599388741835659032403<61>

P62 = 91891485965508071388404658746315616009850224878544027799539749<62>

(19·10146-1)/9 = 2(1)146<147> = 192366985120423<15> · C133

C133 = P38 · P45 · P51

P38 = 29365301023666568488392630000453630649<38>

P45 = 355187872431500922702175275160737857693544593<45>

P51 = 105217497198344900059826621607642715596457417792601<51>

(2·10144+7)/9 = (2)1433<144> = 53611 · 117563 · 60387159023969<14> · C120

C120 = P38 · P82

P38 = 88692373338546605226340701414858466691<38>

P82 = 6583124119103824473232830829207215208475424966357525746284822636946549026969966109<82>

Oct 19, 2004

By Wataru Sakai / GMP-ECM, PPSIQS

2·10178-1 = 1(9)178<179> = 7 · 19697 · 49871 · 2168131776887<13> · 21546540858697<14> · 34452787495073<14> · 702699414074538345359<21> · C109

C109 = P26 · P41 · P43

P26 = 11232286032052640081577527<26>

P41 = 67824241037706050027234164121994583646719<41>

P43 = 3375775122619098833564433321864778716021439<43>

Oct 18, 2004

GGNFS 0.60.3-unstable was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Oct 17, 2004 (2nd)

By Makoto Kamada / PFGW

(1053718-7)/3 is near-repdigit PRP! (53718 digits)

PFGW Version 20031222.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
...snip...
Primality testing (10^53718-7)/3 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 191
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(10^53718-7)/3 is PRP! (369.0068s+0.0255s)

Note:

N = (1053718-7)/3 = 33...331<53718> = PRP53718

N-1 = 2·3·5·(1053717-1)/9 = 2·3·5·11...11<53717> = 2·3·5·C53717

N+1 = 22·(52·1053716-1)/3 = 22·833...33<53717> = 22·(5·1026858+1)/3·(5·1026858-1) = 22·166...667<26859>·499...99<26859> = 22·23·307·C26855·C26859

Oct 17, 2004

By Tyler Cadigan / PPSIQS

(55·10134-1)/9 = 6(1)134<135> = 13 · 36767 · 660263837 · 61946758732347766777697<23> · C98

C98 = P46 · P52

P46 = 8755150783849633265491267457055286984814318113<46>

P52 = 3570416687946609499815611721841848091904442919247713<52>

Oct 16, 2004 (2nd)

By Wataru Sakai / GMP-ECM

2·10181-1 = 1(9)181<182> = 19 · 71 · 7349 · 808897818779368181<18> · C157

C157 = P27 · C130

P27 = 797129087967153857493783971<27>

C130 = [3128725609853561538026773920634567520995491992088880828324972714133336327873248318256123375586149260625874239143237635528827613049<130>]

2·10193-1 = 1(9)193<194> = 61 · 3011 · 3019 · 2630399 · 1921011481<10> · C169

C169 = P28 · C142

P28 = 5467489597378404813936108409<28>

C142 = [1305529637784949287620571177887970771289520181235731640907698902880282231900498703097479220981210951629363692688397047212888405051383997623781<142>]

Oct 16, 2004

GGNFS 0.60.2-unstable was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Oct 15, 2004 (2nd)

GGNFS 0.60.1-unstable was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Oct 15, 2004

By Tyler Cadigan / PPSIQS

(43·10142-7)/9 = 4(7)142<143> = 73 · 5029713022533431<16> · 7982206761553087772094608069<28> · C98

C98 = P47 · P52

P47 = 13161811572942026780272299603740292163817712761<47>

P52 = 1238571941870914213650789099380420961210434567724331<52>

Oct 14, 2004 (3rd)

GGNFS 0.60-unstable was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Oct 14, 2004 (2nd)

By Greg Childers / GGNFS

(19·10137-1)/9 = 2(1)137<138> = 433 · 1153 · 11393 · 368897952710839480161169<24> · C105

C105 = P49 · P56

P49 = 6537808630984692512469327874650028071620851099861<49>

P56 = 15389245976913122179432504758319730080753497050831216747<56>

(19·10138-1)/9 = 2(1)138<139> = 232782754247700067<18> · C121

C121 = P35 · P36 · P51

P35 = 83845459775834452015372760685094399<35>

P36 = 519453467494562654362155883937185937<36>

P51 = 208225584050293597284203129689776748924665335039491<51>

(19·10140-1)/9 = 2(1)140<141> = 222326827 · C132

C132 = P45 · P88

P45 = 394108304678831242112558499262511688888855913<45>

P88 = 2409370758501444138484329720023565745017813043666268787378494727668172943572169242450061<88>

Oct 14, 2004

By Wataru Sakai / GMP-ECM

(88·10137-7)/9 = 9(7)137<138> = 61 · 151381 · 57788731821397588871<20> · C112

C112 = P33 · P79

P33 = 423159888810652517177897177983787<33>

P79 = 4330033931355453127427368400603870758421240640236447768211277207463100054506261<79>

Oct 13, 2004

By Tyler Cadigan / PPSIQS

(2·10152+43)/9 = (2)1517<152> = 3 · 239 · 5009 · 449657941 · 2049787717937<13> · 197698919201521<15> · 3382715237604481<16> · C95

C95 = P36 · P59

P36 = 123507170992907914494904032797740999<36>

P59 = 81276358251977578443368209020381440283647979206625391847573<59>

Oct 12, 2004 (3rd)

33...337 (n≤150) was completed.

Oct 12, 2004 (2nd)

By Greg Childers / GGNFS

(10147+11)/3 = (3)1467<147> = 1162937 · C141

C141 = P57 · P85

P57 = 122298277433855682221983303461516529262928308651913502673<57>

P85 = 2343701062831766762630355127557560272330817932239700191200456367244305886653028541137<85>

(10149+11)/3 = (3)1487<149> = 17 · 292 · 37 · 378223 · 5825627 · 32925367 · 756636899 · C115

C115 = P48 · P67

P48 = 195198074094872806630540943368285016578324654027<48>

P67 = 5880954575013582298632130756027502940541749324006917590815713873903<67>

(10150+11)/3 = (3)1497<150> = 2130699499<10> · 8218293359<10> · 740149080574399<15> · C116

C116 = P41 · P76

P41 = 15627473558923467190534668668177581868687<41>

P76 = 1645761600727067557000325053584468951705606827951606549532721342029062419189<76>

5·10141-1 = 4(9)141<142> = 863 · 864112969 · C130

C130 = P35 · P96

P35 = 33102413419941380298625729200482713<35>

P96 = 202548498000084611654776402535431487378132205253772216085513563043908316903499360835198098115009<96>

5·10142-1 = 4(9)142<143> = 19 · 33738391 · 69976289 · 727879169 · C118

C118 = P44 · P75

P44 = 14451133963291796815528100748696733275771551<44>

P75 = 105969262443706424717542949006868182672629853917824633425083022550272421341<75>

5·10149-1 = 4(9)149<150> = 439 · 6361 · 9892593989592316723951<22> · C122

C122 = P47 · P76

P47 = 12991330986777786451229660905897078106018495159<47>

P76 = 1393208949869384358841491740657456164913361005125028453793652095448657424009<76>

Oct 12, 2004

By Tyler Cadigan / PPSIQS

(2·10158+43)/9 = (2)1577<158> = 3 · 3911 · 12757 · 682183455257780153<18> · 18569608690644895717<20> · 500852893304150454113762519<27> · C87

C87 = P39 · P48

P39 = 171656453521669967343858143055323881547<39>

P48 = 136318752457961309113115770941045842568542636819<48>

Oct 11, 2004 (4th)

By Tyler Cadigan / PPSIQS

(37·10139-1)/9 = 4(1)139<140> = 17170064291<11> · 53006618019086698414143574579147<32> · C98

C98 = P41 · P58

P41 = 18911677647762284989893684069553245761137<41>

P58 = 2388510423164987611147342476383446855248011165523062280439<58>

Oct 11, 2004 (3rd)

Factor tables of 244...441, 244...443, 244...447 and 244...449 are available.

Oct 11, 2004 (2nd)

The condition of 22...227 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=51570+alpha) 100 times.

(2·10151+43)/9, (2·10152+43)/9, (2·10153+43)/9, (2·10155+43)/9, (2·10157+43)/9, (2·10158+43)/9, (2·10159+43)/9, (2·10162+43)/9, (2·10163+43)/9, (2·10164+43)/9, (2·10166+43)/9, (2·10167+43)/9, (2·10168+43)/9, (2·10170+43)/9, (2·10171+43)/9, (2·10172+43)/9, (2·10174+43)/9, (2·10176+43)/9, (2·10177+43)/9, (2·10179+43)/9, (2·10180+43)/9, (2·10183+43)/9, (2·10184+43)/9, (2·10185+43)/9, (2·10186+43)/9, (2·10187+43)/9, (2·10189+43)/9, (2·10190+43)/9, (2·10192+43)/9, (2·10194+43)/9, (2·10196+43)/9, (2·10197+43)/9, (2·10199+43)/9, (2·10200+43)/9, (34/200)

Oct 11, 2004

By Wataru Sakai / GMP-ECM

2·10151-1 = 1(9)151<152> = 401 · 15791 · 320609 · C139

C139 = P29 · P111

P29 = 13051070336175283765241555981<29>

P111 = 754838685673403250817815467686560425964416958861401194449084381071630229722100857179323372193549672196641809541<111>

2·10162-1 = 1(9)162<163> = 127 · 5273 · 450446783 · 424040923727<12> · 6946941874684115687<19> · C118

C118 = P29 · P89

P29 = 44150768863179970138761108743<29>

P89 = 50978294951850258538993701135036765568108019089176244471733547982180755616368273282307049<89>

Oct 10, 2004

By Tyler Cadigan / PPSIQS

(34·10133-7)/9 = 3(7)133<134> = 372 · 60343 · 1557629594509<13> · 8382888599399617<16> · C98

C98 = P37 · P62

P37 = 1868838626555299774986718212188695121<37>

P62 = 18740292929201735880696313935601292593395711295563291441836987<62>

Oct 9, 2004

By Wataru Sakai / GMP-ECM

2·10171-1 = 1(9)171<172> = 6569 · 568471 · 1534359796328829895031<22> · C141

C141 = P25 · C116

P25 = 5602144536868763044479389<25>

C116 = [62307582226426941282730497418239251189478704230641873240737131725763565707384336402366220505143817417223703576438339<116>]

Oct 8, 2004 (2nd)

722...227 (n≤150) and 33...331 (n≤150) were completed.

Oct 8, 2004

By Greg Childers / GGNFS

(65·10148+43)/9 = 7(2)1477<149> = 30319 · 1303787 · C139

C139 = P40 · P49 · P50

P40 = 6924695532357538392015942113619235446521<40>

P49 = 7709243533890924197434092113655130735615595589973<49>

P50 = 34224481685633447311809947418522210620362025399123<50>

(10139+11)/3 = (3)1387<139> = 7 · 165449 · 1932922237<10> · C124

C124 = P46 · P79

P46 = 1447597086558252872609466688690209993094429259<46>

P79 = 1028618843428473398923491637224670996938221974613555125780688474782548389050873<79>

(10149-7)/3 = (3)1481<149> = 97 · 1658927 · 11332213 · 35664040793<11> · C123

C123 = P43 · P80

P43 = 5617135602839255500916665079545771553298613<43>

P80 = 91247200780038965312128628153119391614786243061577711245686454708892750851633197<80>

(10150-7)/3 = (3)1491<150> = 2696167 · 156780139 · 84715134434546281<17> · C118

C118 = P46 · P73

P46 = 6604930489864216126722326114502720837851717003<46>

P73 = 1409326621098177761765122201344192612588820084693889200289238400674958709<73>

Oct 7, 2004

By Tyler Cadigan / PPSIQS

(79·10118-7)/9 = 8(7)118<119> = 3 · 47 · 4024277 · 34089915659071<14> · C97

C97 = P45 · P52

P45 = 883144159821027373966672839952504573443041011<45>

P52 = 5138307307076065050635534448422224366101312899311781<52>

Oct 6, 2004 (2nd)

188...881 (n≤150) was completed.

Oct 6, 2004

By Greg Childers / GGNFS

(17·10147-71)/9 = 1(8)1461<148> = 32 · 11 · 19 · 79 · 107 · 2781801353422423656539918239<28> · C113

C113 = P47 · P67

P47 = 25676953116135086178490153800162757142685512269<47>

P67 = 1663171924588523777382227652703467418748719317652827597186987650887<67>

(17·10150-71)/9 = 1(8)1491<151> = 3 · C150

C150 = P75 · P76

P75 = 105402820794387104653536298689177070169650261803766637528304966641861624359<75>

P76 = 5973555782324552106124283562382297323088488515591965666516908145969488005453<76>

(65·10142+43)/9 = 7(2)1417<143> = 89 · 193 · 198638087 · 2247087431<10> · C121

C121 = P43 · P78

P43 = 9742597873074661129511930834554049809707829<43>

P78 = 966865935733139211288991786743936943283865345411378831384056867611197604830127<78>

(65·10144+43)/9 = 7(2)1437<145> = 3 · 251 · 7331 · C139

C139 = P65 · P74

P65 = 48022449417411814334223229597104761154016667704312594421848222541<65>

P74 = 27243841422266516181382717463539825882527519190626776820706713205388886629<74>

(10144-7)/3 = (3)1431<144> = 479 · 3257 · 127403 · 1672219 · 6038359 · C120

C120 = P58 · P62

P58 = 1902529719932711787220600137563189019784143649015519831397<58>

P62 = 87297596280136341089385935585276804436752469640445637040911007<62>

(10145-7)/3 = (3)1441<145> = 1303 · 2091183973<10> · C133

C133 = P39 · P94

P39 = 378880904950944761348832993283679200643<39>

P94 = 3228786805238941383170279259073448703600543986249677725106177919641344030607291283713411374443<94>

Oct 5, 2004 (5th)

By Tyler Cadigan / PPSIQS

(2·10154-11)/9 = (2)1531<154> = 4679929 · 62151671 · 474111779 · 10123931833<11> · 21340649531177<14> · 124377581827049<15> · C93

C93 = P29 · P31 · P35

P29 = 11155972892775276123423372961<29>

P31 = 2679162778111367510973787621601<31>

P35 = 20063613869583775177852334220694889<35>

Oct 5, 2004 (4th)

Factor Table Search is available.

Examples:

Search prime numbers.

Search composite numbers which consist of 100 digits or less.

Search factors which was discovered by GGNFS.

Search factors which was found by Makoto Kamada.

Oct 5, 2004 (3rd)

By Wataru Sakai / GMP-ECM

10161-9 = (9)1601<161> = 37871278906453241<17> · C145

C145 = P29 · P117

P29 = 21025652136804630508221938561<29>

P117 = 125585804992968912808788945390634517801861766554822671111449018351172498773938268560062296220409535778931448185975791<117>

10195-9 = (9)1941<195> = 1289 · 283435121 · 190918276279<12> · 1608873192799<13> · 387312818354664563<18> · 1079504646683992390751<22> · C122

C122 = P27 · P95

P27 = 296827436308088224012637591<27>

P95 = 71801525491886233491994351008708055401003967702537009426787904436648333892829264331597536123173<95>

Oct 5, 2004 (2nd)

By Tyler Cadigan / PPSIQS

(34·10137-7)/9 = 3(7)137<138> = 50406390252637<14> · 34685456789003348824526610617033<32> · C93

C93 = P46 · P48

P46 = 1547872150201415036131766313731406384544218071<46>

P48 = 139594499354033237182438517098215139294193516747<48>

Oct 5, 2004

The condition of 199...99 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=50250+alpha) 100 times.

2·10151-1, 2·10153-1, 2·10154-1, 2·10155-1, 2·10156-1, 2·10157-1, 2·10158-1, 2·10159-1, 2·10160-1, 2·10162-1, 2·10165-1, 2·10167-1, 2·10168-1, 2·10169-1, 2·10170-1, 2·10171-1, 2·10174-1, 2·10175-1, 2·10176-1, 2·10178-1, 2·10179-1, 2·10180-1, 2·10181-1, 2·10183-1, 2·10186-1, 2·10189-1, 2·10190-1, 2·10191-1, 2·10192-1, 2·10193-1, 2·10195-1, 2·10196-1, 2·10197-1, 2·10199-1, 2·10200-1, (35/200)

The condition of 22...221 was extended to n≤200.

We have not factored following numbers yet. These numbers passed GMP-ECM (B1=50910+alpha) 100 times.

(2·10154-11)/9, (2·10157-11)/9, (2·10158-11)/9, (2·10162-11)/9, (2·10163-11)/9, (2·10164-11)/9, (2·10165-11)/9, (2·10167-11)/9, (2·10168-11)/9, (2·10170-11)/9, (2·10171-11)/9, (2·10173-11)/9, (2·10174-11)/9, (2·10175-11)/9, (2·10176-11)/9, (2·10179-11)/9, (2·10180-11)/9, (2·10182-11)/9, (2·10183-11)/9, (2·10184-11)/9, (2·10185-11)/9, (2·10186-11)/9, (2·10187-11)/9, (2·10188-11)/9, (2·10189-11)/9, (2·10191-11)/9, (2·10192-11)/9, (2·10193-11)/9, (2·10196-11)/9, (2·10198-11)/9, (2·10199-11)/9, (2·10200-11)/9, (32/200)

Oct 4, 2004 (2nd)

By Patrick De Geest

(4·1042262-7)/3 = 133...331<42263> is PRP. This is the largest known PRP in Plateau and Depression numbers.

See also Plateau and Depression Primes (Patrick De Geest).

Oct 4, 2004

By Tyler Cadigan / PPSIQS

(22·10137-1)/3 = 7(3)137<138> = 17 · 73 · 173 · 6671719 · 10568333 · 60742673 · 202488391993093<15> · C97

C97 = P33 · P64

P33 = 512311765871649016717149445233953<33>

P64 = 7687956991006814118171485855493171149932213428300967303883804759<64>

Oct 2, 2004 (4th)

By Tyler Cadigan / PPSIQS

(4·10133-13)/9 = (4)1323<133> = 32 · 881 · 88443650427428754868785226431323<32> · C97

C97 = P47 · P50

P47 = 68594005391360380024254797250897286959710951501<47>

P50 = 92394525921162910215679849872435259743072248714029<50>

Oct 2, 2004 (3rd)

88...887 (n≤150) was completed.

Oct 2, 2004 (2nd)

By Greg Childers / GGNFS

(13·10141-31)/9 = 1(4)1401<142> = 11 · 619 · 898348572287549<15> · C123

C123 = P58 · P65

P58 = 3435189413553562745845330774313551979056266719647909175383<58>

P65 = 68741964319513004279674267230306341436095887451228338365581020147<65>

(13·10145-31)/9 = 1(4)1441<146> = 112 · C144

C144 = P40 · P48 · P56

P40 = 3215091692475905492834991049431234800323<40>

P48 = 869531799058872659572202283364390718753855862811<48>

P56 = 42700861821644302938568173372339627573281339908570890257<56>

(17·10140-71)/9 = 1(8)1391<141> = 197 · 47255407 · 103652035862097857<18> · C114

C114 = P49 · P65

P49 = 4666166461726179380801129928968110270436020676303<49>

P65 = 41951801327579378159478866821820484800548073276834673164905690109<65>

(8·10144-17)/9 = (8)1437<144> = 599 · 241135754907107<15> · C127

C127 = P41 · P86

P41 = 75874025239004842373359386572738631090619<41>

P86 = 81108415893382466766494696285229496838195542104199630796025605211394157625582860602961<86>

(8·10148-17)/9 = (8)1477<148> = 61 · 2963 · 4327 · 2220971 · 49257293 · 252105043583<12> · C114

C114 = P42 · P73

P42 = 107068210544832033178144510647295264556809<42>

P73 = 3848961691473928008685333750034076914162492347136794688130393671496560287<73>

Oct 2, 2004

Factor table of 233...339 is available.

Oct 1, 2004

Factor tables of 211...113, 211...117 and 211...119 are available.

September 2004

Sep 30, 2004 (3rd)

388...883 (n≤150) was completed.

Sep 30, 2004 (2nd)

By Greg Childers / GGNFS

(35·10143-53)/9 = 3(8)1423<144> = 11 · 3400813033692143362347940975577<31> · C113

C113 = P47 · P66

P47 = 39822446802521162148555054998307315520708034161<47>

P66 = 261049071330740757048830626374673546304849204595034145153972051249<66>

(35·10146-53)/9 = 3(8)1453<147> = 71 · 5981 · 113359 · C136

C136 = P61 · P76

P61 = 1480268819384325264781085684978331400775146249333139098019773<61>

P76 = 5457538228209977795726029602237625811827880296502011865351753095329546180419<76>

Sep 30, 2004

By Wataru Sakai / GMP-ECM

9·10159-1 = 8(9)159<160> = 151 · 2081 · 37756997 · C147

C147 = P37 · P111

P37 = 2749349496945658330354039617246556963<37>

P111 = 275909138843910536233458866490589939907450080666251250831272212920006003585355634397268342209549828865520254039<111>

Sep 29, 2004

By Tyler Cadigan / PPSIQS

(37·10125-1)/9 = 4(1)125<126> = 3 · 23 · 71 · 307 · 150587 · 149254163 · 27005742979<11> · C96

C96 = P41 · P55

P41 = 67420974835632498533086420758075874107517<41>

P55 = 6679566951980833263633468017337747460136592113701042969<55>

Sep 28, 2004 (5th)

By Julien Peter Benney

(7·107784+11)/9 is PRP.

Sep 28, 2004 (4th)

22...221 (n≤150) was completed.

Sep 28, 2004 (3rd)

By Greg Childers / GGNFS

(2·10146-11)/9 = (2)1451<146> = 3 · 7 · C145

C145 = P61 · P84

P61 = 1629005499570503911522997110980887938657079503413966178632607<61>

P84 = 649599438725074052277587080056907926964379332648616521940920933450301174280530982343<84>

(2·10150-11)/9 = (2)1491<150> = 279912173263<12> · 458976686907073<15> · C124

C124 = P58 · P66

P58 = 2834188426788549952231733673773047461459519075813368357123<58>

P66 = 610304192083969965409076522824019775128554583673057741177067810273<66>

(35·10140-53)/9 = 3(8)1393<141> = 359 · 577 · 170623768786145750823691763<27> · C110

C110 = P38 · P72

P38 = 24728406160615287305877860914676618707<38>

P72 = 444958612515831389347540610612885488167438846639007749453827719018700141<72>

(8·10139-17)/9 = (8)1387<139> = 7 · 1170563 · 9195458197<10> · 11506362253<11> · C113

C113 = P42 · P71

P42 = 541853661698287032693368052012284236209641<42>

P71 = 18921746304900975852505751265110395654913726325261378404329220798970547<71>

Sep 28, 2004 (2nd)

By Tyler Cadigan / PPSIQS

(8·10125-53)/9 = (8)1243<125> = 83 · 383 · 619 · 40140051714723693674509<23> · C96

C96 = P34 · P62

P34 = 1617387764872172982324268516123627<34>

P62 = 69580553803633007114920480486810142828978681396742673009816691<62>

Sep 28, 2004

By Wataru Sakai / GMP-ECM

9·10163-1 = 8(9)163<164> = 9311 · 9923 · 1563631 · 2134098490901084289819240413<28> · C123

C123 = P35 · P88

P35 = 60061438682395359593398744400877001<35>

P88 = 4860251353176521897528790975585779837716210646651067100277891814302127723420307300678561<88>

(88·10122-7)/9 = 9(7)122<123> = 157 · 1409 · 438427477 · 94161267251<11> · C99

C99 = P32 · P67

P32 = 45940653614093461774921904253449<32>

P67 = 2330570733202423767193315194625818946554610929797213770469865501523<67>

Sep 27, 2004 (5th)

Factor tables of 200...003 and 200...009 are available.

Sep 27, 2004 (4th)

922...229 (n≤150) was completed.

Sep 27, 2004 (3rd)

By Greg Childers / GGNFS

(83·10141+61)/9 = 9(2)1409<142> = 11 · 4337 · 1872939015628631473<19> · C120

C120 = P53 · P67

P53 = 54272364006449135417917424191715164257876553537322123<53>

P67 = 1901739818949460046819138208375310564699275416725059067732453145693<67>

(83·10146+61)/9 = 9(2)1459<147> = 157 · 48216364239555767<17> · C129

C129 = P37 · P92

P37 = 6737715143530254530717600356878452627<37>

P92 = 18081265583937853293018450560900085680497487595808160549311853998971936416529132034859354933<92>

(2·10143-11)/9 = (2)1421<143> = 3 · C142

C142 = P37 · P106

P37 = 1639704346744230467897817374963936809<37>

P106 = 4517526237041105422717248364841109362832890589334397951090334806082732090436300786518717858790161469411223<106>

Sep 27, 2004 (2nd)

The condition of 99...991 was extended to n≤200.

We have not factored following numbers yet. Run GMP-ECM (B1≥50000) first.

10^153-9, 10^159-9, 10^161-9, 10^163-9, 10^165-9, 10^169-9, 10^171-9, 10^173-9, 10^175-9, 10^177-9, 10^179-9, 10^181-9, 10^183-9, 10^185-9, 10^187-9, 10^189-9, 10^191-9, 10^193-9, 10^195-9, (19/200)

Sep 27, 2004

By Makoto Kamada / GGNFS-0.54.4-k1

10157-9 = (9)1561<157> = C157

C157 = P76 · P82

P76 = 1182138400863175552253848266595264231758705488091359346888751281045582124679<76>

P82 = 8459246390015065347380115262012913546306699962332583936149204215042988678809171729<82>

99991_157.poly
factLat.sh (extractive)
ggnfs.log
summary.txt

Sep 26, 2004 (2nd)

By Tyler Cadigan / PPSIQS

(7·10123+11)/9 = (7)1229<123> = 41 · 1429 · 29023 · 60942313 · 104687100851<12> · C95

C95 = P30 · P66

P30 = 383568871677228514534281646481<30>

P66 = 186913935623500644552720987765239281460148290673971815841649202819<66>

Sep 26, 2004

Factor tables of 188...883, 188...889, 199...993 and 199...997 are available.

Sep 25, 2004 (2nd)

Factor tables of 166...663, 166...669, 177...773 and 177...779 are available.

Sep 25, 2004

10149-3 = (9)1487<149> = 19 · 71 · 83 · 37573 · 721606590563161<15> · 1609561207914191556407872402061<31> · C95

C95 = P30 · P65

P30 = 420200185405225537573496373857<30>

P65 = 48704586230979775559414535682143440300694313427376479940972273211<65>

Sep 24, 2004 (3rd)

GGNFS 0.54.5b was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 24, 2004 (2nd)

Factor tables of 155...553, 155...557 and 155...559 are available.

Sep 24, 2004

By Greg Childers / GGNFS

(4·10119+41)/9 = (4)1189<119> = 3767 · C116

C116 = P37 · P79

P37 = 5468351428162845370288634843373069443<37>

P79 = 2157572731254216322797535461742378405090055809165408722439987179245836849818829<79>

(4·10122+41)/9 = (4)1219<122> = 7 · 1190509 · 43648126993<11> · C105

C105 = P43 · P62

P43 = 1355682374562492274028257535179450122541253<43>

P62 = 90128718688220038570007654000671430737058414743221536299348487<62>

(4·10123+41)/9 = (4)1229<123> = 18341 · 2910007 · 6126089 · 51192157 · C98

C98 = P45 · P53

P45 = 788001598394943477222987830954477571791295403<45>

P53 = 33696640755473013504475945049652716797179319979435933<53>

(4·10125+41)/9 = (4)1249<125> = 17 · 29 · 9844186708663<13> · C109

C109 = P52 · P58

P52 = 1533404138434748955067339228171983791194792755281563<52>

P58 = 5972196511516268410199167419596854493297224535950345471897<58>

(4·10126+41)/9 = (4)1259<126> = 47 · 199 · C122

C122 = P28 · P95

P28 = 2893252527708410532977738743<28>

P95 = 16424048027032334977250468790379564247730051161966791325488984093154339188794529669214911213231<95>

(4·10129+41)/9 = (4)1289<129> = 67 · 109 · 313 · 133967 · 4693228361977<13> · C105

C105 = P51 · P55

P51 = 232902447970350783340422379838762899844194911860293<51>

P55 = 1327786570528305761356677665494842809303205078766279093<55>

(4·10130+41)/9 = (4)1299<130> = 3 · 55691 · 85285559 · C117

C117 = P57 · P61

P57 = 107253181340326856748878384566645427907354430330055026519<57>

P61 = 2908208419864634963145751009015726613842860127576032867907153<61>

Sep 23, 2004 (2nd)

Factor tables of 144...447 and 144...449 are available.

Sep 23, 2004

By Tyler Cadigan / PPSIQS

(64·10195-1)/9 = 7(1)195<196> = 13 · 439 · 645877 · 741787444609<12> · 20194065442294414119935380483<29> · 179746009860835570206934469326647488405593736221729237<54> · C93

C93 = P34 · P60

P34 = 2453911908929535375171255435229813<34>

P60 = 291983498833927501377447781952357414915912130035189285430307<60>

Sep 22, 2004

By Tyler Cadigan / PPSIQS

(5·10147+31)/9 = (5)1469<147> = 13 · 29 · 129119 · 8232703 · 4452154780181895301<19> · 1479486472724455175482176443<28> · C87

C87 = P33 · P54

P33 = 595505161404659395002894544770481<33>

P54 = 353416449589679235783582856189198275165958030520153657<54>

Sep 21, 2004 (3rd)

By Wataru Sakai / GMP-ECM

9·10185-1 = 8(9)185<186> = 51506797 · C179

C179 = P37 · C142

P37 = 6651080365041166203291134547420211961<37>

C142 = [2627155446018583376056001129947388070101320462055070329967261485572839484407296033679509907414358095104997570766676583504598716504545452477747<142>]

Sep 21, 2004 (2nd)

Sequence (5·10n+13)/9 = { 7, 57, 557, 5557, 55557, ... } (n≤150) was completed.

Sep 21, 2004

By Greg Childers / GGNFS

(5·10141+13)/9 = (5)1407<141> = 17 · 4936099597171592587<19> · C121

C121 = P53 · P69

P53 = 33701761657256276577940756283838594522347463549612481<53>

P69 = 196445487242682624913904252831967998446323930075923773236971184506143<69>

(5·10142+13)/9 = (5)1417<142> = C142

C142 = P54 · P89

P54 = 120665111524603501081477618600243932272409645287711429<54>

P89 = 46041109027797012227496452577514434934470047064643607309722643103546554142308843339849633<89>

(83·10139+61)/9 = 9(2)1389<140> = 3 · 11 · 19 · 53 · 563 · 1312667 · C127

C127 = P49 · P79

P49 = 3662336709704897069095805506501482949465860726713<49>

P79 = 1025347177134503905396383859019448574941117439030030908633069003023552449572883<79>

Sep 20, 2004

Factor tables of 133...337 and 133...339 are available.

Sep 19, 2004

Factor tables of 122...227 and 122...229 are available.

Sep 18, 2004 (3rd)

Sequence (86·10n+31)/9 = { 99, 959, 9559, 95559, 955559, ... } (n≤150) was completed.

Sep 18, 2004 (2nd)

By Greg Childers / GGNFS

(86·10140+31)/9 = 9(5)1399<141> = 7 · 331883 · 1041670471<10> · C126

C126 = P46 · P80

P46 = 4516102175060756280599235604030246161696107219<46>

P80 = 87433684958660932996293941748919220401982452540216084709225342140147098500015111<80>

(86·10145+31)/9 = 9(5)1449<146> = 32 · 11 · 47 · 263 · 157489 · C135

C135 = P66 · P69

P66 = 748644374794864688961065096979617418385841681617804563480087292231<66>

P69 = 662279557109722383625027011785700167308449647917293861449905366672259<69>

(5·10139+13)/9 = (5)1387<139> = 7 · 3863 · C135

C135 = P51 · P85

P51 = 119593518641097451644193896912291636728002588053467<51>

P85 = 1717896927710932976108335587671600737580141438304167747953842334628585908745228760031<85>

Sep 18, 2004

By Wataru Sakai / GMP-ECM

(34·10124-7)/9 = 3(7)124<125> = 37 · 71 · 9507133 · 37002749319959491<17> · C98

C98 = P35 · P63

P35 = 54160504315818838339683617139143941<35>

P63 = 754762079112596521424663770266038984483850910872151629562729337<63>

Sep 17, 2004 (2nd)

Yahoo! Group for GGNFS users was created.

GGNFS - Yahoo Groups

Sep 17, 2004

GGNFS 0.54.4 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 16, 2004 (3rd)

GGNFS 0.54.3 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 16, 2004 (2nd)

Sequence (89·10n+1)/9 = { 99, 989, 9889, 98889, 988889, ... } (n≤150) was completed.

Sep 16, 2004

By Greg Childers / GGNFS

(89·10138+1)/9 = 9(8)1379<139> = 31 · 7739203631<10> · C128

C128 = P45

P45 = 123848493724489026440104908771242383090771607<45>

P84 = 332811864832857994803825785286396971936555207279064853034369400273436459201384992607<84>

(89·10147+1)/9 = 9(8)1469<148> = 11 · 2423 · 14741 · C140

C140 = P39 · P49 · P53

P39 = 160222624630254869280396258996178652003<39>

P49 = 4972139990969861070890682623316998893525772950021<49>

P53 = 31594192671194606533148648647345097435701380247405111<53>

Sep 14, 2004 (3rd)

Sequence (82·10n+71)/9 = { 99, 919, 9119, 91119, 911119, ... } (n≤150) was completed.

Sep 14, 2004 (2nd)

By Greg Childers / GGNFS

(82·10146+71)/9 = 9(1)1459<147> = 61 · 569 · 11093 · 16706953 · C132

C132 = P62 · P70

P62 = 15053743424163591157391476013331832737622728051781855562824069<62>

P70 = 9408891664939924579917892583360464032946180141104136360744149482265091<70>

Sep 14, 2004

By Wataru Sakai / GMP-ECM, ppmpqs

(5·10139+31)/9 = (5)1389<139> = 3 · 13381169 · 488233961499763027<18> · C114

C114 = P36 · P37 · P41

P36 = 767937389205546486990497899383321239<36>

P37 = 5067987060927461212198258191296636443<37>

P41 = 72832109410715101979304172083529747274603<41>

Sep 13, 2004 (3rd)

Sequence (25·10n-1)/3 = { 83, 833, 8333, 83333, 833333, ... } (n≤150) was completed.

Sep 13, 2004 (2nd)

By Greg Childers / GGNFS

(82·10145+71)/9 = 9(1)1449<146> = 34 · 11 · 4409 · 30570937 · C132

C132 = P53 · P80

P53 = 55623864836423887831193780354836900950336852724991831<53>

P80 = 13639034531999080193140484277331303730420699844795939558191731427804915955621883<80>

(25·10143-1)/3 = 8(3)143<144> = 1512 · 643 · 29129 · 15000224477369<14> · C120

C120 = P48 · P72

P48 = 850059927425215940194387730228305887793457647027<48>

P72 = 153031561240574261950447694587661791245925129000655462949369722678775053<72>

Sep 13, 2004

GGNFS 0.54.2 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 12, 2004

By Makoto Kamada / GGNFS-0.53.3-k2, GGNFS-0.54.1-k1

(4·10150+41)/9 = (4)1499<150> = C150

C150 = P38 · P113

P38 = 24478169540608218973559824375006284619<38>

P113 = 18156767960411845144545021647808332832799204299279924680716228196015707338698208678714543612583310171092766533571<113>

Sep 11, 2004 (3rd)

GGNFS 0.54.1 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 11, 2004 (2nd)

Sequence (13·10n-1)/3 = { 43, 433, 4333, 43333, 433333, ... } (n≤150) was completed.

Sep 11, 2004

By Greg Childers / GGNFS

(13·10143-1)/3 = 4(3)143<144> = 821 · 7993 · 224134284877<12> · C126

C126 = P48 · P78

P48 = 496669957831811171429452328504036234709614664907<48>

P78 = 593188799492163143544655710343277873676156368756362875007640032998963193696199<78>

(25·10141-1)/3 = 8(3)141<142> = 13 · 43766441 · C134

C134 = P57 · P77

P57 = 173646134673467043474614594249996799616095097962318053773<57>

P77 = 84346885144182371325885485048193091944351393978571177194778531824663780319237<77>

Sep 10, 2004 (5th)

By Wataru Sakai / GMP-ECM

(88·10128-7)/9 = 9(7)128<129> = 4159 · 5657 · 2186341 · C116

C116 = P33 · P83

P33 = 501252067274896148186736882778243<33>

P83 = 37921978507996725275019959958606512270468583114190168121096926524710791167838513033<83>

Sep 10, 2004 (4th)

GGNFS 0.54.0 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 10, 2004 (3rd)

By Sander Hoogendoorn / GMP-ECM

9·10165-1 = 8(9)165<166> = 1139239 · C160

C160 = P22 · C139

P22 = 3500008777892854273507<22>

C139 = [2257140180752772341749697563476673520949004624616088331617541248692208685477716800333936267810500726303368685688650280142696027086834845763<139>]

9·10181-1 = 8(9)181<182> = 2347 · 18121 · 14881545317<11> · C165

C165 = P23 · C142

P23 = 18520231788365026399039<23>

C142 = [7678083141389664656001425818220694158822776458038611028631283111975249628251012772571482748321660481753969878560664066088398797796345069148879<142>]

9·10189-1 = 8(9)189<190> = 67 · 133187 · 2078087862871<13> · 234621664993637<15> · C157

C157 = P28 · C129

P28 = 5363095884001110231789672199<28>

C129 = [385707683405733164444530365933755816046832242345670430607839333744882290009141947111896835408591178894659692587255754972460523547<129>]

9·10199-1 = 8(9)199<200> = 311 · 18816601 · 7199849885356048147<19> · 6189868364159015753089<22> · C150

C150 = P19 · C131

P19 = 8780607192536057363<19>

C131 = [39301718485862350257708325333181729090996815780048171845715841482163767806759091111427975609647926520399156269244884232809787052921<131>]

Sep 10, 2004 (2nd)

GGNFS 0.53.4 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Sep 10, 2004

By Wataru Sakai / GMP-ECM

9·10197-1 = 8(9)197<198> = 31 · 277 · C195

C195 = P23 · C172

P23 = 27450632285963828291729<23>

C172 = [3818112268196165689479781790439330543302891662224712896124961773277885163454921823655935042268853704582463791302464990137598241649983644542032759069272259846593508442000013<172>]

Sep 8, 2004 (3rd)

Sequence (4·10n+23)/9 = { 7, 47, 447, 4447, 44447, ... } (n≤150) was completed.

Sep 8, 2004 (2nd)

By Greg Childers / GGNFS

(4·10150+23)/9 = (4)1497<150> = 32 · 14797 · 158129 · C140

C140 = P52 · P88

P52 = 2334639100316582423542633998614479963495682843452583<52>

P88 = 9040033073803432887815150453074684725159462725714073113819607020985016556962672188533077<88>

(13·10137-1)/3 = 4(3)137<138> = 393253967 · 1142265150635677<16> · C114

C114 = P49 · P66

P49 = 5827423332237870322314881927068091355028309484501<49>

P66 = 165540967720274491075300161169534948362158630988747150913146422587<66>

Sep 8, 2004

By Wataru Sakai / GMP-ECM

(5·10132+31)/9 = (5)1319<132> = 17 · 15009607 · C124

C124 = P35 · P90

P35 = 16735349127842839384417436402568419<35>

P90 = 130099154892445905531232574715219228257936537877690891576918266610176625381368629581225019<90>

Sep 7, 2004 (3rd)

By Sander Hoogendoorn

9·10163-1 = 8(9)163<164> = 9311 · 9923 · 1563631 · C150

C150 = P28 · C123

P28 = 2134098490901084289819240413<28>

C123 = [291913688629840742869263333478236850875137905645395736028272329354747978590525243351837422492661183198777698321810798675561<123>]

9·10169-1 = 8(9)169<170> = 90911 · 303273671083<12> · C154

C154 = P21 · P153

P21 = 561921476752175312039<21>

P153 = 5809192057492029790189790649473348809407304780607105559887659626527691939992391503927629486440677147928852285888430859909715432233957<133>

9·10183-1 = 8(9)183<184> = 9587 · 44803933 · 328987231 · C164

C164 = P25 · P140

P25 = 2440572839378229347582719<25>

P140 = 26095932910686069765618451295488481733475751249529060617603572778843532932969652780988006968716186630596900105613502368966849560241018262121<140>

9·10187-1 = 8(9)187<188> = 107 · 3091427 · C180

C180 = P21 · C160

P21 = 119847129180121192841<21>

C160 = [2270241721559984930272736143311910112693495887639753969987718778079115797333387754225729923122144151094026523595963349024633942322055857934743702122096103206951<160>]

Sep 7, 2004 (2nd)

By Sander Hoogendoorn

(64·10167-1)/9 = 7(1)167<168> = 3 · 17430641850992347<17> · 1507214810701852948504954498877<31> · C121

C121 = P31 · P91

P31 = 2593393711071875340499604499083<31>

P91 = 3479038412691528923419866920945000559517759572016377269174396284827135012176337635978462281<91>

(64·10177-1)/9 = 7(1)177<178> = 13 · 43 · 67 · 641 · 304879 · 1430811465791<13> · 145377867948394877437832769951054564028056043<45> · C109

C109 = P28 · P30 · P52

P28 = 2486758115223396550967154991<28>

P30 = 257817544682932484846649464881<30>

P52 = 7285151607634411586597669155389338444323201940852071<52>

(64·10189-1)/9 = 7(1)189<190> = 13 · 31 · 1307 · 9643 · 16111 · 168927683 · 5434428449<10> · 710050492681<12> · 9557531723783932333<19> · 35846499715122706776413163888590388065147<41> · C87

C87 = P39 · P49

P39 = 182561575784510959989401173628946017923<39>

P49 = 2131455913202100114324989458676266259381078561077<49>

Sep 7, 2004

By Sander Hoogendoorn

(64·10167-1)/9 = 7(1)167<168> = 3 · 17430641850992347<17> · C152

C152 = P31 · C121

P31 = 1507214810701852948504954498877<31>

C121 = [9022516340051690763495090685189602263225102783722102169688190088102308544830931331235226799541233270412550586475614588323<121>]

(64·10195-1)/9 = 7(1)195<196> = 13 · 439 · 645877 · 741787444609<12> · 179746009860835570206934469326647488405593736221729237<54> · C122

C122 = P29 · C93

P29 = 20194065442294414119935380483<29>

C93 = [716501784999487801171216138669504140498635676344979947291466821869221874333608342721140142591<93>]

Sep 6, 2004 (3rd)

By Makoto Kamada

R49081+6, R86453+6, R86453+2 and R86453+8 are composite.

As "Factorizations of 11...117" says:

(106k+1+53)/9 is divisible by 7.

(1034k+25+53)/9 is divisible by 4013.

R49081+6 = (1049081-1)/9+6 = (1049081+53)/9 = (106·8180+1+53)/9 is divisible by 7.

R86453+6 = (1086453-1)/9+6 = (1086453+53)/9 = (1034·2542+25+53)/9 is divisible by 4013.

As "Factorizations of 11...113" says:

(1018k+17+17)/9 is divisible by 19.

R86453+2 = (1086453-1)/9+2 = (1086453+17)/9 = (1018·4802+17+17)/9 is divisible by 19.

R86453+8 little confuses us. In the same way,

(1052364k+34089+71)/9 is divisible by 104729.

R86453+8 = (1086453-1)/9+8 = (1086453+71)/9 = (1052364·1+34089+71)/9 is divisible by 104729.

Sep 6, 2004 (2nd)

Sequence (10n+17)/9 = { 3, 13, 113, 1113, 11113, ... } (n≤150) was completed.

Sep 6, 2004

By Greg Childers / GGNFS

(10146+17)/9 = (1)1453<146> = 13 · 1231 · C141

C141 = P36 · P52 · P54

P36 = 438093756688394904258681753902386243<36>

P52 = 5023228213095364349383280538083151469018517484491963<52>

P54 = 315504902521584066530740748554192812824625874515224819<54>

(10148+17)/9 = (1)1473<148> = 3 · 7 · 1051 · C143

C143 = P40 · P104

P40 = 1027191010958335312343169808383374823067<40>

P104 = 49009951146811381275847466159640285794901276734209720419172068637840787902160249833635533661924144332909<104>

Sep 5, 2004

Conditions of the sequence (64·10n-1)/9 = { 71, 711, 7111, 71111, 711111, ... } and 9·10n-1 = { 89, 899, 8999, 89999, 899999, ... } were extended to n≤200.

We have not factorized following numbers yet. Run GMP-ECM (B1≥250000) first.

(64·10151-1)/9, (64·10157-1)/9, (64·10161-1)/9, (64·10163-1)/9, (64·10167-1)/9, (64·10169-1)/9, (64·10173-1)/9, (64·10177-1)/9, (64·10181-1)/9, (64·10185-1)/9, (64·10187-1)/9, (64·10189-1)/9, (64·10191-1)/9, (64·10193-1)/9, (64·10195-1)/9, (64·10197-1)/9, (64·10199-1)/9, (17/200)

9·10155-1, 9·10159-1, 9·10163-1, 9·10165-1, 9·10169-1, 9·10171-1, 9·10173-1, 9·10177-1, 9·10181-1, 9·10183-1, 9·10185-1, 9·10187-1, 9·10189-1, 9·10191-1, 9·10193-1, 9·10197-1, 9·10199-1, (17/200)

Sep 4, 2004 (3rd)

Sequence (5·10n-41)/9 = { 1, 51, 551, 5551, 55551, ... } (n≤150) was completed.

Sep 4, 2004 (2nd)

By Greg Childers / GGNFS 0.53.3

(4·10143+23)/9 = (4)1427<143> = 13 · C142

C142 = P51 · P92

P51 = 180844134716075035203997990871394431806442451443269<51>

P92 = 18904696158218976770356643450736744237863202773063745264948680236412794860271753591597064351<92>

(5·10143-41)/9 = (5)1421<143> = 33 · 23 · 29 · 216916329106936233353<21> · C119

C119 = P47 · P72

P47 = 90598328670329288633752170604448516198086340879<47>

P72 = 156973182953920998467116851061533821887338330176601859281927461141694097<72>

(5·10146-41)/9 = (5)1451<146> = 3 · 17 · 47 · C143

C143 = P56 · P88

P56 = 13516118890631063865273661782358529123478184587876781679<56>

P88 = 1714776241251344387094512862437122338817972507003457126221272519176089410866002866913477<88>

Sep 4, 2004

By Wataru Sakai / GMP-ECM

(34·10136-7)/9 = 3(7)136<137> = 37 · 7561 · 17627 · 33034501 · 537464580563<12> · 106397931249683<15> · C94

C94 = P34 · P60

P34 = 5266615485269965446457200154214233<34>

P60 = 770006950366641907581458326988091801669850181785441305478499<60>

(5·10134+31)/9 = (5)1339<134> = 293957 · 44997707753<11> · 83394628547<11> · C107

C107 = P30 · P78

P30 = 138866219249377123128336908279<30>

P78 = 362675824798389919823466254642372711644808581986822726155119511526421051854983<78>

Sep 2, 2004

By Greg Childers / GGNFS 0.53.3

(7·10132-61)/9 = (7)1311<132> = 35 · 78681091949<11> · C119

C119 = P57 · P62

P57 = 997159532317710164827409930329006977759922101974333857913<57>

P62 = 40795685327010248173017671377143396808763033998584125184263381<62>

(7·10133-61)/9 = (7)1321<133> = 56883344330411<14> · 1157987595398831<16> · C105

C105 = P39 · P66

P39 = 605590275489498678158994613991181901667<39>

P66 = 194978896828514501026116372320202578329571184138844238719786421093<66>

(7·10134-61)/9 = (7)1331<134> = 599 · 51599 · C127

C127 = P50 · P77

P50 = 33590633004144418105975015304787218817644473943831<50>

P77 = 74915077847348830254424937905257609877425606983958772187549932272034696889941<77>

Sep 1, 2004 (2nd)

By Greg Childers / GGNFS 0.53.3

(7·10128-61)/9 = 77...771<128> = 83 · 5017511 · C120

C120 = P50 · P70

P50 = 41898366721982735345452155476439819713064825086237<50>

P70 = 4457506767999863893087424223511112803488068968019975028810921032313691<70>

(7·10129-61)/9 = 77...771<129> = 3 · C129

C129 = P40 · P90

P40 = 2004019751938548505602825576080732027539<40>

P90 = 129369612753801448206766034833512222723128676656403384621304657427751534950891311922173763<90>

Sep 1, 2004

By Wataru Sakai / GMP-ECM

(88·10121-7)/9 = 977...77<122> = 193 · 18216906809<11> · C110

C110 = P30 · C80

P30 = 543098398934116820600769928163<30>

C80 = [51207042619214580326770717794607953096741049490737309279078438743985183013967667<80>]

(88·10132-7)/9 = 977...77<133> = 3 · 29 · 1429 · 330749 · 10113404043467<14> · C110

C110 = P31 · C79

P31 = 5555454819131271767810517200293<31>

C79 = [4232268025350110505638603754126975557672854401820692974551059282484805493945121<79>]

By Makoto Kamada / PPSIQS 1.1

(88·10132-7)/9 = 977...77<133> = 3 · 29 · 1429 · 330749 · 10113404043467<14> · 5555454819131271767810517200293<31> · C79

C79 = P36 · P43

P36 = 560996190255377500506099490941179599<36>

P43 = 7544201010390981992746447100393963449963279<43>

(88·10121-7)/9 = 977...77<122> = 193 · 18216906809<11> · 543098398934116820600769928163<30> · C80

C80 = P33 · P47

P33 = 849372735117096335241019546017641<33>

P47 = 60288069656668539414818301579223067728720316987<47>

August 2004

Aug 31, 2004 (2nd)

Sequence (5·10n-23)/9 = { 3, 53, 553, 5553, 55553, ... } (n≤150) was completed.

Aug 31, 2004

By Greg Childers / GGNFS

(5·10144-23)/9 = 55...553<144> = 3155473 · C138

C138 = P61 · P77

P61 = 3457898337391254117443536803587089986426888551811788124829981<61>

P77 = 50915592927019281212453401230452149699776576675503934503083410807471594464581<77>

(5·10150-23)/9 = 55...553<150> = 3124063013<10> · C141

C141 = P34 · P108

P34 = 1261351634852468232589667781970541<34>

P108 = 140984554188332077855633489967688233437420652572411041963485055154719514641574805797228505081879605516177441<108>

Aug 30, 2004

By Wataru Sakai / GMP-ECM

(5·10136+31)/9 = 55...559<136> = 32 · 19 · 14621 · 18405487608033979<17> · C114

C114 = P29 · P85

P29 = 22941531353226945978587822711<29>

P85 = 5262408723788222083958932368465628124821942929809754825892965345331732331829246044221<85>

(88·10125-7)/9 = 977...77<126> = 103 · 1104638413<10> · 783570542195239159<18> · C98

C98 = P33 · P65

P33 = 583194596093677893676999249215487<33>

P65 = 18805773661709255464759023344806978999117917846849495140292588971<65>

(88·10134-7)/9 = 977...77<135> = 109 · 2269471297<10> · 279911946799<12> · 856899311599<12> · C101

C101 = P26 · P75

P26 = 49976932281996619715258291<26>

P75 = 329737352937526175571243655849882152236634405766781729375262653015197094839<75>

Aug 29, 2004 (2nd)

By Greg Childers / GGNFS

(5·10143-23)/9 = 55...553<143> = 587 · 5969437 · 363320389 · C125

C125 = P41 · P84

P41 = 96315368735175588476997855956059367718617<41>

P84 = 453075583452401617266699849132802617393128642784210542825421600112582684159010445899<84>

Aug 29, 2004

By Makoto Kamada / PFGW

1026718-108906-1 is near-repdigit prime. (26718 digits)

1030504-1010168-1 is near-repdigit prime. (30504 digits)

Aug 28, 2004 (3rd)

By Naoki Yamamoto / GMP-ECM, PPSIQS 1.1

(4·10139-13)/9 = 44...443<139> = 3 · 347 · 9066214008695924081<19> · C117

C117 = P35 · P39 · P43

P35 = 62758738670313835736654307681801469<35>

P39 = 860577449091221010153116454199427374951<39>

P43 = 8719199566569262614948284612004217364358257<43>

Aug 28, 2004 (2nd)

By Greg Childers / GGNFS

(5·10142-23)/9 = 55...553<142> = 3 · 17 · C141

C141 = P50 · P91

P50 = 67446337988576193814235887298581645667909842134703<50>

P91 = 1615098241391384562749769450064252517974558843846458794999503329618544609394159962629906901<91>

Aug 28, 2004

By Sander Hoogendoorn / GGNFS

(34·10121-7)/9 = 377...77<122> = 37 · 59 · C119

C119 = P43 · P76

P43 = 2885175855914863701516781901606315598600683<43>

P76 = 5998054156309717055110960940861832877646996441285735446346101979722675862293<76>

Aug 27, 2004 (2nd)

Factor table of 122...223 is available.

Aug 27, 2004

By Greg Childers / GGNFS

(5·10133-23)/9 = 55...553<133> = 3 · 73 · 79 · 199 · 1505173 · C121

C121 = P44 · P77

P44 = 46723373906581656680817154017202356736601543<44>

P77 = 22944711285892422900279830474026033242608228109256425452324948591607523522873<77>

(5·10141-23)/9 = 55...553<141> = 7 · 73 · 747982158741485693<18> · C121

C121 = P55 · P66

P55 = 2337328675718309158903020591142384471616803828915676963<55>

P66 = 621864218337745482757167500083886259558150403580690738504658519097<66>

Aug 26, 2004 (5th)

Sequence 2·10n-1 = { 19, 199, 1999, 19999, 199999, ... } (n≤150) was completed.

Aug 26, 2004 (4th)

By Chris Monico / GGNFS

2·10132-1 = 199...99<133> = 383 · 6784703 · 40846423 · 295764098205281929<18> · C98

C98 = P36 · P63

P36 = 157992194582767457565322208346460391<36>

P63 = 403241538412822815665069568615264515364295352454530261564930183<63>

Aug 26, 2004 (3rd)

By Wataru Sakai / GMP-ECM

(34·10137-7)/9 = 377...77<138> = 50406390252637<14> · C124

C124 = P32 · C93

P32 = 34685456789003348824526610617033<32>

C93 = [216074437871417469140229483512985570728754485831228584104580782638769496740849010032758535037<93>]

Aug 26, 2004 (2nd)

By Greg Childers / GGNFS

(7·10118-61)/9 = 77...771<118> = 3217 · 25297654516081<14> · C101

C101 = P38 · P64

P38 = 15532685161648299645436808908256508059<38>

P64 = 6152869061347022773120137671779564447700348458674270239224253297<64>

(7·10124-61)/9 = 77...771<124> = 23 · 148573 · C118

C118 = P37 · P82

P37 = 1729703780752569274687317509531141257<37>

P82 = 1315879336314025102410131461657237752084658495968833748838537800733316050062033257<82>

(5·10127-23)/9 = 55...553<127> = 3 · 177544559 · C119

C119 = P53 · P66

P53 = 57735393220072586184214785431113466220986058930404477<53>

P66 = 180657811404142454615368294277776931300547360361648960048421496457<66>

(5·10130-23)/9 = 55...553<130> = 33 · 4049 · 57753354473<11> · C114

C114 = P38 · P77

P38 = 19960569960792207752495397053020759637<38>

P77 = 44082457912202275382610636840555331907749721721065039824037003201618677031711<77>

Aug 26, 2004

By Sander Hoogendoorn / GGNFS

3·10130-1 = 299...99<131> = C131

C131 = P42 · P90

P42 = 176410843726584853883407743387462128062837<42>

P90 = 170057573368314684049302929168844425493413216950195208787238174395441995530703625941928227<90>

Aug 25, 2004 (5th)

By Wataru Sakai / GMP-ECM

(5·10147+31)/9 = 55...559<147> = 13 · 29 · 129119 · 8232703 · 4452154780181895301<19> · C114

C114 = P28 · C87

P28 = 1479486472724455175482176443<28>

C87 = [210461319855963603918690047463997122821686720568503127833902340218293951960145917799017<87>]

Aug 25, 2004 (4th)

Sequence (2·10n+43)/9 = { 7, 27, 227, 2227, 22227, ... } (n≤150) was completed.

Aug 25, 2004 (3rd)

By Naoki Yamamoto / GMP-ECM

(4·10133-13)/9 = 44...443<133> = 32 · 881 · C129

C129 = P32 · C97

P32 = 88443650427428754868785226431323<32>

C97 = [6337710609168435045816071777774001848170814820004013594434185050821845551425814831622495237307529<97>]

Aug 25, 2004 (2nd)

By Greg Childers / GGNFS

(2·10150+43)/9 = 22...227<150> = 3671 · C146

C146 = P42 · P105

P42 = 157565285946882496580150516924132711926663<42>

P105 = 384186906691672283239484922312826833955667843655411472913536560158364186826432903253690140355517421267699<105>

(5·10126-23)/9 = 55...553<126> = 17 · 2423 · C122

C122 = P60 · P62

P60 = 699371641821031509426181243514691610033944032212980992934229<60>

P62 = 19284888882897143716756472125298651081954215492789755961542427<62>

Aug 25, 2004

By Sander Hoogendoorn / GGNFS

3·10125-1 = 299...99<126> = 7 · 3599650081<10> · 31612646761<11> · C105

C105 = P46 · P59

P46 = 3876544332029444008036492867365402990466431683<46>

P59 = 97153246083586305759374376504412500632762391535023918322219<59>

Aug 24, 2004 (3rd)

By Sander Hoogendoorn

(55·102779-1)/9 is prime.

Aug 24, 2004 (2nd)

GGNFS 0.53.3 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Aug 24, 2004

By Sander Hoogendoorn / GGNFS 0.53.0 with getdeps 0.50.2-k1

5·10133-1 = 499...99<134> = 7 · 71 · 219487417057<12> · 2348810983951<13> · C108

C108 = P38 · P71

P38 = 15643468407459141953163921151000061497<38>

P71 = 12474492012328826373816556204599871102049686859053368900342040470592073<71>

Aug 23, 2004 (2nd)

Condition of the sequence 10n-3 = { 7, 97, 997, 9997, 99997, ... } was extended to n≤150.

Following numbers were not factorized. These numbers might have small factors. You should run GMP-ECM (B1≥1000000) first.

n= 141, 146, 147, 148, 149, (5/150)

Aug 23, 2004

By Greg Childers / GGNFS 0.53.2

(2·10146+43)/9 = 22...227<146> = 32 · 29 · C143

C143 = P43 · P101

P43 = 3364565907180457097034187412279371804597387<43>

P101 = 25305675747513146684875882899371352586297206368096475611848955976490346440281246471121840525358003461<101>

Aug 22, 2004 (3rd)

By Naoki Yamamoto / GGNFS 0.50.2

(4·10128-13)/9 = 44...443<128> = 23 · 43 · 512412863 · C116

C116 = P51 · P66

P51 = 333206455823654062100588260759434130906808772074837<51>

P66 = 263201136283162454275794566273264043568002234611743477143224398277<66>

Aug 22, 2004 (2nd)

GGNFS 0.53.2 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Aug 22, 2004

By Naoki Yamamoto / GGNFS 0.50.2, PPSIQS 1.1

(4·10129-13)/9 = 44...443<129> = 229 · C127

C127 = P32 · P41 · P55

P32 = 20990037785105128323588237213979<32>

P41 = 54502554364749898092285546838629172994617<41>

P55 = 1696492415514857958127622430338131526395673614569962069<55>

Aug 21, 2004 (3rd)

By Naoki Yamamoto / GGNFS 0.50.2

(4·10124-13)/9 = 44...443<124> = 32 · 26459 · 1045621041241625955707<22> · C98

C98 = P35 · P63

P35 = 30367480109022487445766221681028821<35>

P63 = 587784969575581161395939998890201991302322526714771636885549999<63>

Aug 21, 2004 (2nd)

By Makoto Kamada

I clearly should have tried GMP-ECM more.

Results of GGNFS 0.53.0
Factorizer: GGNFS 0.53.0 by Chris Monico
Execution environment: Pentium 4 (3.06GHz), Windows XP, Cygwin
name parameters results
target
poly
skew RLIM
ALIM
LPBR
LPBA
MFBR
MFBA
RLAMBDA
ALAMBDA
siever QSTEP q-loops factors total
actual
99997_149 C125=(10149-3)/19/71/83/37573/P15
(1030)5-30<150>
3 1600000
1600000
25
25
42
42
1.88
1.88
12 800000 6 P31·C95 36.29
36.80

Aug 21, 2004

By Greg Childers / GMP-ECM

(34·10131-7)/9 = 377...77<132> = 19 · 67601 · C126

C126 = P28 · P98

P28 = 6288769795552204180769775851<28>

P98 = 46769635893058267878190776473401799344503349258949702146522667174623480094831320247302033067906033<98>

Aug 20, 2004 (3rd)

By Chris Monico / GGNFS

2·10137-1 = 199...99<138> = 107933154040501<15> · C124

C124 = P59 · P66

P59 = 11254877967108971721971687364747575335643268954022536802019<59>

P66 = 164639613139898133672159836253458304835231081639583063417570849921<66>

Aug 20, 2004 (2nd)

By Naoki Yamamoto / GGNFS 0.50.2

(4·10125-13)/9 = 44...443<125> = 7 · 93377 · 240860290487<12> · C108

C108 = P31 · P78

P31 = 1061760791562605750846153441939<31>

P78 = 265881203190276539563970491198910438199516859054681554008060898087257465997209<78>

Aug 20, 2004

By Greg Childers / GMP-ECM

(34·10132-7)/9 = 377...77<133> = 32 · 1867 · 1748743559555400006807950141<28> · C102

C102 = P28 · P74

P28 = 7254004109979341312421744721<28>

P74 = 17723343506004936697214614039918927960791058454059566778726810617202213319<74>

(34·10139-7)/9 = 377...77<140> = 37 · 1586537 · 2330145454548179<16> · C117

C117 = P31 · P87

P31 = 1619770177395862286483247847039<31>

P87 = 170509290882093697207008859530456309564425733897850238400787099667581196837729899566793<87>

Aug 19, 2004 (5th)

By Wataru Sakai / GMP-ECM

(34·10129-7)/9 = 377...77<130> = 3 · 277 · 15811637 · 19183430041663<14> · C107

C107 = P32 · P75

P32 = 30113967432941796834668647331809<32>

P75 = 497696182350347055977921428273088348975758183194450101962994877260301281773<75>

Aug 19, 2004 (4th)

By Chris Monico / GGNFS

2·10140-1 = 199..99<141> = 89 · 68567 · 411986842103<12> · 78243273145651897<17> · C106

C106 = P41 · P65

P41 = 45790969898680950598430026489151331148057<41>

P65 = 22203152531205841279242744607049040699497136455068620741800643479<65>

Aug 19, 2004 (3rd)

By Naoki Yamamoto / GGNFS 0.50.2

(4·10120-13)/9 = 44...443<120> = 17 · 29 · 1951 · C114

C114 = P48 · P67

P48 = 126278279929905556957812282763062906900442138493<48>

P67 = 3659187263304819072653186507809952999110494563658336236607612963757<67>

(4·10118-13)/9 = 44...443<118> = 3 · 269389 · 4143961337<10> · C103

C103 = P39 · P64

P39 = 775433748534841428512105225274185871533<39>

P64 = 1711417528326269878672672868878672958755897011537865961679653449<64>

Aug 19, 2004 (2nd)

By Makoto Kamada

Results of GGNFS 0.53.0
Factorizer: GGNFS 0.53.0 by Chris Monico
Execution environment: Pentium 4 (3.06GHz), Windows XP, Cygwin
name parameters results
target
poly
skew RLIM
ALIM
LPBR
LPBA
MFBR
MFBA
RLAMBDA
ALAMBDA
siever QSTEP q-loops factors total
actual
99997_145 C131=(10145-3)/7/107/P12
(1029)5-3<145>
2 1000000
1000000
25
25
42
42
1.89
1.89
12 500000 8 P55·P76 25.75
26.03

Aug 19, 2004

By Greg Childers / GGNFS-0.52.1

(2·10145+43)/9 = 22...227<145> = 7 · 239 · 197558191 · 30733767413<11> · 1064894417201<13> · C111

C111 = P40 · P71

P40 = 7548491687442602199312838584500034844247<40>

P71 = 27215353068933707944920442554488103229476570627617679875175622257104599<71>

By Greg Childers / GMP-ECM, PPSIQS

(4·10126-13)/9 = 44...443<126> = 181 · 1783981 · 2187208687<10> · C108

C108 = P33 · P33 · P44

P33 = 145119096374045890132496165483233<33>

P33 = 379384042130033365903045831353401<33>

P44 = 11430226472250843355124233756188951341826253<44>

Aug 18, 2004 (4th)

By Chris Monico / GMP-ECM

2·10142-1 = 199...99<143> = 7 · 9554829631<10> · 4356731702671<13> · 3357467657868616871<19> · C101

C101 = P34 · P67

P34 = 2187736421927986737235449390719177<34>

P67 = 9344183469892461100358281997257285354029613953632153751125132345671<67>

Aug 18, 2004 (3rd)

By Naoki Yamamoto / PPSIQS 1.1

(7·10137+11)/9 = 77...779<137> = 13 · 1039 · 408241 · 26181751369<11> · 3425292729398808720905941333<28> · C90

C90 = P32 · P58

P32 = 22056639529761150661156954369573<32>

P58 = 7130898895763021156191882973421912329046913869904778581777<58>

Aug 18, 2004 (2nd)

By Chris Monico / GGNFS

2·10143-1 = 199...99<144> = 644351574301<12> · C132

C132 = P39 · P94

P39 = 107281422616573668503595416894220191851<39>

P94 = 2893227456310286462832991811810130099788185702416662782780831395802057171334344263213571023649<94>

Aug 18, 2004

By Makoto Kamada

Results of GGNFS 0.53.0.

Results of GGNFS 0.53.0 on Pentium 4 3.06GHz + Windows XP + Cygwin
name version target
poly
factor
skew RLIM
ALIM
LPBR
LPBA
MFBR
MFBA
RLAMBDA
ALAMBDA
QSTEP siever shortcut
getdeps
total
actual
99997_139 GGNFS
0.53.0
99...997<139>
(1028)5-30<140>
C112=P41·P71
3 800000
800000
25
25
42
42
1.80
1.80
400000 12 5
6
14.72
14.80

Aug 17, 2004 (3rd)

By Greg Childers

(2·10142+43)/9 = 22...227<142> = C142

C142 = P44 · P98

P44 = 85575960030413375991725497538275202907116371<44>

P98 = 25967832805293130914623433239564146332704548526760355957782902914023432604012069669809063815161537<98>

Aug 17, 2004 (2nd)

By Naoki Yamamoto / PPSIQS 1.1

(4·10135-13)/9 = 44...443<135> = 487 · 84319 · 124557435973<12> · 2797096370368950528020003<25> · C92

C92 = P43 · P49

P43 = 3501974296552962694014683900191202199676961<43>

P49 = 8871009204635018234101741616969553488078528522909<49>

By Naoki Yamamoto / GMP-ECM

(7·10137+11)/9 = 77...779<137> = 13 · 1039 · 408241 · 26181751369<11> · C117

C117 = P28 · C90

P28 = 3425292729398808720905941333<28>

C90 = [157283666467016791459278588493585530666059307917051439689052861990003340364439962061071221<90>]

Aug 17, 2004

GGNFS-0.53.0 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Aug 16, 2004 (4th)

Factor tables of the near-repdigit palindrome sequence 77...77477...77, 77...77577...77, 77...77677...77, 99...99299...99, 99...99899...99 are available. Near-repdigit Palindrome forms (R)wD(R)w are completely factored up to 101 digits.

Aug 16, 2004 (3rd)

By Greg Childers / GMP-ECM

(8·10124-53)/9 = 88...883<124> = 3 · 73 · 17 · 1003295831<10> · C111

C111 = P33 · P78

P33 = 533252834868991076123023980274187<33>

P78 = 949775583879503059080554641404277630343016126240250646001790651451482941038323<78>

By Greg Childers / GMP-ECM, PPSIQS

(8·10150-53)/9 = 88...883<150> = 61 · 173 · 5911811 · 3977381638220226078712047067<28> · C112

C112 = P31 · P36 · P47

P31 = 1262586736045044638972457650263<31>

P36 = 180055297964424173888575711364616079<36>

P47 = 15757474264116676493899622251753222363620467539<47>

By Greg Childers / GGNFS-0.52.1

(2·10139+43)/9 = 22...227<139> = 72 · 163 · 1237 · 333292525991<12> · C120

C120 = P45 · P76

P45 = 250032617848968707843053187291507341768566071<45>

P76 = 2699055776113772740729745272715963145141623773257945023853997234998414725053<76>

(2·10140+43)/9 = 22...227<140> = 3 · 31 · 1069 · 8964601 · 30421352050471<14> · 285569714646679<15> · C100

C100 = P37 · P64

P37 = 1537826626889528440102962149670111199<37>

P64 = 1866370374076115987720915143645308809137896395487265990911695741<64>

Aug 16, 2004 (2nd)

By Chris Monico / GGNFS-0.52.2

2·10144-1 = 199...99<145> = 31 · 9804138075439<13> · C130

C130 = P35 · P96

P35 = 13854961586932530041353553255527433<35>

P96 = 474956195168874037512374864466717106402173543729681853735275008639338252700754042774999705598967<96>

Aug 16, 2004

By Sander Hoogendoorn / ggnfs-0.50.2-k1

(8·10116-53)/9 = 88...883<116> = 367 · 9043 · 95090691059444371<17> · C93

C93 = P32 · P61

P32 = 70432600953289405607699156781551<32>

P61 = 3999052930997618606487937766796750548209350357198059429827483<61>

Aug 15, 2004 (4th)

By Naoki Yamamoto / GGNFS 0.50.2

(16·10117-7)/9 = 177...77<118> = 197 · 1210163 · 2294141 · C103

C103 = P34 · P69

P34 = 3366193491864394615092466070341489<34>

P69 = 965624317230638336861113164255644815470547736072360700302995506212843<69>

Aug 15, 2004 (3rd)

By Naoki Yamamoto / GGNFS 0.50.2, PPSIQS 1.1

(13·10134-1)/3 = 433...33<135> = 199 · 7177 · C129

C129 = P39 · P43 · P48

P39 = 310443695806204825883048853941991091621<39>

P43 = 5785687201900892982007414968214381142462459<43>

P48 = 168922803190060510326666688051641536230900596989<48>

By Naoki Yamamoto / PPSIQS 1.1

(46·10148-1)/9 = 511...11<149> = 32 · 193 · 359 · 40430864797<11> · 22431655423337<14> · 1251360360918225535713445002829<31> · C89

C89 = P38 · P52

P38 = 42057935411015848231340866859995766233<38>

P52 = 1717182112351141063777768046172842443193154091976929<52>

Aug 15, 2004 (2nd)

By Chris Monico / GGNFS

2·10148-1 = 199...99<149> = 7 · C148

C148 = P54 · P95

P54 = 117070574659995165200777586374365068986623688168229103<54>

P95 = 24405303086969361747536590638875719351910103103955718453805022842339158858638099335114643253319<95>

Aug 15, 2004

By Greg Childers / GGNFS-0.52.1

(2·10128+43)/9 = 22...227<128> = 32 · 331 · 12541 · C120

C120 = P58 · P63

P58 = 1000344265034890698594181838433694614479773335378392497189<58>

P63 = 594614271324990197436080568035620507861369527178899595166636737<63>

(2·10129+43)/9 = 22...227<129> = 139 · 6133 · 71363 · 39741047095727<14> · C104

C104 = P47 · P58

P47 = 20258864215419377654796177065819979543859152227<47>

P58 = 4537035977305463554114827190992685878369459699025736038723<58>

(2·10132+43)/9 = 22...227<132> = 17 · 25163 · C126

C126 = P60 · P67

P60 = 196959804603855884145383854955199894753944509737958282726147<60>

P67 = 2637536889245416809305135888586468429618408002108774236518191211971<67>

(2·10133+43)/9 = 22...227<133> = 7 · 59 · 113 · C128

C128 = P36 · P38 · P56

P36 = 266826656904029035443015530298752551<36>

P38 = 15777624776497722546638020690112501273<38>

P56 = 11310665340782789985942630553853205383547938874605745521<56>

(2·10135+43)/9 = 22...227<135> = 109 · 24889 · 18963649 · 6013186489<10> · 310929595079563<15> · C97

C97 = P35 · P62

P35 = 49324426672587319939477856618057831<35>

P62 = 46838486383247495945892705345162490638183050272054527763817419<62>

Aug 14, 2004 (4th)

By Tetsuya Kobayashi / GMP-ECM 5.0.3

(82·10139-1)/9 = 911...11<140> = 72 · 13 · 22745010213596190913<20> · 39018381622916411765473<23> · C96

C96 = P27 · P69

P27 = 672037649153157760391664637<27>

P69 = 239818630401442350150517403201814834134176811816856060030914476606831<69>

(46·10135-1)/9 = 511...11<136> = 479 · C134

C134 = P29 · C105

P29 = 46154078138132146557551248199<29>

C105 = [231190363516601815875245621524025323063245909981915517274853408346607442950108028978835915150679748856991<105>]

(52·10133-7)/9 = 577...77<134> = 32 · 53 · C132

C132 = P27 · P105

P27 = 507161535575400433388365477<27>

P105 = 238833997115881069691548632721734130353784577435020569573433120826879103881898021999882972026521882938113<105>

5·10146-1 = 499...99<147> = 1324743175841<13> · 41231655271646690609789<23> · C112

C112 = P33 · P80

P33 = 491797844488087910675065491701111<33>

P80 = 18613194785067937897308160940271109215879924182776436506899598937897470234894541<80>

(8·10150-71)/9 = 88...881<150> = 7 · 39119 · 74975514714601<14> · 3953010438312526830606053<25> · C107

C107 = P30 · P32 · P46

P30 = 278093556698362052053293534853<30>

P32 = 20097196725658504721430579226829<32>

P46 = 1959692207996245702222602127514306060796873037<46>

(37·10148-1)/9 = 411...11<149> = 7 · 351343 · 15715685701<11> · C133

C133 = P35 · P98

P35 = 21065758028443297907249484416012389<35>

P98 = 50491636065502153240509298781996095334209499692636542105438958927122662225516148030340946437926599<98>

3·10144-1 = 299...99<145> = 114960971 · 2213287753<10> · C128

C128 = P30 · P99

P30 = 108090137887270909297090797793<30>

P99 = 109080439628348269202774046214310086366771298172396864071466868126105645656536199141927505676107861<99>

(28·10140-1)/9 = 311...11<141> = C141

C141 = P32 · P110

P32 = 28061244394528078097445236936881<32>

P110 = 11086860822600495496089798493845024271017940020968874041788390705256335001099077800139750826481064002684323831<110>

(46·10129-1)/9 = 511...11<130> = 17 · 19 · 82240334137855241<17> · C111

C111 = P34 · P34 · P44

P34 = 2674032226448216912556195682541261<34>

P34 = 4058621363993797320237221962751579<34>

P44 = 17728939570931867503068789999212267866115483<44>

(46·10148-1)/9 = 511...11<149> = 32 · 193 · 359 · 40430864797<11> · 22431655423337<14> · C119

C119 = P31 · C89

P31 = 1251360360918225535713445002829<31>

C89 = [72221134370216050511886139455047439541624002248961467278999502369658735430252413113238457<89>]

(73·10123-1)/9 = 811...11<124> = 29 · 2927 · 144100861 · C111

C111 = P32 · C80

P32 = 63833739956555856215699127353593<32>

C80 = [10388258895723777777326223736958021452464103794984537490479460124159085376982729<80>]

(73·10129-1)/9 = 811...11<130> = 809 · 9723253213<10> · C118

C118 = P27 · P91

P27 = 848035601727306124412985569<27>

P91 = 1215923209499907110359099149008584747886873725147568593926890646948761420775922583207060507<91>

(73·10134-1)/9 = 811...11<135> = 13881683 · C128

C128 = P30 · C99

P30 = 269001190545339915526867145161<30>

C99 = [217212105758048703274010767129432057546261389285898400665761853003366980068691694075671343515862997<99>]

(73·10143-1)/9 = 811...11<144> = 7 · 582319 · 223470319 · C129

C129 = P29 · P101

P29 = 56223336320445107851116811063<29>

P101 = 15837436546409483213789519639504868703318612432957682219628275351899328538773456582356006613264313511<101>

(73·10147-1)/9 = 811...11<148> = 4159 · 17747 · 1166927 · C134

C134 = P31 · P104

P31 = 5211981027531516487669631329999<31>

P104 = 18068411228607373367533120273425957835243258126098442269324290869126076885106512239894555942041618508259<104>

(43·10124-7)/9 = 477...77<125> = 4219 · 1850749 · C115

C115 = P31 · P85

P31 = 1829658182397745082611987252939<31>

P85 = 3344251535561118609019392015412413893530067677471043320719122483668509889510526481053<85>

By Makoto Kamada / PPSIQS 1.1

(73·10123-1)/9 = 811...11<124> = 29 · 2927 · 144100861 · 63833739956555856215699127353593<32> · C80

C80 = P38 · P42

P38 = 16851944024522236784620221321632467021<38>

P42 = 616442760586388278887103869502804909104749<42>

Aug 14, 2004 (3rd)

By Naoki Yamamoto / GMP-ECM

(88·10145-7)/9 = 977...77<146> = 197 · 16937 · 2652168012682425937332375349<28> · C113

C113 = P29 · P85

P29 = 10494560093981267791683167017<29>

P85 = 1052863760281934042939222037220079887789397898463048988151570459130673394086322002521<85>

Aug 14, 2004 (2nd)

By Naoki Yamamoto / GGNFS 0.50.2

(2·10129-17)/3 = 66...661<129> = 56149 · 269195509511<12> · C113

C113 = P46 · P67

P46 = 5850093849009154750695732932179251467340256621<46>

P67 = 7539387594423886122474188626010642810713734707297642446847656344419<67>

Aug 14, 2004

By Wataru Sakai / GMP-ECM

(88·10145-7)/9 = 977...77<146> = 197 · 16937 · C140

C140 = P28 · C113

P28 = 2652168012682425937332375349<28>

C113 = [11049342003053844732883196766217892563493538977511315244647157237917799253367565480991912205020696144074738049857<113>]

Aug 13, 2004 (5th)

By Naoki Yamamoto / GGNFS 0.50.2

(88·10116-7)/9 = 977...77<117> = 624278792959867<15> · C103

C103 = P33 · P70

P33 = 740524292869073229988058449820401<33>

P70 = 2115057948046324213103243818118224005976352820802067289787971722593331<70>

Aug 13, 2004 (4th)

By Chris Monico / GGNFS

2·10149-1 = 199...99<150> = 59 · 8885059 · C141

C141 = P31 · P111

P31 = 1493309014925537823429198505631<31>

P111 = 255486514302691494846148453167109949281503703507120073976338942411963652635881540252707023179121976597815727409<111>

Aug 13, 2004 (3rd)

By Greg Childers / GGNFS

(2·10117+43)/9 = 22...227<117> = 239 · 1327 · 3119 · C108 = P46 · P63

P46 = 1602380498589551460844803694041803071803326713<46>

P63 = 140196650172888378636539392161737752562515331031081392670520997<63>

Aug 13, 2004 (2nd)

By Naoki Yamamoto / GGNFS-0.50.2

(5·10117+31)/9 = 55...559<117> = 13 · 519917644084338582319771<24> · C92

C92 = P45 · P48

P45 = 346062737628772422538383221785890093185552101<45>

P48 = 237517026412700840486947528737713794462517971333<48>

(5·10146+31)/9 = 55...559<146> = 3243941 · 1398873744713<13> · 695031043209532567098808030379149<33> · C95

C95 = P35 · P60

P35 = 39503056720157868435026638079206339<35>

P60 = 445903749438031877158379025823963572610293551734734557460293<60>

Aug 13, 2004

GGNFS-0.52.2 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Aug 12, 2004 (3rd)

By Wataru Sakai / GMP-ECM

(88·10119-7)/9 = 977...77<120> = 315303250430129350630357<24> · C97

C97 = P33 · P65

P33 = 152458436617826712499433931140047<33>

P65 = 20340435765872929924195496749772356003903484474400699753398423363<65>

Aug 12, 2004 (2nd)

By Naoki Yamamoto / GGNFS 0.50.2

(16·10154-61)/9 = 177...771<155> = 132 · 127 · C150

C150 = P40 · P111

P40 = 3733121936303998720580918507923629269009<40>

P111 = 221878321587930532169969709902563560847331538413982435341417449466367100689787271320174821863118816102475066813<111>

(5·10113+31)/9 = 55...559<113> = 72 · C112

C112 = P41 · P71

P41 = 43720746141733364946107849658114339806371<41>

P71 = 25932467950045189401837833609812116498751235726707090602373851852516221<71>

By Naoki Yamamoto / GMP-ECM

(5·10129+31)/9 = 55...559<129> = 13 · 43 · 1272231689<10> · 11160255697127399<17> · C101

C101 = P35 · P67

P35 = 17321531270228804971420531802867243<35>

P67 = 4041001865615899813621236180480845269006050736592447296930252650437<67>

Aug 12, 2004

GGNFS-0.52.1 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Aug 11, 2004 (2nd)

By Sander Hoogendoorn / ggnfs-0.50.2-k1

(5·10116+31)/9 = 55...559<116> = 172 · 3679800784648829<16> · C98

C98 = P32 · P67

P32 = 44334860269035801667552039407673<32>

P67 = 1178311185643301456111174295447537534022224985031162773715621064043<67>

Aug 11, 2004

GGNFS-0.52.0 was released. This version includes ggnfs-0.50.2-k1.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Aug 10, 2004

By Wataru Sakai / GMP-ECM

(5·10123+31)/9 = 55...559<123> = 13 · 229 · 6661 · 10949 · 3361177 · 2619474031<10> · C96

C96 = P32 · P65

P32 = 18272483111100886415621718646609<32>

P65 = 15904928508226266154222347295244079475097632916793327874442395241<65>

Aug 9, 2004 (6th)

(Aug 11, 2004) ggnfs-0.50.2-k1 is included to GGNFS-0.52.0.

ggnfs-0.50.2-k1 was released. This patch accelerates getdeps of GGNFS 0.50.2. In getdeps.c, makeMasterIndex() calls fread() and fwrite() over and over, so this routine takes long wasting time especially on Cygwin. The same is looked about addNewRelations3(). ggnfs-0.50.2-k1 changes the function to take not wasting time but large memory. Changes will be included in GGNFS in the future.

ggnfs-0.50.2-k1.txt
Some results of ggnfs-0.50.2-k1
target<digits>
factor
poly skew RLIM
ALIM
LPBR
LPBA
MFBR
MFBA
RLAMBDA
ALAMBDA
QSTEP total time
actual time
(34·10115-7)/9 = 377...777<116>
C105 = P37 · P68
34·(1023)5-7 1 400000
400000
25
25
38
38
1.71
1.71
50000 2.0 hours
2.1 hours
(34·10116-7)/9 = 377...777<117>
C107 = P46 · P60
340·(1023)5-7 1 400000
400000
25
25
38
38
1.71
1.71
50000 2.90 hours
3.07 hours
(34·10118-7)/9 = 377...777<119>
C96 = P41 · P56
17·(1024)5-350 3 450000
450000
25
25
38
38
1.83
1.83
50000 3.55 hours
3.78 hours
(4·10115-13)/9 = 44...443<115>
C111 = P33 · P79
(2·1023)5-104 3 400000
400000
25
25
38
38
1.85
1.85
50000 2.01 hours
2.13 hours
(4·10116-13)/9 = 44...443<116>
C109 = P46 · P63
5·(2·1023)5-52 2 400000
400000
25
25
38
38
1.75
1.75
50000 2.01 hours
2.17 hours
(8·10115-53)/9 = 88...883<115>
C111 = P41 · P71
(2·1023)5-212 4 400000
400000
25
25
38
38
1.75
1.75
50000 1.69 hours
1.88 hours

Aug 9, 2004 (5th)

Condition of the sequence (8·10n-53)/9 = { 3, 83, 883, 8883, 88883, ... } was extended to n≤150.

Following numbers were not factorized. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.

n= 116, 117, 118, 122, 124, 125, 126, 129, 130, 132, 135, 136, 139, 142, 143, 144, 146, 148, 149, 150, (20/150)

Aug 9, 2004 (4th)

Condition of the sequence (4·10n-13)/9 = { 3, 43, 443, 4443, 44443, ... } was extended to n≤150.

Following numbers were not factorized. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.

n= 118, 120, 124, 125, 126, 127, 128, 129, 133, 135, 136, 137, 139, 141, 143, 144, 146, 147, 149, 150, (20/150)

Aug 9, 2004 (3rd)

By Naoki Yamamoto / PPSIQS 1.1

(88·10142-7)/9 = 977...77<143> = 17 · 21491 · 12889824783089<14> · 299476320250181152930460992793<30> · C95

C95 = P47 · P49

P47 = 13245760762206208300793072742910185771632215651<47>

P49 = 5234174633003279598976699261396818482965422304033<49>

Aug 9, 2004 (2nd)

By Naoki Yamamoto / GGNFS-0.50.2

(5·10128+31)/9 = 55...559<128> = C128

C128 = P32 · P97

P32 = 38269214212140348621764618632681<32>

P97 = 1451703587316704504219071457325686645925023851742369363924810363182131249318712352433397460201039<97>

Aug 9, 2004

Condition of the sequence (34·10n-7)/9 = { 37, 377, 3777, 37777, 377777, ... } was extended to n≤150.

Following numbers were not factorized. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.

n= 121, 123, 124, 127, 128, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 142, 143, 147, 149, 150, (20/150)

Aug 8, 2004

By Naoki Yamamoto / GGNFS-0.50.2

(5·10148+31)/9 = 55...559<148> = 3 · 17 · C147

C147 = P44 · P103

P44 = 48927720345537554079204669065308406118675509<44>

P103 = 2226395611819538088138623926667538986963803982837221614882581319995207895365189900082209127633525519401<103>

Aug 7, 2004 (4th)

By Wataru Sakai / GMP-ECM

(5·10146+31)/9 = 55...559<146> = 3243941 · 1398873744713<13> · C128

C128 = P33 · P95

P33 = 695031043209532567098808030379149<33>

C95 = [17614561105781635495651811321705417120485475600235294076950813661998769837908505718148946397327<95>]

Aug 7, 2004 (3rd)

Factor table of the near-repdigit palindrome sequence 33...33733...33 is available.

Aug 7, 2004 (2nd)

By Sander Hoogendoorn

5·10135-1 = 499...99<136> = C136

C136 = P60 · P77

P60 = 269003202410838504214036520941412612134351136344950318928159<60>

P77 = 18587139317262429780586757996354609670472835010983311369908899791500395369761<77>

Aug 7, 2004

Factor table of the near-repdigit palindrome sequence 77...77377...77 is available.

Aug 6, 2004

Factor tables of the near-repdigit palindrome sequence 11...11711...11, 11...11811...11, 33...33833...33, 77...77177...77, 99...99199...99, 99...99799...99 are available.

Aug 5, 2004 (2nd)

By Sander Hoogendoorn / GGNFS-0.42.0

5·10130-1 = 499...99<131> = 739 · 1129 · 1779149 · 37524595431275311<17> · C102

C102 = P40 · P63

P40 = 7628309663740789043344274685157484199841<40>

P63 = 117672497216416907975811138393270288338026728779873725975710671<63>

Aug 5, 2004

By Wataru Sakai / GMP-ECM

(79·10126-7)/9 = 877...77<127> = 337 · 4721 · 73637 · 119869 · 7474153 · 1022663261<10> · C95

C95 = P32 · P64

P32 = 20934653464832126854449165578597<32>

P64 = 3906225375647472141875367898907852805403416735828228781396251017<64>

Aug 4, 2004

Factor tables of the near-repdigit palindrome sequence 77...77977...77, 99...99599...99 are available.

Aug 3, 2004 (3rd)

Factor tables of the near-repdigit palindrome sequence 77...77877...77, 99...99499...99 are available.

Aug 3, 2004 (2nd)

Condition of the sequence (88·10n-7)/9 = { 97, 977, 9777, 97777, 977777, ... } was extended to n≤150.

Following numbers were not factorized. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.

n= 116, 119, 121, 122, 125, 127, 128, 130, 132, 134, 137, 138, 141, 142, 143, 144, 145, 146, 149, 150, (20/150)

Aug 3, 2004

Condition of the sequence (5·10n+31)/9 = { 9, 59, 559, 5559, 55559, ... } was extended to n≤150.

Following numbers were not factorized. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.

n= 113, 116, 117, 123, 126, 128, 129, 130, 132, 134, 135, 136, 137, 139, 140, 142, 146, 147, 148, 150, (20/150)

Aug 2, 2004 (5th)

By Naoki Yamamoto / GGNFS-0.50.2

(4·10116+41)/9 = 44...449<116> = 7 · 337 · 2039 · 26753002217<11> · C99

C99 = P38 · P61

P38 = 44794759861299396985200448488293440259<38>

P61 = 7710323090519545020480623649489753373694054004099076008805283<61>

By Naoki Yamamoto / PPSIQS 1.1

(37·10147-1)/9 = 411...11<148> = 23 · 61 · 257 · 14065141 · 2002045231<10> · 16106441408411<14> · 3574843806050081<16> · C97

C97 = P34 · P63

P34 = 8382239055754299828581187813116803<34>

P63 = 838945471965205785933350926848623267517006821503864790379243727<63>

Aug 2, 2004 (4th)

Factor tables of the near-repdigit palindrome sequence 11...11411...11, 11...11511...11 and 11...11611...11 are available.

Aug 2, 2004 (3rd)

By Naoki Yamamoto / GGNFS-0.50.2

(7·10129-1)/3 = 233...33<130> = 460973 · 2805891978037<13> · 5542822167307<13> · C99

C99 = P45 · P54

P45 = 496581743478488996713861801354111444216964147<45>

P54 = 655403347174745853386934264992436518045116721863278677<54>

(7·10113+11)/9 = 77...779<113> = 13 · 41 · 317 · 4049231 · 659079229 · C93

C93 = P33 · P60

P33 = 507527545879734298342291428748409<33>

P60 = 339859381634013658446000254171861064394439537000913446780329<60>

(7·10115+11)/9 = 77...779<115> = 3 · 43 · 23561 · 2182451195879<13> · C97

C97 = P48 · P49

P48 = 204630175486239665441834420067922388530171436419<48>

P49 = 5730043032793768756673983042924268914827505976591<49>

Aug 2, 2004 (2nd)

By Chris Monico / GGNFS

2·10150-1 = 199...99<151> = 17 · 336263 · 6516017 · 11385821807<11> · C127

C127 = P38 · P89

P38 = 55120529024967151191001971500609072753<38>

P89 = 85554335523575100570067317351631393271852473171138400561538366131132422284355387689070967<89>

Aug 2, 2004

By Wataru Sakai / GMP-ECM

(79·10135-7)/9 = 877...77<136> = 67 · C135

C135 = P32 · P104

P32 = 11929546337170934826957294007451<32>

P104 = 10982111550657510700513355288216179071140051766262673835508750420486872948294203183491129951906834483681<104>

(7·10131-61)/9 = 77...771<131> = 67 · 617 · 1823 · 310621183 · 48346728036539<14> · C101

C101 = P37 · P65

P37 = 6853714382111772333567001250060157467<37>

P65 = 10027316802528728876840365539723496805982556831028807023311815417<65>

Aug 1, 2004 (4th)

By Naoki Yamamoto / GGNFS-0.50.2

(7·10144-1)/3 = 233...33<145> = C145

C145 = P47 · P98

P47 = 37466137662297732968966339042619987350087992783<47>

P98 = 62278459401524391449909039884972845130019000157718994827933933144917142216395425263726960259325851<98>

Aug 1, 2004 (3rd)

By Sander Hoogendoorn / NFSX 1.8

(79·10119-7)/9 = 877...77<120> = 173 · 223 · 3221 · 91757 · 1074533 · C101

C101 = P33 · P69

P33 = 156477338651555641824995709430741<33>

P69 = 457859759985964363716052010340892271341496432063774626160703756819043<69>

By Sander Hoogendoorn / GGNFS-0.42.0

5·10125-1 = 499...99<126> = 31 · 992445257 · C116

C116 = P35 · C81

P35 = 36167938192618912257635160348826241<35>

C81 = [449343018205749408245949108992786992858072894255838328977051237721820163447966617<81>]

By Makoto Kamada / PPSIQS 1.1

5·10125-1 = 499...99<126> = 31 · 992445257 · 36167938192618912257635160348826241<35> · C81

C81 = P36 · P45

P36 = 541041326367575421678108269681570849<36>

P45 = 830515149780762684023194221858216749394061433<45>

Aug 1, 2004 (2nd)

Condition of the sequence (7·10n+11)/9 = { 9, 79, 779, 7779, 77779, ... } was extended to n≤150.

Following numbers were not factorized. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.

n= 113, 115, 117, 119, 122, 123, 124, 126, 129, 133, 134, 135, 137, 139, 141, 142, 143, 145, 147, 148, (20/150)

Aug 1, 2004

Condition of the sequence (4·10n+41)/9 = { 9, 49, 449, 4449, 44449, ... } was extended to n≤150.

Following numbers were not factorized yet. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.

n= 116, 119, 122, 123, 125, 126, 129, 130, 131, 132, 133, 135, 140, 142, 143, 145, 147, 148, 149, 150, (20/150)

July 2004

Jul 31, 2004

By Sander Hoogendoorn

(79·10120-7)/9 = 877...77<121> = 1973 · 17589721 · C111

C111 = P52 · P59

P52 = 3647603796195563296887624217864148310447270429610909<52>

P59 = 69341125512577351283194098596051851745852661752751688209241<59>

Jul 30, 2004 (4th)

By Naoki Yamamoto / GGNFS-0.42.0

(5·10125-23)/9 = 55...553<125>= 73 · 547 · 3391 · 1635497 · 8511649 · C104

C104 = P50 · P54

P50 = 57825114673387146834563010233705010037136332567081<50>

P54 = 509694043275954779862018223457964767725872259446162301<54>

Jul 30, 2004 (3rd)

GGNFS-0.50.2 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Jul 30, 2004 (2nd)

By Naoki Yamamoto / GGNFS-0.42.0

(2·10130+7)/9 = 22...223<130> = 32 · 13 · 19 · 1423 · 1551317117327979089261<22> · C102

C102 = P48 · P55

P48 = 444393718392193325525367381067708903784680905533<48>

P55 = 1019001040424840666261118066908241563639658856415896199<55>

(79·10115-7)/9 = 877...77<116> = 3 · 19 · 127 · C113

C113 = P44 · P69

P44 = 42034016908010046021378526723248273108709559<44>

P69 = 288472959872801474661886852720633634410793341412133936141410803462577<69>

Jul 30, 2004

Factor table of the sequence 7·10n+1 = { 71, 701, 7001, 70001, 700001, ... } (n≤100) is available.

Jul 29, 2004 (3rd)

By Tetsuya Kobayashi / GGNFS 0.41.1 with gnfs-lasieve4e

(25·10137-1)/3 = 833...33<138> = C138

C138 = P49 · P90

P49 = 1638545571355283827888850394797548229861836865827<49>

P90 = 508581114801745534164695080669826850365678387521375675524443722168064117995925288317879079<90>

By Tetsuya Kobayashi / GMP-ECM 5.0.3 (B1=1000000)

(82·10134-1)/9 = 911...11<135> = 6960383 · 69163136827<11> · 163163049593<12> · C107

C107 = P28 · C79

P28 = 4001114788721318238000734929<28>

C79 = [2899083327033291743797371234836308744527855240678176062632160165611049600111043<79>]

5·10123-1 = 499...99<124> = 89 · 2111 · C119

C119 = P31 · P88

P31 = 8215978320845452759352519383001<31>

P88 = 3239160589249899026971792199328906772388800723424699494389476245714793002129219351491281<88>

5·10136-1 = 499...99<137> = 49739 · 37933257899<11> · C122

C122 = P39 · C84

P39 = 247427558723526151962343402114292522351<39>

C84 = [107103765782521606380635529965406725526768538275161946579155860869152331675644483609<84>]

(46·10133-1)/9 = 511...11<134> = 3 · 29 · 919 · 32059 · 45289 · 1831064236756717727<19> · C102

C102 = P24 · C78

P24 = 901419944778877323261361<24>

C78 = [266751648491328423758308659758450582355989730986836507230434702559126958408771<78>]

(55·10140-1)/9 = 611...11<141> = 13 · 17 · 47 · 367 · 8907795174011<13> · C122

C122 = P30 · P92

P30 = 286967102471285815138735294727<30>

P92 = 62713588098969121341231164916244678281825463895878747428903824319231137581779849372395294447<92>

(73·10139-1)/9 = 811...11<140> = 3 · 783566963 · C131

C131 = P25 · C106

P25 = 4777344126483896523285239<25>

C106 = [7222648056323288116333995397594572469155800784650472685188934228183853141171710545082417781751284704098841<106>]

(22·10127-1)/3 = 733...33<128> = 47 · 457 · 60133 · 530397844244647<15> · C105

C105 = P25 · P80

P25 = 5106554452273521819702917<25>

P80 = 20962582244356588993925045053439691694812836183923171778828616196732382735765581<80>

By Makoto Kamada / PPSIQS 1.1

(82·10134-1)/9 = 911...11<135> = 6960383 · 69163136827<11> · 163163049593<12> · 4001114788721318238000734929<28> · C79

C79 = P32 · P47

P32 = 32265017822641920375578480451101<32>

P47 = 89852215268229761835890756896531657804867643743<47>

(46·10133-1)/9 = 511...11<134> = 3 · 29 · 919 · 32059 · 45289 · 1831064236756717727<19> · 901419944778877323261361<24> · C78

C78 = P39 · P40

P39 = 171058051535971858079912374255284920921<39>

P40 = 1559421764109321246261486637921914105851<40>

5·10136-1 = 499...99<137> = 49739 · 37933257899<11> · 247427558723526151962343402114292522351<39> · C84

C84 = P39 · P45

P39 = 192354257809333079137411266279438005089<39>

P45 = 556804757026412458852371557261880118927562681<45>

Jul 29, 2004 (2nd)

GGNFS-0.50.1 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Jul 29, 2004

By Naoki Yamamoto / GGNFS-0.42.0

(2·10136+7)/9 = 22...223<136> = 3 · 13 · C134

C134 = P40 · P95

P40 = 1208403718344969580010976922953219153737<40>

P95 = 47153162568960726558585743667934255258026493976547097688772198069171183804381407635463744713361<95>

Jul 28, 2004

GGNFS-0.50.0 was released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Jul 27, 2004

By Naoki Yamamoto / GGNFS-0.42.0

(8·10130-71)/9 = 88...881<130> = 31 · 362791645874116663<18> · C111

C111 = P30 · P82

P30 = 351127620084747953086032902879<30>

P82 = 2250937896568268128530971256845564419903608981264290387459314036523226283091874263<82>

Jul 26, 2004 (2nd)

Condition of sequence (79·10n-7)/9 = { 87, 877, 8777, 87777, 877777, ... } was extended to n≤150.

Following numbers have not factorized yet. These numbers may have small factors. You should run GMP-ECM (B1≥1000000?) first.

n=

115,

118,

119,

120,

124,

126,

130,

131,

132,

133,

135,

136,

137,

140,

141,

142,

145,

146,

148,

149,

(20/150)

Jul 26, 2004

By Naoki Yamamoto / GGNFS-0.42.0

(8·10125-71)/9 = 88...881<125> = 3 · 13 · 17 · 89 · 173 · C118

C118 = P48 · P70

P48 = 922504058548251284436573284168962093370710273699<48>

P70 = 9439077542687304031267742292486251570088463036922530791706458855090329<70>

Jul 25, 2004 (3rd)

By Wataru Sakai / GMP-ECM

(37·10127-1)/9 = 411...11<128> = 635821 · C122

C122 = P33 · P90

P33 = 469488855864230005483461314336129<33>

P90 = 137720648445416062792457424757472821995659748083558641360826441310501439598398121157011779<90>

Jul 25, 2004 (2nd)

By Naoki Yamamoto / GGNFS-0.42.0

(8·10120-71)/9 = 88...881<120> = 7 · 41109083 · C112

C112 = P28 · P84

P28 = 7250708775037199879025189199<28>

P84 = 426021175353918824704540396267389351147465945869342287540201528994822049771054339499<84>

Jul 25, 2004

By Naoki Yamamoto / GGNFS-0.41.4

(7·10130-43)/9 = 77...773<130> = 3 · 73 · C128

C128 = P44 · P85

P44 = 11513012705773495975285166902174933952342767<44>

P85 = 3084767465253160394715823429783026037611212382543171576253540671002826546426303736601<85>

Jul 24, 2004

By Makoto Kamada / GGNFS-0.42.0

2·10123-1 = 199...99<124> = 109 · 217114861 · 2825376469<10> · C104

C104 = P31 · P73

P31 = 7802871694458922680414327278941<31>

P73 = 3833391338808287460914354109964295906385875484435011906494407451701606919<73>

Jul 23, 2004

By Chris Monico / GGNFS

2·10130-1 = 199...99<131> = 7 · 311043047257<12> · C118

C118 = P42 · C77

P42 = 316679239119493368730697918313185363275679<42>

C77 = [29006268639903695165654583513611219242606418776618136746986456859685764635119<77>]

By Makoto Kamada / PPSIQS 1.1

C77 = P37 · P40

P37 = 5855691034209378660658810843429609687<37>

P40 = 4953517607135850515490609742784611284137<40>

Jul 22, 2004 (4th)

By Chris Monico / GGNFS

2·10125-1 = 199...99<126> = C126

C126 = P55 · P71

P55 = 5593144113982773671594705011644916102525868355090939299<55>

P71 = 35758063072253600104111297707041995548298752568202917692898922932429301<71>

Jul 22, 2004 (3rd)

Sequence 6·10n-1 = { 59, 599, 5999, 59999, 599999, ... } (n≤150) was completed.

Jul 22, 2004 (2nd)

By Chris Monico / GGNFS

6·10149-1 = 599...99<150> = 1217 · 2089 · 58543 · 2467331209438569905957<22> · C118

C118 = P47 · P72

P47 = 10987226447999824436534198115279323138230080781<47>

P72 = 148707109019575208847647232019368309061651691482221984454276421168203433<72>

Jul 22, 2004

By Naoki Yamamoto / GGNFS-0.41.4

(7·10124-1)/3 = 233...33<125>= 2063983 · C119

C119 = P51 · P68

P51 = 216429803459198692982079852449385736358543491058747<51>

P68 = 52234038440848787045388167594052526859221296895405324688852732106433<68>

Jul 21, 2004 (3nd)

By Naoki Yamamoto / GGNFS-0.41.4

(73·10119-1)/9 = 811...11<120> = 7 · C120

C120 = P47 · P73

P47 = 35843307395754477763182390342136107571429116643<47>

P73 = 3232765732069151961623791427793961705222005358158797460862734751550729611<73>

Jul 21, 2004 (2nd)

By Wataru Sakai / GMP-ECM

(37·10139-1)/9 = 411...11<140> = 17170064291<11> · C130

C130 = P32 · C98

P32 = 53006618019086698414143574579147<32>

C98 = [45170739181216532842550406375567476783907764256353010839594573481785115842469425710359529501499143<98>]

(37·10140-1)/9 = 411...11<141> = 32 · 23478857 · 187440991 · C125

C125 = P38 · P87

P38 = 13747752321728679995707324065371137717<38>

P87 = 754993970727815294680343917937805369161805137527893698330319252874619963080619076996101<87>

Jul 21, 2004

By Naoki Yamamoto / GGNFS-0.41.4

(52·10120-7)/9 = 577...77<121> = 53 · 71 · 419 · 19739490466243<14> · C102

C102 = P40 · P63

P40 = 1227279797212489371909157653353692586057<40>

P63 = 151263125442334610939196931165683423322159672814236639084655291<63>

Jul 20, 2004 (3rd)

By Naoki Yamamoto

2·10119-1 = 199...99<120> = 117839 · C115

C115 = P43 · P72

P43 = 2883845398187423145137576280203368673508491<43>

P72 = 588530497766278656698413595437639465348609061819280096585286457602098451<72>

Jul 20, 2004 (2nd)

By Makoto Kamada

Results of GGNFS on Pentium 4 (3.06GHz) + Windows XP + Cygwin

version target<digits>
factor
poly skew RLIM
ALIM
LPBR
LPBA
MFBR
MFBA
RLAMBDA
ALAMBDA
QSTEP total time
actual time
7 0.41.4 10125-3 = 99...997<125>
224027 · P47 · P74
(1025)5-3 2 500000
500000
25
25
38
38
1.7
1.7
50000 3.8 hours
7.4 hours
8 0.42.0 10116-3 = 99...997<116>
563 · 1321 · 8774317 · P46 · P59
10·(1023)5-3 1 600000
600000
25
25
40
40
1.5
1.5
200000 3.2 hours
4.5 hours
9 0.42.0 10118-3 = 99...997<118>
13 · 8461 · 89293 · P50 · P60
1000·(1023)5-3 1 700000
700000
25
25
40
40
1.5
1.5
300000 2.9 hours
3.5 hours
10 0.42.0 10135-3 = 99...997<135>
P52 · P84
(1027)5-3 2 800000
800000
25
25
42
42
1.8
1.8
200000 10.1 hours
13.5 hours

Jul 20, 2004

By Wataru Sakai

(2·10147+43)/9 = 22...227<147> = C147

C147 = P29 · P36 · P83

P29 = 37552884739371336887267500859<29>

P36 = 110000162020693591815991881775726199<36>

P83 = 53796108039117408201713122464668477028900137584676342534723577710785928545348290047<83>

Jul 19, 2004

By Chris Monico

6·10148-1 = 599...99<149> = 23 · 143623072438553111<18> · 70116191139095712136541<23> · C108

C108 = P41 · P68

P41 = 15621998636651197677331299592611109051271<41>

P68 = 16582281729960152020747008046431377081820647054098938825685245773453<68>

Jul 18, 2004 (2nd)

GGNFS-0.42.0 released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Jul 18, 2004

By Naoki Yamamoto

(4·10125-31)/9 = 44...441<125> = C125

C125 = P60 · P66

P60 = 248045852618693759570106685428526539565533569384576825285099<60>

P66 = 179178341323715918528397067044394058335935028042832254100223016459<66>

(5·10124-23)/9 = 55...553<124> = 3 · C124

C124 = P51 · P73

P51 = 893705583790618947435784683592956843318755685731321<51>

P73 = 2072105048283676593750713609645700636020171033758333979718460244891352931<73>

Jul 17, 2004 (4th)

By Naoki Yamamoto

(5·10119-23)/9 = 55...553<119> = 53 · 90563537 · 2224349341<10> · C100

C100 = P36 · P65

P36 = 187609016630476561110373570775917331<36>

P65 = 27735854278888576215443083404195516851216822681668421792490681163<65>

Jul 17, 2004 (3rd)

By Tetsuya Kobayashi

(10143+17)/9 = 11...113<143> = 19 · 31 · 11491 · 22751 · C131

C131 = P61 · P70

P61 = 7908246882089534594555942744181688982089557175312923025313951<61>

P70 = 9124386260745537835102797877137484716469225695387556753991581197371887<70>

Jul 17, 2004 (2nd)

By Makoto Kamada

Results of GGNFS on Pentium 4 (3.06GHz) + Windows XP + Cygwin

version target<digits>
factor
poly skew RLIM
ALIM
LPBR
LPBA
MFBR
MFBA
RLAMBDA
ALAMBDA
QSTEP total time
actual time
1 0.41.2 (8·10114-53)/9 = 88...883<114>
P34 · C81
(2·1023)5-2120 5 2000000
2000000
26
26
42
42
1.3
1.3
20000 7.1 hours
13.3 hours
2 0.41.3 (5·10120+31)/9 = 55...559<120>
P49 · P72
5·(1024)5+31 3 500000
500000
24
24
38
38
1.6
1.6
50000 3.2 hours
5.3 hours
3 0.41.3 (7·10120+11)/9 = 77...779<120>
P32 · P88
7·(1024)5+11 2 500000
500000
25
25
38
38
1.7
1.7
50000 2.5 hours
4.4 hours
4 0.41.3 10117-3 = 99...997<117>
P55 · P63
100·(1023)5-3 1 400000
400000
25
25
38
38
1.5
1.5
50000 2.7 hours
6.0 hours
5 0.41.4 10109-3 = 99...997<109>
7 · P38 · P71
(1022)5-30 3 500000
500000
25
25
38
38
1.5
1.5
50000 1.1 hours
1.9 hours
6 0.41.4 10115-3 = 99...997<115>
7 · 149 · 16427 · P40 · P69
(1023)5-3 2 500000
500000
25
25
38
38
1.4
1.4
50000 1.7 hours
3.3 hours

I have selected skews and RLAMBDA/ALAMBDAs by 10th total yield. Other parameters were fudged. There must be more suitable parameters.

Jul 17, 2004

By Sander Hoogendoorn

(7·10126-1)/3 = 233...33<127> = 36599 · C122

C122 = P60 · P63

P60 = 291965541022167296632730595847741169431527057154038568667521<60>

P63 = 218361449631728650471984224440960698283205756071761554163079827<63>

(7·10127-1)/3 = 233...33<128>= 60959186188089983484687287<26> · C102

C102 = P39 · P64

P39 = 144850314733653665213197978942886043511<39>

P64 = 2642519383355819879708918820190613987026818882460409722093336069<64>

(7·10128-1)/3 = 233...33<129>= 109 · 8742499 · C120

C120 = P41 · P79

P41 = 77877997769970034113523979977916297438059<41>

P79 = 3144125831637334009151211168060361696898829767955771631140002228700313194095657<79>

Jul 16, 2004 (2nd)

GGNFS v.0.41.4 released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Jul 16, 2004

GGNFS v.0.41.3 released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Jul 15, 2004 (3rd)

By Chris Monico

6·10139-1 = 599...99<140> = 17 · 2357 · 6709 · 496808164133221337<18> · C114

C114 = P43 · P72

P43 = 4275770358901813485322672221773875286668931<43>

P72 = 105070756286372434011307124537088529236674420342309905106523868789281077<72>

Jul 15, 2004 (2nd)

By Makoto Kamada

Elements of near-repdigit number sequence:

(1016-2)·10n-1 = {

9999999999999997,

99999999999999979,

999999999999999799,

9999999999999997999,

99999999999999979999,

999999999999999799999,

9999999999999997999999,

99999999999999979999999, ... }

are almost but not always composite.

The smallest prime in these was not found to n=110000.

Note:

  1. (1016-2)·102k+1-1 is divisible by 11.
  2. (1016-2)·104k+2-1 is divisible by 101.
  3. (1016-2)·106k-1 is divisible by 13.
  4. (1016-2)·106k+4-1 is divisible by 7.
  5. (1016-2)·107k+2-1 is divisible by 239.
  6. (1016-2)·108k+4-1 is divisible by 73.
  7. (1016-2)·108k+4-1 is divisible by 137.
  8. (1016-2)·1013k+2-1 is divisible by 53.
  9. (1016-2)·1015k+12-1 is divisible by 31.
  10. (1016-2)·1016k+8-1 is divisible by 17.
  11. (1016-2)·1016k+8-1 is divisible by 5882353.
  12. (1016-2)·1018k+1-1 is divisible by 19.
  13. (1016-2)·1022k+14-1 is divisible by 23.
  14. (1016-2)·1028k+25-1 is divisible by 29.
  15. (1016-2)·1033k+11-1 is divisible by 67.
  16. (1016-2)·1041k+23-1 is divisible by 83.

Room for prime numbers: 1.31576% (388800/29549520)

Jul 15, 2004

GGNFS v.0.41.2 released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Jul 14, 2004 (3rd)

GGNFS v.0.41.1 released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Jul 14, 2004 (2nd)

By Chris Monico

6·10141-1 = 599...99<142> = 7 · 479 · C139

C139 = P65 · P74

P65 = 35327731857341516423182890620321111244744477883437596583879711889<65>

P74 = 50652623205819106586824840511922265124168640897434731460921381256530991847<74>

Jul 14, 2004

By Sander Hoogendoorn

(7·10150-1)/3 = 233...33<151> = 19 · 335884748059317734050810927349<30> · C120

C120 = P40 · P81

P40 = 1656407169596851767131315698363624983493<40>

P81 = 220732254445715797928245090773037861558474026138077170374261766409837462325690751<81>

Jul 13, 2004 (4th)

By Wataru Sakai

(7·10149-61)/9 = 77...771<149> = C149

C149 = P39 · C111

P39 = 555630322675904218078384300423796723653<39>

C111 = [139981161221010397731653123017062767499842036659860080769697961983570117014800778312472409366714045213400567407<111>]

Jul 13, 2004 (3rd)

By Sander Hoogendoorn

(61·10120-7)/9 = 677...77<121> = 32 · 17 · 313 · 1502987851<10> · C107

C107 = P48 · P60

P48 = 769095172291155299809287732928578049718910690979<48>

P60 = 122437936566411560805221573149092548059705384693679579533217<60>

(2·10120+61)/9 = 22...229<120> = 72 · 1063 · 44089 · C110

C110 = P47 · P64

P47 = 11200236287247211181934403375766314826763384907<47>

P64 = 8639740696019352260317859873267702861881740151079805356221852129<64>

(7·10120-43)/9 = 77...773<120> = 23 · C119

C119 = P36 · P84

P36 = 102165204408322819933727342963099351<36>

P84 = 330997479196724579176111165293540401558561359962238965514361224529925201626434999901<84>

(7·10122-43)/9 = 77...773<122> = 73 · 1039 · C118

C118 = P52 · P66

P52 = 1963666150444404452829528614185472574739439242044157<52>

P66 = 522215152466060223488145283129274835706883419009259617206112044487<66>

(7·10143-1)/3 = 233...33<144> = 1146846869760203<16> · C129

C129 = P35 · P36 · P58

P35 = 51763936059520850997759562751711951<35>

P36 = 777522035561894672181953942573574943<36>

P58 = 5055118650917024060336128295945772426930885972968542774127<58>

(2·10121+61)/9 = 22...229<121> = 3 · 157 · 29873 · C114

C114 = P55 · P59

P55 = 5087693224796052814910739831858442806993418962113835491<55>

P59 = 31043224357292935627500849820033660133689097108260130795393<59>

(82·10135-1)/9 = 911...11<136> = 32 · C136

C136 = P39 · P45 · P52

P39 = 607316047369248293566354411238647737151<39>

P45 = 213033528841359464186747362757178511330756709<45>

P52 = 7824671526942467199291684638157740801870532676801181<52>

611...11<1358> = (55·101357-1)/9 is definitely prime.

Jul 13, 2004 (2nd)

By Chris Monico

6·10137-1 = 599...99<138> = 71 · C136

C136 = P58 · P79

P58 = 2601072877662976526413355286135870141909302028099951147977<58>

P79 = 3248930200273718904077988718142805395852874875460986707043132492411918302127297<79>

Jul 13, 2004

By Wataru Sakai

(2·10143+43)/9 = 22...227<143> = 3 · 1291 · 450569675766019819<18> · C122

C122 = P28 · P94

P28 = 9686081683177098475223715931<28>

P94 = 1314709807173945124386524551786317959588529415262456959495075086473055274219732117053667996891<94>

Jul 12, 2004

GGNFS v.0.41.0 released.

GGNFS - A Number Field Sieve implementation (Chris Monico)

Jul 11, 2004 (4th)

By Makoto Kamada

What is the smallest prime number in near-repdigit number sequence {

9999999999999997,

99999999999999979,

999999999999999799,

9999999999999997999,

99999999999999979999,

999999999999999799999,

9999999999999997999999,

99999999999999979999999, ... } ?

Jul 11, 2004 (3rd)

By Chris Monico

6·10134-1 = 599...99<135>= 79801 · C130

C130 = P36 · P95

P36 = 240458481986789454962421757018820831<36>

P95 = 31268195286873997919154627378571722629648454815768807050327560441530709249665151616666073434729<95>

Jul 11, 2004 (2nd)

By Naoki Yamamoto

(2·10119+43)/9 = 22...227<119> = 32 · 157 · 2022900106936136601473<22> · C94

C94 = P29 · P66

P29 = 26550670740348141947894497129<29>

P66 = 292816395343023768827154264637322763527201607748172416530321363487<66>

(2·10149+43)/9 = 22...227<149> = 3 · 79 · 743 · 1416118947268564408923749<25> · 4105354947813472293827850631<28> · C92

C92 = P32 · P60

P32 = 95634550674317561833810565581261<32>

P60 = 226978676377348478562826106912938216911856503846449947239983<60>

Jul 11, 2004

By Chris Monico

6·10132-1 = 599..99<133> = 379 · 26813 · C126

C126 = P38 · P89

P38 = 30156062637902914306358977610009037869<38>

P89 = 19579067133088202404308295814147018632082970323640711916809910912410948535945312249307573<89>

Jul 10, 2004 (4th)

Sequence 9·10n-1 = { 89, 899, 8999, 89999, 899999, ... } (n≤150) was completed.

Sequence 10n-9 = { 1, 91, 991, 9991, 99991, ... } (n≤150) was completed.

Sequence 8·10n-1 = { 79, 799, 7999, 79999, 799999, ... } (n≤150) was completed.

Jul 10, 2004 (3rd)

By Tetsuya Kobayashi

9·10147-1 = 899...99<148> = 245811829401098369<18> · C131

C131 = P44 · P87

P44 = 44854455549564788096962189425408270743305049<44>

P87 = 816270574399695328594421683160134958538390249344775592075492092574375764259533960310679<87>

10143-9 = 99...991<143> = 43 · 4987 · C138

C138 = P37 · P101

P37 = 8103911869384742969083926875701596043<37>

P101 = 57543658086818917236653328425662353297036755376057033707756606095232065216600744427923471045358733757<101>

8·10139-1 = 799...99<140> = 6091 · 140549 · C131

C131 = P39 · P93

P39 = 315629643981739741939850476307408788621<39>

P93 = 296070980580545525000553977228269871399892395614879440949871202002667026497102834455766946141<93>

8·10143-1 = 799...99<144> = 421 · 21130570079<11> · C131

C131 = P59 · P73

P59 = 18272127674428823726544022791611007628769109020464392876611<59>

P73 = 4921614077405375881718089592543043830624657814006183510609464661039312751<73>

Jul 10, 2004 (2nd)

By Sander Hoogendoorn

(46·10125-1)/9 = 511...11<126> = 409813 · 1838759047<10> · 98062989493633<14> · C97

C97 = P39 · P58

P39 = 899943089887960510690718870944943284081<39>

P58 = 7685720617133864808422488886600325578420341161519163866637<58>

(2·10121+7)/9 = 22...223<121> = 33 · 45597521 · C112

C112 = P53 · P60

P53 = 13331026330569732653390091113196743038813193671667807<53>

P60 = 135400074662843530365122095572985252948229939391443206328467<60>

Definitely prime numbers

777377...77<1338> = (69964·101334-7)/9. This is the smallest prime number in { 7773, 77737, 777377, 7773777, 77737777, 777377777, ... }.

977...77<471> = (88·10470-7)/9.

977...77<764> = (88·10763-7)/9.

911...11<402> = (82·10401-1)/9.

911...11<456> = (82·10455-1)/9.

877...77<321> = (79·10320-7)/9.

877...77<327> = (79·10326-7)/9.

877...77<640> = (79·10639-7)/9.

877...77<720> = (79·10719-7)/9.

877...77<775> = (79·10774-7)/9.

877...77<903> = (79·10902-7)/9.

Probably prime numbers

977...77<7008> = (88·107007-7)/9.

977...77<7307> = (88·107306-7)/9.

977...77<9756> = (88·109755-7)/9.

Jul 10, 2004

By Chris Monico

6·10123-1 = 599...99<124> = 7 · 17 · 12377044669733<14> · C109

C109 = P54 · P56

P54 = 211603440423510579728862990143594923009829638741241111<54>

P56 = 19251501438454645628266285085602708447115558638247654467<56>

Jul 9, 2004

By Wataru Sakai

(2·10140+7)/9 = 22...223<140> = 5957256493<10> · C130

C130 = P40 · P90

P40 = 5777027076711499587422658237034853150629<40>

P90 = 645708916957404373686773843048147366831642929387462446972666663787531227763529926414396559<90>

Jul 8, 2004

Factor tables 100...007, 100...009 and 400...001 are available.

Jul 7, 2004 (2nd)

By Sander Hoogendoorn

(2·10109+43)/9 = 22...227<109> = 7 · 4793 · C104

C104 = P29 · P37 · P38

P29 = 95461175163577098073008468173<29>

P37 = 9801214825949041244854273342081274021<37>

P38 = 70790557494804005235983009008396525469<38>

(2·10111+43)/9 = 22...227<111> = 1747 · 12197 · 11370335081341<14> · C90

C90 = P38 · P53

P38 = 23933167943194394982716044480682387363<38>

P53 = 38323759459901128287487494073761024992779761689416091<53>

(2·10114+43)/9 = 22...227<114> = 222659 · 5729367461<10> · C99

C99 = P40 · P60

P40 = 1216300455323894766302412873853041903787<40>

P60 = 143218686190909825776424673236694309615952451079218209133079<60>

(82·10131-1)/9 = 911...11<132> = 97 · 24776867 · 627766960201<12> · C111

C11 = P35 · P77

P35 = 28478200367184199496414172084739201<35>

P77 = 21205192680942403119614384595818926952802356192763448040951662355401430005189<77>

(46·10120-1)/9 = 511...11<121> = 157 · 1423 · 421409 · C120

C120 = P28 · P38 · P45

P28 = 2093628483910668289303364351<28>

P38 = 35014638654705434124874572432541786721<38>

P45 = 740555643790530730635260129126097699385298659<45>

Jul 7, 2004

Generalized quasi-repdigit D(R)wE started. Factor tables 100...003, 166...667 and 300...001 are available.

Jul 6, 2004 (3rd)

By Makoto Kamada

777377...77<1338> = (69964·101334-7)/9 is smallest PRP in { 7773, 77737, 777377, 7773777, 77737777, 777377777, ... }.

Jul 6, 2004 (2nd)

By Sander Hoogendoorn

(82·10125-1)/9 = 911...11<126> = 17 · 1399 · 2823113 · 5541038707<10> · 626888245812011<15> · C91

C91 = P39 · P52

P39 = 986685793349459082532438396040963585551<39>

P52 = 3959280393312056085661664117687896858427492615264167<52>

(55·10121-1)/9 = 611...11<122> = 61 · 89 · 15661 · C114

C114 = P38 · P77

P38 = 53344673524943647082187149467449801557<38>

P77 = 13473790405074270168089556946887741540044377669236061865129217421055690110267<77>

Jul 6, 2004

By Kenichiro Yamaguchi

(46·10119-1)/9 = 511...11<120> = 158749 · 11837197134956259019<20> · C96

C96 = P33 · P63

P33 = 359603486688632859309734419042003<33>

P63 = 756365218688046022247041424371729854664983854348160527375669827<63>

(2·10136+43)/9 = 22...227<136> = 79 · 288527 · 215447101 · 608443487 · 6299750923<10> · 53306863079<11> · C91

C91 = P37 · P54

P37 = 2764727566478052553723862798027363423<37>

P54 = 801039966988081525396280603210257154637589683527439307<54>

Jul 5, 2004 (4th)

By Makoto Kamada

9999999799...99<19560> = 99999998·1019552-1 is prime.

Jul 5, 2004 (3rd)

The clauses of room for prime numbers were added. These informations show the maximum of the rate of the elements which is not divisible by small factors appearing periodically.

Jul 5, 2004 (2nd)

By Sander Hoogendoorn

(55·10106-1)/9 = 611...11<107> = 139 · 135696168123071<15> · C91

C91 = P36 · P55

P36 = 358429678586941908462329716952042503<36>

P55 = 9039279870672013375894830071967000488456328170142634973<55>

(55·10109-1)/9 = 611...11<110> = 852199 · C104

C104 = P43 · P61

P43 = 8225457442764843630927283457066986366463077<43>

P61 = 8718044873213628288885827703404609285279312719351484145970957<61>

(55·10113-1)/9 = 611...11<114> = 50703535951<11> · C104

C104 = P51 · P53

P51 = 582913994751618149452545303863432797312131797036431<51>

P53 = 20676520238336954157045104298999086966049129032729831<53>

(55·10115-1)/9 = 611...11<116> = 67 · 202591481 · C106

C106 = P32 · P75

P32 = 29263904532934703282389971089821<32>

P75 = 153848025465289770904658675376941745436626486193414230190801447835216795033<75>

(82·10108-1)/9 = 911...11<109> = 32 · 29 · 67 · 409 · C103

C103 = P36 · P67

P36 = 158675253508605407665225234734076823<36>

P67 = 8028298730113089256895440958395265979745780916450826598482481233079<67>

(82·10130-1)/9 = 911...11<131> = 25343 · 618437 · C121

C121 = P45 · P76

P45 = 634733522564762890244412679651218802698376273<45>

P76 = 9158543637307165316585354839174692830641907461273119797171181879769082529877<76>

Jul 5, 2004

By Wataru Sakai

(55·10111-1)/9 = 611...11<112> = 32 · 73 · 1574773 · C103

C103 = P27 · P76

P27 = 129523101504856161079684963<27>

P76 = 9705509861708257273773510972451806910093279864654142901189711709595743392247<76>

Jul 4, 2004 (2nd)

Condition of sequence (2·10n+43)/9 = { 7, 27, 227, 2227, 22227, ... } was extended to n≤150.

Following numbers have not factorized yet. These numbers may have small factors. You should run ECM [B1≥1000000?] first.

n=

109,

111,

114,

117,

119,

128,

129,

132,

133,

135,

136,

139,

140,

142,

143,

145,

146,

147,

149,

150,

(20/150)

Jul 4, 2004

By Sander Hoogendoorn

(37·10118-1)/9 = 411...11<119> = 7 · 2113 · 11437 · 99426499 · C103

C103 = P30 · P74

P30 = 242545362933982125628559922991<30>

P74 = 10077537735966263582017919371566619305164464911649088384505894437689028537<74>

(37·10119-1)/9 = 411...11<120> = 3 · 48341581 · C112

C112 = P47 · P66

P47 = 19612536679885364752045727762937528250045901491<47>

P66 = 144538432745915509561388922808736083086432263760564636960999504347<66>

(82·10119-1)/9 = 911...11<120> = 131 · 3259 · 18401 · 9619321997<10> · C101

C101 = P44 · P57

P44 = 31759965772503331184048671331803914822312757<44>

P57 = 379620601726565857081910303667116317038444850845058241671<57>

(82·10120-1)/9 = 911...11<121> = 3 · 23 · 335953 · C114

C114 = P52 · P62

P52 = 6092406052096057239922497361126599915259580078653033<52>

P62 = 64514136344856250069170421567897533255504136995215173249839731<62>

(82·10121-1)/9 = 911...11<122> = 7 · 13 · 263 · 12422398896722178812177<23> · C96

C96 = P37 · P59

P37 = 6875495046758823526175889150014173981<37>

P59 = 44572270530863074149631458695942281814874814716737127300991<59>

(73·10120-1)/9 = 811...11<121> = 293 · 887459 · C113

C113 = P39 · P74

P39 = 928762845661299740974009878361850251169<39>

P74 = 33586101702047225049369792987120908245818021888514043400038915625571527337<74>

Jul 3, 2004

By Kenichiro Yamaguchi

(2·10129+7)/9 = 22...223<129> = 34421 · 3519559 · 83659943 · 2696856358639<13> · C97

C97 = P38 · P60

P38 = 43467205463406142590599443250751622211<38>

P60 = 187041791368819057526369442463859368268039784258931849438031<60>

Jul 2, 2004 (2nd)

By Sander Hoogendoorn

(37·10104-1)/9 = 411...11<105> = 33 · 983 · 4799 · 6151 · C93

C93 = P45 · P49

P45 = 129025506159454833829469553664991608321902523<45>

P49 = 4066959843038454882743884002829481627969782379873<49>

(37·10105-1)/9 = 411...11<106> = 1996543 · 38290201 · C92

C92 = P37 · P55

P37 = 7867668762422834794584037715526664519<37>

P55 = 6835130850094977398746593548880827324601693761754935383<55>

(37·10111-1)/9 = 411...11<112> = 41 · C111

C111 = P32 · P79

P32 = 32900192953430841459559463081993<32>

P79 = 3047732967765795782286608540265904792223900425610536924962333181968890243736247<79>

(37·10116-1)/9 = 411...11<117> = 3 · 41 · 667393201327<12> · C103

C103 = P38 · P66

P38 = 12869116594580787491702279084538958819<38>

P66 = 389155873266856680764011951615896691671223998982635489326733532889<66>

(82·10112-1)/9 = 911...11<113> = 1016371 · C107

C107 = P33 · P74

P33 = 961710560945923780278466564888081<33>

P74 = 93212615197155374454712621114762464563887615799914869556688254085005194061<74>

(82·10114-1)/9 = 911...11<115> = 3 · 1087 · 183992288657<12> · C101

C101 = P33 · P68

P33 = 350222702847654619939973026326353<33>

P68 = 43358737406012044916467091699940873261879252754302702512159419585331<68>

Jul 2, 2004

By Wataru Sakai

(7·10137-1)/3 = 233...33<138> = 5897 · 28567199 · 2013451476373<13> · 3381296717702867<16> · C99

C99 = P30 · P69

P30 = 806083271688154958515880951639<30>

P69 = 252390868613930971196418746042261077838969195392269931528262392170539<69>

(55·10117-1)/9 = 611..11<118> = 3 · 7 · 125791 · 132888271 · 446560644667<12> · C92

C92 = P28 · P65

P28 = 2001700036961160150104009419<28>

P65 = 19475347766081839597610171633433912439406404786126941166738797347<65>

Jul 1, 2004 (2nd)

Condition of sequence (55·10n-1)/9 = { 61, 611, 6111, 61111, 611111, ... } was extended to n≤150.

Following numbers have not factorized yet. These numbers may have small factors. You should run ECM [B1≥1000000?] first.

n=

106,

109,

111,

113,

115,

117,

121,

128,

133,

134,

136,

137,

139,

140,

141,

145,

146,

147,

148,

149,

(20/150)

Jul 1, 2004

By Sander Hoogendoorn

(82·10105-1)/9 = 911...11<106> = 3 · 16493 · C102

C102 = P30 · P72

P30 = 202903131587738734658796583871<30>

P72 = 907531439759426124864348535370178399993450926608763721721428412026636479<72>

June 2004

Jun 30, 2004 (2nd)

Condition of sequence (82·10n-1)/9 = { 91, 911, 9111, 91111, 911111, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

105,

108,

112,

114,

119,

120,

121,

125,

130,

131,

134,

135,

137,

139,

144,

145,

146,

147,

148,

150,

(20/150)

Jun 30, 2004

Condition of sequence (37·10n-1)/9 = { 41, 411, 4111, 41111, 411111, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

104,

105,

111,

116,

118,

119,

124,

125,

127,

128,

132,

136,

137,

139,

140,

141,

143,

147,

148,

(19/150)

Jun 29, 2004

By Wataru Sakai

(7·10113-61)/9 = 77...771<113> = 164071 · C108

C108 = P32 · P77

P32 = 15657240180871560861397889472511<32>

P77 = 30276696807247563131834157051474945924672208419575110084039590168346878944291<77>

(7·10139-1)/3 = 233...33<140> = 97 · 43349612217589489459<20> · C118

C118 = P29 · P89

P29 = 92191282147576282327046626507<29>

P89 = 60190781096843889180574332791736121345192818031460980236899860552367407255842519233590853<89>

(7·10127-1)/3 = 233...33<128> = C128

C128 = P26 · C102

P26 = 60959186188089983484687287<26>

C102 = [382769764368870914299196165382289700653587785053094460543806339515936501231866338145853172758279698259<102>]

Jun 28, 2004

By Sander Hoogendoorn

(73·10112-1)/9 = 811...11<113> = 3 · 19 · 9344879 · C105

C105 = P38 · P68

P38 = 10706904706214958746506351356519255053<38>

P68 = 14222235813687816531103133484794874356750365603892533502465656170229<68>

(73·10113-1)/9 = 811...11<114> = 7 · 67 · 617 · 2053 · 4630723 · C99

C99 = P35 · P65

P35 = 12732080914894100599126485912790289<35>

P65 = 23157154936770838301766203436448068386765572609185635015995020877<65>

(73·10116-1)/9 = 811...11<117> = 23 · 1531 · 328103 · 9869857 · C100

C100 = P42 · P59

P42 = 165220423474037603303412870061037663554883<42>

P59 = 43051920657988170527500532097758031147884924296223330528279<59>

Jun 26, 2004 (2nd)

By Tetsuya Kobayashi

(5·10146-17)/3 = 166...661<147> = 7 · C146

C146 = P37 · P110

P37 = 1138365013140279936801790284665785169<37>

P110 = 20915544253985060148440675632045178089382928893179578794652787706339837025997038021812310920825581421031172867<110>

(23·10141+1)/3 = 766...667<142> = 11 · 443 · 236128169443<12> · 1106751044417<13> · C115

C115 = P44 · P72

P44 = 22338360360468005265599576333311848544273079<44>

P72 = 269501468800486634890594296286411801336875692534051146326470739210361271<72>

Jun 26, 2004 (2nd)

Sequence (5·10n-17)/3 = { 11, 161, 1661, 16661, 166661, ... } (n≤150) was completed.

Sequence (23·10n+1)/3 = { 77, 767, 7667, 76667, 766667, ... } (n≤150) was completed.

Jun 26, 2004

By Wataru Sakai

(7·10115-61)/9 = 77...771<115> = 5927 · C112

C112 = P29 · P83

P29 = 17478280431202086397405680487<29>

P83 = 75079591361986744553105725858443190109552529947254157878222972999835280327819906779<83>

(7·10132-1)/3 = 233..33<133> = 19 · 106695110789<12> · 727295133833231<15> · C106

C106 = P27 · P79

P27 = 495180738797335607630501803<27>

P79 = 3195981379584448522341974688808361163303854932209686092870505614398770919051791<79>

Jun 23, 2004

By Naoki Yamamoto

(7·10122-61)/9 = 77...771<122> = 47 · 7674820192951<13> · 18541290860036677<17> · C92

C92 = P27 · P65

P27 = 750443539998324866431514753<27>

P65 = 5496423364276826364201302573184309145049941443740046685989420103<65>

(7·10123-61)/9 = 77...771<123> = 32 · 116981 · 49680053 · 1089530803397127317<19> · C92

C92 = P39 · P53

P39 = 334956706308041778525531292210912060459<39>

P53 = 40746231703905456589278753224006001491134686622036861<53>

Jun 22, 2004 (2nd)

Condition of sequence (7·10n-61)/9 = { 1, 71, 771, 7771, 77771, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

113,

115,

118,

122,

123,

124,

128,

129,

131,

132,

133,

134,

138,

139,

140,

145,

146,

147,

149,

150,

(20/150)

Jun 22, 2004

By Wataru Sakai

(2·10119+7)/9 = 22...223<119> = 17 · 2071644451<10> · C108

C108 = P35 · P73

P35 = 93908811329570508550272588323170553<35>

P73 = 6719191214356169351611915828935976306063961795617665117693268061849946173<73>

Jun 21, 2004

By Sander Hoogendoorn

6·10119-1 = 599...99<120> = 43 · 1549 · C115

C115 = P38 · P78

P38 = 10018997581702311832247721815336646001<38>

P78 = 899098152507238243502902200991643338169558507864629178588274218406618965304257<78>

Jun 19, 2004 (3rd)

Sequence (64·10n-1)/9 = { 71, 711, 7111, 71111, 711111, ... } (n≤150) was completed.

Jun 19, 2004 (2nd)

By Tetsuya Kobayashi

(64·10149-1)/9 = 711...11<150> = 3 · C150

C150 = P61 · P90

P61 = 2313004823989771488921428886787243292858867172342094729868707<61>

P90 = 102480130857731949196682162076687359640400142791389525543172263004914310328958751232102191<90>

Jun 19, 2004

By Naoki Yamamoto

(73·10149-1)/9 = 811...11<150> = 72 · 283 · 446889809957966316653<21> · 4235873951025100034297<22> · C104

C104 = P25 · P80

P25 = 1266921784142905536406633<25>

P80 = 24389592902799800640423679178798171060946841191471464117352565965397179486057961<80>

Jun 18, 2004

Condition of sequence (73·10n-1)/9 = { 81, 811, 8111, 81111, 811111, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

112,

113,

116,

119,

120,

122,

123,

128,

129,

130,

134,

137,

138,

139,

142,

143,

146,

147,

148,

149,

(20/150)

Jun 17, 2004

By Sander Hoogendoorn

(13·10132-1)/3 = 433...33<133> = 17 · 389 · 11717 · C125

C125 = P47 · P79

P47 = 28514995206212330195559267632791773570653814169<47>

P79 = 1961253998675146347514532723267858352133555433237340979969288177198899206218517<79>

Jun 15, 2004

By Sander Hoogendoorn

(13·10135-1)/3 = 433...33<136> = 7 · 47 · 889454451327364627153<21> · C113

C113 = P43 · P70

P43 = 2072851865878764442016913029223865256071751<43>

P70 = 7143881136179272380186490187484607138063294385467881744127201565057659<70>

Jun 14, 2004

By Sander Hoogendoorn

(13·10141-1)/3 = 433...33<142> = 7 · 509 · 563 · 1821731 · 1761953129<10> · 1971658275584819462821<22> · C99

C99 = P44 · P56

P44 = 24176656192237126563151438146240479808680549<44>

P56 = 14118592382778721496079692509934891357041052987563510967<56>

Jun 13, 2004

By Sander Hoogendoorn

(13·10119-1)/3 = 433...33<120> = 370477 · C115

C115 = P53 · P62

P53 = 20583986961396757045936638086864949707818196023695803<53>

P62 = 56823940674990535907861824938400228680138095452420210022548043<62>

(13·10133-1)/3 = 433...33<134> = 146136971 · C126

C126 = P38 · P89

P38 = 23885692510526031230715257315951940737<38>

P89 = 12414354963245512471165731620961586411756703956512081998059151915173929602262141857480479<89>

(13·10146-1)/3 = 433...33<147> = 1429 · 407573 · 39315282870462988035173123<26> · C113

C113 = P33 · P80

P33 = 771971383563553871458372402076087<33>

P80 = 24514433198804248184950030620853493824559802681503737392436532011492112163142649<80>

Jun 12, 2004

By Sander Hoogendoorn

(13·10125-1)/3 = 433...33<126> = 63949 · 1629888441991<13> · C109

C109 = P46 · P63

P46 = 6147685935880900080547602428175394492188862351<46>

P63 = 676267921210283033805356583941013848314894195261480962356924737<63>

(13·10131-1)/3 = 433...33<132> = 19 · 283 · 6609982271<10> · C119

C119 = P35 · P36 · P49

P35 = 25166687321793668188103345284761413<35>

P36 = 424330292358680550726872064997610147<36>

P49 = 1141699146940993353185219525240900785117346743109<49>

Jun 10, 2004

By Sander Hoogendoorn

(46·10116-1)/9 = 511...11<117> = 7 · 31129657873<11> · C106

C106 = P39 · P67

P39 = 935526674796497625630799421573865249311<39>

P67 = 2507187185904102684878717389941789367778557924538338747679387631791<67>

6·10120-1 = 599...99<121> = 431 · 3931 · 29179 · C111

C111 = P41 · P70

P41 = 22147367289078430552209050468690669789449<41>

P70 = 5479973071803456301883906240611609272432415855628157465355568241290929<70>

2·10118-1 = 199...99<119> = 7 · 17 · 228023 · C111

C111 = P36 · P75

P36 = 935187333561872655816153034416501361<36>

P75 = 788144343693189519772431006559145070846257778116348967005552162769367495807<75>

Jun 9, 2004

By Sander Hoogendoorn

2·10117-1 = 199...99<118> = 1047589 · C112

C112 = P35 · P77

P35 = 85168019463062283512091014704502999<35>

P77 = 22416227110785555037014333292452400377314259442753749222567258532701137582309<77>

3·10117-1 = 299...99<118> = 17 · 103 · 7717 · 1343893 · C105

C105 = P33 · P72

P33 = 698810987349616407838127758561787<33>

P72 = 236408012483724037920438356017353423704940485863994051049626928720839267<72>

(13·10116-1)/3 = 433...33<117> = 17 · 210011 · 83332661747<11> · C100

C100 = P39 · P61

P39 = 146516877180274527149583736508724650731<39>

P61 = 9940957697340997015417443393844668494547618833464313339447087<61>

Jun 8, 2004

By Sander Hoogendoorn

3·10113-1 = 299...99<114> = 72 · 29 · 8139497 · C104

C104 = P48 · P57

P48 = 183196997235114666313664862887412748867877758421<48>

P57 = 141583048280838478129901762617470802340141205501351431287<57>

3·10116-1 = 299...99<117> = 13 · 191 · 419 · 342803 · C105

C105 = P40 · P66

P40 = 3080389672652381470662675187786673261869<40>

P66 = 273073929335371915922432805053316071687914686044309883829457031841<66>

Jun 4, 2004

By Naoki Yamamoto

(7·10123-1)/3 = 233...33<124> = 491 · C121

C121 = P33 · P89

P33 = 170220884055907671842649150123463<33>

P89 = 27917880980887515812619355132923513202464203505243949190368499491175998427036902452861001<89>

May 2004

May 31, 2004

By Naoki Yamamoto

(7·10133-1)/3 = 233...33<134> = 23 · 31 · 353 · 3607 · 4787 · 699792361 · 3904341908732501<16> · C97

C97 = P34 · P63

P34 = 5131056462682647143380688455985791<34>

P63 = 382982691330251443221587418660893430247790138019406239558489683<63>

(7·10150-1)/3 = 233...33<151> = 19 · C150

C150 = P30 · C120

P30 = 335884748059317734050810927349<30>

C120 = [365622488825160205153705205662720222924619474120643276309059711659952336337582975112200217104591970410701506722197773243<120>]

May 30, 2004

By Naoki Yamamoto

(13·10113-1)/3 = 433...33<114> = 19 · C113

C113 = P35 · P78

P35 = 45800041278938118549130221851788633<35>

P78 = 497969366554868606359758411939328925750050853699722017337131646875937090377679<78>

May 29, 2004

By Naoki Yamamoto

(7·10149-1)/3 = 233...33<150> = 30853 · 8296247 · 2353232767<10> · 264235581411709<15> · 1801403161765577<16> · C99

C99 = P30 · P70

P30 = 405830732573010613747654621973<30>

P70 = 2005329185009279663384512089127045616452253726372350154563592642457601<70>

May 28, 2004 (2nd)

By Sander / SNFS

(46·10115-1)/9 = 511...11<116> = 3 · 47 · 658579 · C108

C108 = P42 · P67

P42 = 228877708591289820908254845608651729149231<42>

P67 = 2404832510246669269292539473464359171618519632785613828793162210079<67>

By Naoki Yamamoto / http://www.alpertron.com.ar/ECM.HTM

(7·10122-1)/3 = 233...33<123> = 29504712739<11> · 2651207986088639<16> · C97

C97 = P36 · P62

P36 = 229929370163667522285804530758088773<36>

P62 = 12973200964484509642990877747286384010229308118942573774674501<62>

May 28, 2004

By Makoto Kamada

9998·104604-1 = 999799...99<4608> is near-repdigit prime.

9998·1017780-1 = 999799...99<17784> is near-repdigit prime.

>pfgw -n -tp -u0 -q"9998*10^4604-1"
PFGW Version 20031222.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]

Primality testing 9998*10^4604-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 69.84%
9998*10^4604-1 is prime! (8.0681s+0.0139s)

>pfgw -n -tp -u0 -q"9998*10^17780-1"
PFGW Version 20031222.Win_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]

Primality testing 9998*10^17780-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 69.88%
9998*10^17780-1 is prime! (184.8771s+0.0040s)

May 27, 2004

By Naoki Yamamoto

(22·10115-1)/3 = 733...33<116> = 449 · C114

C114 = P46 · P69

P46 = 1589392966057039972616161059201697498443801767<46>

P69 = 102759929681542263366018057338071988806791801495521421516353967127651<69>

(13·10112-1)/3 = 433...33<113> = 191 · 3965393 · C104

C104 = P36 · P68

P36 = 604749871346171042794960325061155857<36>

P68 = 94607749140050184748195011728693905595812738965120476399230275205963<68>

May 26, 2004

By Naoki Yamamoto

(10116+53)/9 = 11...117<116> = 631 · C113

C113 = P53 · P61

P53 = 11526725738214368469633700629285252401031855384929683<53>

P61 = 1527644044973876197755769498429806850347483992872651422450329<61>

May 25, 2004

By Naoki Yamamoto

6·10116-1 = 599...99<117> = C117

C117 = P46 · P72

P46 = 2342090630142461438660076396094112368358070139<46>

P72 = 256181375852011342805382689051963508114368392834344932319990234698993741<72>

(7·10119-43)/9 = 77...773<119> = 288394514528185645818913<24> · C96

C96 = P42 · P55

P42 = 198847031436135376990837974634976619276829<42>

P55 = 1356280204877732565773995903830143965508261852891150449<55>

May 24, 2004

By Naoki Yamamoto

(61·10105-7)/9 = 677...77<106> = 3 · 29 · C104

C104 = P41 · P64

P41 = 32148274203793268831534339250005187593153<41>

P64 = 2423318004715875237085797454768846554550215342970015001720151607<64>

(8·10110-71)/9 = 88...881<110> = 33 · 43 · 47 · 107 · 1657 · C100

C100 = P32 · P69

P32 = 17482455018321939827204777920237<32>

P69 = 525543530548990224655205437930526769887413862536485408822128741629361<69>

May 23, 2004

By Naoki Yamamoto

(7·10106-43)/9 = 77...773<106> = 32 · 73 · C104

C104 = P42 · P62

P42 = 135454626977966912830050699632472790843057<42>

P62 = 87396957968302333604157198148392451856826312567917001744792877<62>

May 22, 2004

By Naoki Yamamoto

(2·10114+7)/9 = 22...223<114> = 227744423 · C105

C105 = P38 · P68

P38 = 46388076775344031604169485115695530757<38>

P68 = 21034556913321933041770219922820321305866591917084027325536346282693<68>

(4·10110-31)/9 = 44...441<110> = 173 · 997 · C105

C105 = P53 · P53

P53 = 15109195222042198220948269885597385829718858350367013<53>

P53 = 17054338855627479213934023025101143375324490926767397<53>

May 21, 2004 (3rd)

By Naoki Yamamoto

6·10112-1 = 599...99<113> = 7873 · C109

C109 = P39 · P71

P39 = 627064686431686180556447069365942930637<39>

P71 = 12153424154991108248207141560671491643347371910061844293900500637895099<71>

May 21, 2004 (2nd)

By Makoto Kamada

(34·1018155-7)/9 = 377...77<18156> is PRP.

May 21, 2004

By Naoki Yamamoto

(8·10112-71)/9 = 88...881<112> = C112

C112 = P33 · P80

P33 = 485067313962472488439347747143603<33>

P80 = 18325062590336859694276228865377928058153164816809446347805530847002505332697227<80>

May 20, 2004 (2nd)

By Phil Carmody

2·10401-1 = 199...99<402> is prime.

2·10785-1 = 199...99<786> is prime.

2·101325-1 = 199...99<1326> is prime.

2·102906-1 = 199...99<2907> is prime.

2·105407-1 = 199...99<5408> is prime.

2·105697-1 = 199...99<5698> is prime.

2·105969-1 = 199...99<5970> is prime.

2·107517-1 = 199...99<7518> is prime.

3·101311-1 = 299...99<1312> is prime.

5·10390-1 = 499...99<391> is prime.

5·10594-1 = 499...99<595> is prime.

6·10490-1 = 599...99<491> is prime.

6·10613-1 = 599...99<614> is prime.

6·101624-1 = 599...99<1625> is prime.

6·102000-1 = 599...99<2001> is prime.

6·102994-1 = 599...99<2995> is prime.

8·10550-1 = 799...99<551> is prime.

8·10796-1 = 799...99<797> is prime.

8·101219-1 = 799...99<1220> is prime.

8·102012-1 = 799...99<2013> is prime.

8·102846-1 = 799...99<2847> is prime.

9·10935-1 = 899...99<936> is prime.

May 20, 2004

By Phil Carmody

(2·101494-11)/9 = 22...221<1494> is prime.

(4·10492-13)/9 = 44...443<492> is prime.

May 19, 2004

By Naoki Yamamoto

2·10113-1 = 199...99<114> = 4650259 · C107

C107 = P35 · P72

P35 = 89387497645595816161332104338818611<35>

P72 = 481145107556798585845390975569987436831798400147931324271186928514607751<72>

(2·10112+7)/9 = 22...223<112> = 32 · 132 · 19 · 23 · 173 · 1013 · C101

C101 = P45 · P57

P45 = 103924798360847252900346836263614426182389237<45>

P57 = 183570164108890724311962475702790923594683411145278898823<57>

May 17, 2004 (3rd)

By Naoki Yamamoto

2·10109-1 = 199...99<110> = 19 · C109

C109 = P53 · P56

P53 = 21114980841716492601531213816684580682795131715128639<53>

P56 = 49852357756711903215458867437681135752537509295755288539<56>

May 17, 2004 (2nd)

By Makoto Kamada

(7·106459-1)/3 = 233...33<6460> is PRP.

(7·1010582-1)/3 = 233...33<10583> is PRP.

May 17, 2004

By Naoki Yamamoto

5·10114-1 = 499...99<115> = 126583211 · C107

C107 = P31 · P35 · P42

P31 = 1447145884664060547607987361879<31>

P35 = 58295675470326978906201157594508111<35>

P42 = 468214914404256693353199842140909817566661<42>

May 16, 2004

Condition of sequence (7·10n-1)/3 = { 23, 233, 2333, 23333, 233333, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

124,

126,

127,

128,

129,

132,

134,

137,

139,

140,

141,

143,

144,

146,

147,

148,

150,

(17/150)

May 15, 2004

By Naoki Yamamoto

2·10120-1 = 199...99<121> = 127 · 6520884276873089204884529<25> · C94

C94 = P42 · P53

P42 = 232643528042555620464254561737409431506439<42>

P53 = 10380751776128730049253466514320685686318545305162727<53>

May 13, 2004

By Naoki Yamamoto

2·10129-1 = 199...99<130> = 29 · 31 · 484733313451<12> · 41463885135837930748140461<26> · C90

C90 = P41 · P49

P41 = 50291757440027988007781239460876655467039<41>

P49 = 2200901625430665915052040182443813421490599481669<49>

(22·10103-1)/3 = 733...33<104> = 19 · 1397625682847<13> · C91

C91 = P45 · P47

P45 = 109883611684940338056961947669759168699899399<45>

P47 = 25131825002810270252734351319028774815434515919<47>

(22·10121-1)/3 = 733...33<122> = 17 · 19 · 23 · 73 · 43577 · 2659535643452017029431<22> · C91

C91 = P41 · P50

P41 = 35256478889201173322466131920101577265537<41>

P50 = 33093761094034578075875176578877782742336554802871<50>

May 12, 2004

By Naoki Yamamoto

(43·10145-7)/9 = 477...77<146> = 53 · 995479159 · 1031732937611898444256444168590625309<37> · C99

C99 = P35 · P65

P35 = 41524900155093747577542885295980451<35>

P65 = 21136935007095307846080272590651188357697506848553079390837868989<65>

May 11, 2004

Condition of sequence (22·10n-1)/3 = { 73, 733, 7333, 73333, 733333, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

103,

115,

118,

121,

125,

127,

129,

135,

136,

137,

139,

140,

141,

142,

143,

144,

145,

146,

147,

149,

(20/150)

May 10, 2004

By Naoki Yamamoto

2·10116-1 = 199...99<117> = 1414973875906225217477423519<28> · C90

C90 = P34 · P56

P34 = 2166851807361589573177075751475697<34>

P56 = 65230748710190317012308794178134036269360841135247689393<56>

May 9, 2004 (2nd)

Condition of sequence 2·10n-1 = { 19, 199, 1999, 19999, 199999, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

109,

113,

116,

117,

118,

119,

120,

123,

125,

129,

130,

132,

137,

140,

142,

143,

144,

148,

149,

150,

(20/150)

May 9, 2004

By Makoto Kamada

5·10106-1 = 499...99<107> = 19 · 61 · C104

C104 = P48 · P56

P48 = 448580653183815696347596509441422230841080789699<48>

P56 = 96171420178862927652971517159689674091160642927176945539<56>

May 8, 2004 (2nd)

By Naoki Yamamoto

(25·10144-7)/9 = 277...77<145> = 47103151453<11> · 31839879341764061<17> · 14383880316104586858828304961<29> · C90

C90 = P40 · P50

P40 = 5232093742073114093725709327773272546161<40>

P50 = 24610732722036069413879504444522722139488936085689<50>

(61·10144-7)/9 = 677...77<145> = 3 · 26701 · 209581 · 18248307261571<14> · 10974689155546186175618317723<29> · C94

C94 = P42 · P52

P42 = 469186194512159628589287694073018761362341<42>

P52 = 4296616559387993849962861028224532418481985117419063<52>

(28·10127-1)/9 = 311...11<128> = 281 · 307 · 238599056062709776815461419063<30> · C94

C94 = P39 · P56

P39 = 107554330787428224166772754609776501813<39>

P56 = 14053166861603880222824059670432645508929757889981227607<56>

May 8, 2004

By Naoki Yamamoto

(28·10139-1)/9 = 311...11<140> = 23 · 401 · 6869442431<10> · 8201790277<10> · 151723915832626286918993436841007<33> · C84

C84 = P34 · P51

P34 = 1046070491078451817587498267478589<34>

P51 = 377223005511673979186119699372574922813654796022657<51>

(13·10122-1)/3 = 433...33<123> = 3858529 · 28224583 · 81709702023292518690005684521<29> · C80

C80 = P37 · P44

P37 = 2507902984127301658576638719322271127<37>

P44 = 19417281900219598336760656571835498686930957<44>

(13·10123-1)/3 = 433...33<124> = 7 · 53 · 167 · 881 · 2239 · 17789 · 2381744689844379917707219967<28> · C81

C81 = P40 · P42

P40 = 1075763853860339303442821734177317890269<40>

P42 = 777925533527685318766194885772532655994553<42>

May 7, 2004

By Tetsuya Kobayashi

6·10109-1 = 599...99<110> = 1097 · 177127 · C102

C102 = P32 · P70

P32 = 40526865419503344030560725081973<32>

P70 = 7619331015587068965128617236216530435918061305625862481832120448431677<70>

6·10122-1 = 599...99<123> = 19 · 653 · C119

C119 = P31 · P89

P31 = 2200147865988584750385205954057<31>

P89 = 21980248526216090623720530301482643199731747929704216226269719100413363351565439099025201<89>

6·10145-1 = 599...99<146> = 195053 · 141166257655213649896544716751749<33> · C109

C109 = P31 · P33 · P46

P31 = 4434268676207479109989143296941<31>

P33 = 166472072107891429498688521947067<33>

P46 = 2951918244671889720741543537462059850380439361<46>

(43·10132-7)/9 = 477...77<133> = 53 · 359 · 66042962426411671<17> · C112

C112 = P29 · P83

P29 = 39497365451597721319005420529<29>

P83 = 96263346154501070386456640323908028424093263790447228189038637435728194844219252189<83>

(43·10145-7)/9 = 477...77<146> = 53 · 995479159 · C135

C135 = P37 · C99

P37 = 1031732937611898444256444168590625309<37>

C99 = [877709115754338411331068021578059389846137164391353412463769213512709616627986341698090996243134039<99>]

(43·10148-7)/9 = 477...77<149> = 1303 · 3307 · 1675755311<10> · 278534297117<12> · 9992176821755603<16> · C106

C106 = P33 · P37 · P37

P33 = 729009003254478020627785253793391<33>

P37 = 1250502752200851532078754712130856591<37>

P37 = 2607836726119230613173722809451411357<37>

(2·10115+7)/9 = 22...223<115> = 3 · 2111 · 419059 · C105

C105 = P33 · P73

P33 = 269030601130809864498212068276549<33>

P73 = 3112441116444247743889279179616437584284824828415555461928913078952182341<73>

(2·10132+7)/9 = 22...223<132> = 461 · 1961595343<10> · C120

C120 = P33 · P88

P33 = 149304530301433541614272950389291<33>

P88 = 1645902684055324617855608273026808923606630267577606872525954887431643942752028685234511<88>

(2·10133+7)/9 = 22...223<133> = 3 · 4092233 · 1307931910231<13> · C114

C114 = P33 · P81

P33 = 424814383108965677778685648075483<33>

P81 = 325777833102930425413619004632980511551365206440383694360863857960806620637699249<81>

(2·10141+7)/9 = 22...223<141> = 1171 · 4133 · 574931249 · C125

C125 = P34 · P92

P34 = 6593494772741607446454582942280577<34>

P92 = 12112494848047720158381219135095901764288321518461483499555531920883196702345694182587469057<92>

(61·10119-7)/9 = 677...77<120> = 1117 · 2963 · C114

C114 = P37 · P77

P37 = 2482867040228760874738763473913341739<37>

P77 = 82480073191204085479276961599941715332454202055744480615029787929386302794933<77>

(61·10133-7)/9 = 677...77<134> = 29 · 67 · 617 · 21061 · 6183340553224673677<19> · C105

C105 = P33 · P73

P33 = 169996189666691841085123740618869<33>

P73 = 2553806684404383920744365758186857811999030277231264378877580416414570819<73>

(61·10144-7)/9 = 677...77<145> = 3 · 26701 · 209581 · 18248307261571<14> · C122

C122 = P29 · C94

P29 = 10974689155546186175618317723<29>

C94 = [2015913172777181345006219909644560227234582809640183805456132031404556222050282467471683706483<94>]

(28·10127-1)/9 = 311...11<128> = 281 · 307 · C123

C123 = P30 · C94

P30 = 238599056062709776815461419063<30>

C94 = [1511478957243868288518174989600984458708944569116374772543833320455471124010008768435801151491<94>]

(28·10135-1)/9 = 311...11<136> = 3 · 10300469367242916451<20> · C117

C117 = P28 · P89

P28 = 7683930573457486564648081513<28>

P89 = 13102489491397317646769416780137888945330964323802773376155529927060182429351919042059799<89>

(28·10139-1)/9 = 311...11<140> = 23 · 401 · 6869442431<10> · 8201790277<10> · C116

C116 = P33 · C84

P33 = 151723915832626286918993436841007<33>

C84 = [394601854621686336057357714877387805062905168503946221557031031151782715409106390973<84>]

(28·10142-1)/9 = 311...11<143> = 7301597 · 11562898307297<14> · 4916511500456033<16> · C107

C107 = P30 · P32 · P47

P30 = 193191252769849956505439432831<30>

P32 = 33595572112247073555344073339779<32>

P47 = 11547936770994507682778259324179946656817378287<47>

(28·10144-1)/9 = 311...11<145> = 3 · C145

C145 = P29 · P33 · P84

P29 = 68259441937979744951640698797<29>

P33 = 130522260397986637978317952371613<33>

P84 = 116398383092931351479137105146603590908252840941503083126928866253479361451337974517<84>

(4·10124-31)/9 = 44...441<124> = 43 · 24919 · C118

C118 = P38 · P81

P38 = 11578161099816162269427205005018334709<38>

P81 = 358243919751125298475790293910368747977594305052401111960967180951511906668436697<81>

(4·10143-31)/9 = 44...441<143> = 17 · 3301 · 61751 · 96447577123495031663959<23> · C111

C111 = P35 · P38 · P39

P35 = 35523077573886332368246595773591211<35>

P38 = 28329591767966294953591274834762673511<38>

P39 = 132140765536130978616755260743630500857<39>

(5·10146-23)/9 = 55...553<146> = 29 · 79 · C143

C143 = P32 · P34 · P78

P32 = 56376969024279576866496705219899<32>

P34 = 2934101843429802800504208201178283<34>

P78 = 146597140168419262238347549195494033972176933900417591587574178676482142753699<78>

(25·10122-7)/9 = 277...77<123> = 149 · 432203005921<12> · C109

C109 = P27 · P83

P27 = 305822511104657599256520391<27>

P83 = 14104379922638793303803028982808294618660795959132972234966360826100464667756354443<83>

(25·10126-7)/9 = 277...77<127> = 14281313 · C120

C120 = P26 · P94

P26 = 24367111951648478835570347<26>

P94 = 7982249586308571558279035113372584668517567603848805949951631134738108329429098002611305363507<94>

(25·10134-7)/9 = 277...77<135> = 19 · 1151 · 13696372960641691<17> · C114

C114 = P30 · P85

P30 = 816084122061997150910869368403<30>

P85 = 1136391751813014522129772402920004468881575512526399152097026061387364335612111816021<85>

(25·10138-7)/9 = 277...77<139> = 250436567 · 21233880635302301<17> · C114

C114 = P36 · P78

P36 = 575137150380187795406853839548278763<36>

P78 = 908236527602227094029906541512299873104933122247776475697571611771394236381737<78>

(25·10144-7)/9 = 277...77<145> = 47103151453<11> · 31839879341764061<17> · C118

C118 = P29 · C90

P29 = 14383880316104586858828304961<29>

C90 = [128765660662798935697533889774445840220504110516570378538403638764989713531572725903989929<90>]

(16·10145-7)/9 = 177...77<146> = 17 · 1423 · 442319 · 185314267 · 3272527157663<13> · C115

C115 = P31 · P85

P31 = 1117393136413365693223828137437<31>

P85 = 2451827669519946121034508853611143468541152052644330468964158838483579870841589792369<85>

(13·10117-1)/3 = 433...33<118> = 72 · C116

C116 = P29 · P30 · P59

P29 = 15393506714064146394203206757<29>

P30 = 368352803395909168644736753739<30>

P59 = 15596403866485701426897856305491954242481123335810296359779<59>

(13·10122-1)/3 = 433...33<123> = 3858529 · 28224583 · C109

C109 = P29 · C80

P29 = 81709702023292518690005684521<29>

C80 = [48696659221201773114991589510331275769710151067036157521850137706368342683578539<80>]

(13·10123-1)/3 = 433...33<124> = 7 · 53 · 167 · 881 · 2239 · 17789 · C109

C109 = P28 · C81

P28 = 2381744689844379917707219967<28>

C81 = [836864169964103352333049268635740403822633789822072771337775388804763273915704757<81>]

(13·10146-1)/3 = 433...33<147> = 1429 · 407573 · C138

C138 = P26 · C113

P26 = 39315282870462988035173123<26>

C113 = [18924440913757233153404901191015610413215014628255280580970177797506582244240073347954639836575791228929932734463<113>]

April 2004

Apr 28, 2004

By Naoki Yamamoto

(43·10107-7)/9 = 477...77<108> = 3 · 1543 · 37501333 · C97

C97 = P36 · P62

P36 = 268237075051339506511523295724451491<36>

P62 = 10260611767132578820218414037016160633739304885020214885313971<62>

Apr 27, 2004

By Naoki Yamamoto

(46·10105-1)/9 = 511...11<106> = 29 · 1753 · 4944154679<10> · C92

C92 = P34 · P58

P34 = 9425358802508525102649479397759493<34>

P58 = 2157473485612788066221168950504556742280177187881084840649<58>

(46·10109-1)/9 = 511...11<110> = 3 · 2968934383064059373<19> · C91

C91 = P29 · P63

P29 = 41047289944857646903093226857<29>

P63 = 139800581916770400551778625120537112131203048684938651744217817<63>

(46·10130-1)/9 = 511...11<131> = 32 · 73 · 6621430727<10> · 6728565940753<13> · 22844764349203<14> · C92

C92 = P39 · P53

P39 = 921568000268286504364247144025983172323<39>

P53 = 82939522578366486889482278740816972256715449218931657<53>

(46·10146-1)/9 = 511...11<147> = 7 · 73 · 114614918434137035789291171<27> · 1252099921574660469069126749<28> · C91

C91 = P40 · P52

P40 = 5378554907418632396008777863809729095171<40>

P52 = 1295831931739910232332987466902941518921393335926789<52>

6·10108-1 = 599...99<109> = 983 · 1319 · 2879 · C100

C100 = P31 · P32 · P38

P31 = 1377936220991900892143876049623<31>

P32 = 15727768119140553102115299513499<32>

P38 = 74167742155184056600770204460124004389<38>

6·10115-1 = 599...99<116> = 353 · 29753 · 98809 · 279777283 · C96

C96 = P38 · P58

P38 = 89915295521439214464304782013102496477<38>

P58 = 2298281675665954480084479869603733788667763610645868165769<58>

6·10150-1 = 599...99<151> = 93931177 · 651403633 · 136869075743<12> · 403194830459926779059034451<27> · C97

C97 = P31 · P66

P31 = 4233495431238640401985025576851<31>

P66 = 419731849111705803960797413538714348813708997815204603705035287073<66>

Apr 24, 2004

Condition of sequence (46·10n-1)/9 = { 51, 511, 5111, 51111, 511111, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

105,

109,

115,

116,

119,

120,

125,

126,

127,

129,

130,

133,

135,

137,

141,

143,

145,

146,

148,

149,

(20/150)

Apr 20, 2004

By Naoki Yamamoto

(61·10137-7)/9 = 677...77<138> = 389 · 631 · 480167 · 83278259 · 318706812443<12> · 782549473481<12> · C96

C96 = P28 · P29 · P40

P28 = 5186584541590777505486161061<28>

P29 = 25192563188309963512192683149<29>

P40 = 2118982890903677493346019815216660853173<40>

(2·10139+7)/9 = 22...223<139> = 32 · 8486210581<10> · 6156313139653<13> · 4880507932475165839<19> · C96

C96 = P36 · P61

P36 = 817109772026772175728461872273899083<36>

P61 = 1185127410836767685755312331250837119392662598402888284264467<61>

(2·10147+7)/9 = 22...223<147> = 7151 · 22643 · 1430921 · 2348581 · 2454003667<10> · 323605016573996672507<21> · C96

C96 = P29 · P67

P29 = 75546046947925085369108394647<29>

P67 = 6807119018864928857272004130073752530647097895912993722383741851377<67>

Apr 16, 2004

By Naoki Yamamoto

6·10121-1 = 599...99<122> = 1783 · 432163 · 58395497057<11> · 529061209631<12> · C91

C91 = P29 · P62

P29 = 31111982718582936591461576351<29>

P62 = 81010135135456790395247016252114523867836377342910257137933843<62>

Apr 14, 2004 (2nd)

Condition of sequence 6·10n-1 = { 59, 599, 5999, 59999, 599999, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

108,

109,

112,

115,

116,

119,

120,

121,

122,

123,

132,

134,

137,

139,

141,

145,

148,

149,

150,

(19/150)

Apr 14, 2004

By Naoki Yamamoto

5·10117-1 = 499...99<118> = 23 · 2067841977583213889<19> · C99

C99 = P39 · P60

P39 = 773956372891384392141906610342793159273<39>

P60 = 135833953232315983621727763569180848191814905661946744078129<60>

(4·10122-31)/9 = 44...441<122> = 41 · 367 · 1483 · 1613 · 8188101117457<13> · C99

C99 = P47 · P52

P47 = 37199331872889137534783406270984191699091449263<47>

P52 = 4053906291837251048685279637731757885571591397276527<52>

Apr 12, 2004

By Naoki Yamamoto

(2·10106+7)/9 = 22...223<106> = 3 · 13 · 59 · 3323 · 13399 · C95

C95 = P42 · P53

P42 = 743983320722512131033234267009237809440019<42>

P53 = 29154455843845849700306419720970556041402986749161821<53>

(43·10104-7)/9 = 477...77<105> = 3 · 67 · C103

C103 = P39 · P65

P39 = 185392847431402052360655003647272670633<39>

P65 = 12821443235131860552080923191399927987512992318570776432045323969<65>

Apr 11, 2004 (2nd)

Condition of sequence (43·10n-7)/9 = { 47, 477, 4777, 47777, 477777, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

104,

107,

118,

121,

124,

127,

128,

129,

132,

133,

135,

136,

138,

139,

142,

143,

145,

147,

148,

149,

150,

(21/150)

Apr 11, 2004

By Naoki Yamamoto

(2·10111+7)/9 = 22...223<111> = 97 · 5771081621262690683<19> · C90

C90 = P29 · P61

P29 = 56958187395497515079848690649<29>

P61 = 6969512080474052578876774896363036007547149622542570862159077<61>

Apr 10, 2004

By Naoki Yamamoto

(61·10107-7)/9 = 677...77<108> = 157 · 179 · 19853308877069<14> · C91

C91 = P38 · P53

P38 = 58276019278733258760353591653516862947<38>

P53 = 20845478301475772097318861831763485519735834582896513<53>

(61·10111-7)/9 = 677...77<112> = 35 · 9871 · 344664799369433<15> · C91

C91 = P28 · P64

P28 = 1560773166512050647257440877<28>

P64 = 5252707034262033971211409319604914039023885965235006929108814049<64>

(61·10113-7)/9 = 677...77<114> = 164443 · 62717503 · 84243242477<11> · C90

C90 = P45 · P46

P45 = 389496820482749004699211424659822744179148351<45>

P46 = 2002830442986946774664791687039738311228128719<46>

(61·10124-7)/9 = 677...77<125> = 15227 · 111781 · 101151313 · 124673551624588433<18> · C91

C91 = P32 · P59

P32 = 95487705047218658287728754303319<32>

P59 = 33068285276795186583709312118814124498598177207244524529521<59>

Apr 9, 2004

Condition of sequence (2·10n+7)/9 = { 3, 23, 223, 2223, 22223, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

106,

111,

112,

114,

115,

119,

121,

129,

130,

132,

133,

136,

139,

140,

141,

143,

144,

147,

148,

149,

(20/150)

Apr 8, 2004

Condition of sequence (61·10n-7)/9 = { 67, 677, 6777, 67777, 677777, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

105,

107,

111,

113,

119,

120,

121,

124,

128,

129,

133,

135,

137,

141,

143,

144,

146,

147,

148,

150,

(20/150)

Apr 6, 2004

By Naoki Yamamoto

(25·10133-7)/9 = 277..77<134> = 3 · 349 · 414811151 · 13315982839<11> · 706391092489601<15> · C97

C97 = P45 · P53

P45 = 302947587969126582778790931963186733044997309<45>

P53 = 22444733591272588919605986012055058713103159535424091<53>

Apr 5, 2004

By Philippe Strohl

(4·10120-31)/9 = 44...441<120> = 32 · 257257194539<12> · C108

C108 = P30 · P78

P30 = 355328659305971856691980097253<30>

P78 = 540228144372240173282537397853857906091969158159388948832466469088719724315447<78>

(4·10135-31)/9 = 44...441<135> = 3 · 7 · 14246417 · 195698445084810190688521<24> · C103

C103 = P28 · P32 · P44

P28 = 7337407243068639315729822341<28>

P32 = 22762654378748961590139932992219<32>

P44 = 45450601132254346298608031096189988017756507<44>

(4·10138-31)/9 = 44...441<138> = 32 · 16463169519086683<17> · C121

C121 = P26 · P96

P26 = 15052243376800449743967619<26>

P96 = 199278428923120369994002434664701408471507014586007875901129416373348579379533218434803280967937<96>

Apr 1, 2004

By Naoki Yamamoto

(4·10123-31)/9 = 44...441<123> = 3 · 7 · 3739 · 26953911540871967117322709<26> · C93

C93 = P27 · P67

P27 = 134916690983200652266546217<27>

P67 = 1556521924266909590456518618516071755525262680248884281305260520763<67>

March 2004

Mar 25, 2004

By Tetsuya Kobayashi

(16·10206-61)/9 = 177...771<207> = 3 · 15725091139<11> · 475800748495892867<18> · 4901783965719986289006496835311<31> · 490788208443118459113864108769759<33> · C115

C115 = P52 · P64

P52 = 1517999133476517856754106431080765696307429236392467<52>

P64 = 2168793065506607897851349768372855861079489954737258129969373083<64>

Mar 22, 2004

By Naoki Yamamoto

(28·10108-1)/9 = 311...11<109> = 3 · 53 · 83 · 225767 · C100

C100 = P31 · P69

P31 = 9723127465647490740903656178329<31>

P69 = 107392478101279201565968868184871485812597446568363928944263227421741<69>

(28·10125-1)/9 = 311...11<126> = 257 · 2087 · 116349679 · 4256013934461701<16> · C97

C97 = P30 · P67

P30 = 225063260416102750225001751763<30>

P67 = 5204597068991878300139972119622046965779245555044591966878220075377<67>

Mar 21, 2004

By Naoki Yamamoto

(28·10150-1)/9 = 311...11<151> = 32 · 6971 · 125197 · 846913 · 93685696889<11> · 1199903662141<13> · 1403106237540005447447<22> · C91

C91 = P36 · P55

P36 = 567366079746132403265113884152652067<36>

P55 = 5226026584128553669613574839501952755233031877382069609<55>

Mar 20, 2004

By Makoto Kamada

(1030178-7)/3 = 33...331<30178> is PRP.

Mar 19, 2004

By Naoki Yamamoto

(5·10103-23)/9 = 55...553<103> = 33 · 479 · 14831 · C95

C95 = P39 · P57

P39 = 135492852316761805702885567232415592399<39>

P57 = 213767361597141467189483702362146780084852487507513012589<57>

(5·10121-23)/9 = 55...553<121> = 32 · 2549 · 51683 · 104277280195479733<18> · C95

C95 = P34 · P62

P34 = 1424466634007269855706995652120057<34>

P62 = 31544631539776040528239100066406254298955790866023655121437571<62>

(4·10127-31)/9 = 44...441<127> = 172 · 41 · 46026849228433<14> · 71949037960901166647<20> · C90

C90 = P40 · P50

P40 = 7103789343326574329334834944201001693067<40>

P50 = 15944447340647925549501009560670874103179901018677<50>

Mar 18, 2004

Condition of sequence (28·10n-1)/9 = { 31, 311, 3111, 31111, 311111, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

108,

125,

126,

127,

128,

133,

134,

135,

136,

139,

140,

142,

143,

144,

146,

147,

148,

149,

150,

(19/150)

Mar 17, 2004 (2nd)

Condition of sequence (4·10n-31)/9 = { 1, 41, 441, 4441, 44441, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

110,

120,

122,

123,

124,

125,

127,

129,

130,

131,

132,

133,

135,

136,

137,

138,

140,

142,

143,

(19/150)

Mar 17, 2004

By Naoki Yamamoto

(5·10112-23)/9 = 55...553<112> = 32 · 50507113595606501<17> · C95

C95 = P40 · P55

P45 = 6403080060763641922588220745106558311083<40>

P55 = 1908725622469250623474020224210228992726832956376396399<55>

(5·10131-23)/9 = 55...553<131> = 149 · 367 · 727 · 105397 · 108439 · 8714427881165179517<19> · C95

C95 = P33 · P63

P33 = 123816942265945344177124035462931<33>

P63 = 113320385502626783963811188944973780359904217272923500376785713<63>

(5·10135-23)/9 = 55...553<135> = 7 · 18930581 · 192654767 · 3798930791<10> · 5744276036646289<16> · C93

C93 = P35 · P59

P35 = 17205102554785565619396753533899799<35>

P59 = 57960457317470169762501929894091291134940494145014709498277<59>

(5·10137-23)/9 = 55...553<137> = 179 · 1400884856787571<16> · 2039014704489051619502147<25> · C96

C96 = P29 · P67

P29 = 39860085076042197788610136133<29>

P67 = 2725922122249473047406282462854993248837935158566993847665936202167<67>

(25·10108-7)/9 = 277...77<109> = 13516870503719267<17> · C93

C93 = P37 · P57

P37 = 1398028735162292033424875903054858003<37>

P57 = 146995908966490923010585407878846761495962086618539625177<57>

(25·10112-7)/9 = 277...77<113> = 3 · 83392503673496501773<20> · C93

C93 = P41 · P52

P41 = 44887847001983328764241524432269784017861<41>

P52 = 2473548648872387047850109357122859674933202190382203<52>

(25·10127-7)/9 = 277...77<128> = 32 · 97 · 24623 · 49232582858554851192302312789<29> · C92

C92 = P38 · P54

P38 = 67928417335307810404567461242282386211<38>

P54 = 386400939653868595312031689210522278469949288917423897<54>

Mar 11, 2004

By Tetsuya Kobayashi

8·10149-1 = 799...99<150> : C120 = 1022989353719819366635703816501<31> · P90

Mar 2, 2004

Condition of sequence (5·10n-23)/9 = { 3, 53, 553, 5553, 55553, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

103,

112,

119,

121,

124,

125,

126,

127,

130,

131,

133,

135,

137,

141,

142,

143,

144,

146,

150,

(19/150)

February 2004

Feb 29, 2004

By Naoki Yamamoto

(25·10105-7)/9 = 277...77<106> : C90 = 21913684872530270860228322669774586383<38> · P53

(25·10115-7)/9 = 277...77<116> : C91 = 81185786637570081125592174938383<32> · P59

(25·10130-7)/9 = 277...77<131> : C91 = 2045078183167382392105719896839879<34> · P57

Feb 28, 2004

Condition of sequence (25·10n-7)/9 = { 27, 277, 2777, 27777, 277777, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

105,

108,

112,

115,

122,

126,

127,

130,

131,

133,

134,

138,

141,

142,

143,

144,

146,

147,

148,

(19/150)

Feb 27, 2004

By Naoki Yamamoto

(16·10118-7)/9 = 177...77<119> : C95 = 219954452699454468814477311194986381961<39> · P56

(2·10132-17)/3 = 66...661<132> : C95 = 11021645949130450389404474025015609077<38> · P58

Feb 24, 2004

By Tetsuya Kobayashi

(10120+53)/9 = 11...117<120> : C100 = 919980363085976017239419811733<30> · 27719630905018574740352261857832569<35> · P35

(10124+53)/9 = 11...117<124> : C100 = 33280695318549701225253203674337<32> · P68

(10133+53)/9 = 11...117<133> : C111 = 122130921961536849873054098272931<33> · P79

(2·10118+61)/9 = 22...229<118> : C110 = 1466493749868054488829513061006883<34> · P77

(2·10123+61)/9 = 22...229<123> : C95 = 570047520183618351939679<24> · P71

(2·10125+61)/9 = 22...229<125> : C106 = 8700713369875389808104767058107<31> · P75

(2·10127+61)/9 = 22...229<127> : C115 = 15120691899455652359581447979<29> · P87

(2·10147+61)/9 = 22...229<147> : C127 = 967640298481865238655151873<27> · P100

(2·10127-17)/3 = 66...661<127> : C111 = 9052240448936995716833229863460401<34> · P77

(2·10138-17)/3 = 66...661<138> : C111 = 67878751009298290080057376805921<32> · 1324835335577104982446717974844763215073<40> · P40

(2·10150-17)/3 = 66...661<150> : C144 = 140172354350442194189481612214919<33> · P112

(7·10117-43)/9 = 77...773<117> : C112 = 219963366682115621854587583<27> · P86

(7·10131-43)/9 = 77...773<131> : C128 = 241132400974799183305217<24> · P105

(7·10139-43)/9 = 77...773<139> : C124 = 2388244380500145705197283737<28> · 23440121176680920265969089669<29> · P68

(7·10143-43)/9 = 77...773<143> : C125 = 44469666660757781600487511<26> · C100

(7·10146-43)/9 = 77...773<146> : C103 = 951389881668436174463816735729<30> · P73

(8·10126-71)/9 = 88...881<126> : C114 = 26794209605759549323741377211159<32> · P82

(8·10127-71)/9 = 88...881<127> : C96 = 110200847210304023324324034241<30> · P67

3·10142-1 = 299...99<143> : C138 = 93717112244395171896790558091<29> · P109

3·10149-1 = 299...99<150> : C127 = 25970585924786847027298660631<29> · P99

5·10112-1 = 499...99<113> : C100 = 17580027457273324381682122351<29> · P72

5·10129-1 = 499...99<130> : C117 = 46464233742069111351508303<26> · P91

(52·10144-7)/9 = 577...77<145> : C117 = 3924307085206602653466442605817<31> · P86

(52·10149-7)/9 = 577...77<150> : C122 = 1405742527016958541959699689<28> · 67226748758879644967302995709<29> · 343156546515091237037855140567<30> · P36

Feb 23, 2004

By Naoki Yamamoto

(16·10150-7)/9 = 177...77<151> : C151 = 9227879618237474333996784667<28> · P123

(2·10106+61)/9 = 22...229<106> : C103 = 16041019969006016083801394482607<32> · P71

Feb 22, 2004

Condition of sequence (16·10n-7)/9 = { 17, 177, 1777, 17777, 177777, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

117,

118,

123,

124,

127,

130,

131,

132,

136,

138,

140,

141,

143,

144,

145,

146,

147,

149,

150,

(19/150)

Feb 21, 2004

By Naoki Yamamoto

(10115+53)/9 = 11...117<115> : C94 = 26999081551714895266052372627562119942067647<44> · P51

Feb 20, 2004

By Naoki Yamamoto

(13·10107-1)/3 = 433...33<108> : C100 = 631136411876732358037838277857<30> · 22377643566681524178136692009181<32> · P39

Feb 19, 2004

By Naoki Yamamoto

(13·10148-1)/3 = 433...33<149> : C89 = 1017608343849102724174892897711<31> · P59

5·10108-1 = 499...99<109> : C95 = 226966348667797098201473126585921<33> · P63

Feb 18, 2004 (2nd)

Condition of sequence (13·10n-1)/3 = { 43, 433, 4333, 43333, 433333, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

107,

112,

113,

116,

117,

119,

122,

123,

125,

131,

132,

133,

134,

135,

137,

141,

143,

146,

148,

(19/150)

Feb 18, 2004

By Naoki Yamamoto

(10117+53)/9 = 11...117<117> : C93 = 720450202679701035782572256039634111006859<42> · P51

(2·10109+61)/9 = 22...229<109> : C96 = 23234645008056921138012548362183981801418532833<47> · P49

Feb 17, 2004

By Naoki Yamamoto

(2·10124+61)/9 = 22...229<124> : C93 = 11889450439077229255747506989<29> · P65

(8·10107-71)/9 = 88...881<107> : C105 = 4683428044274788695884568685501718594255477<43> · P62

Feb 16, 2004

By Naoki Yamamoto

(7·10114-43)/9 = 77...773<114> : C92 = 392683364208062786439084499110609141179745943<45> · P48

(7·10133-43)/9 = 77...773<133> : C92 = 43362385535072735982061300160921<32> · P61

(10119+53)/9 = 11...117<119> : C93 = 993486692546458312155371304998269<33> · P60

5·10128-1 = 499...99<129> : C91 = 42588483156191111202485499558026020951227589<44> · P48

By Naoki Yamamoto + Tetsuya Kobayashi

(10144+53)/9 = 11...117<144> : C89 = 12180168124480952482664005335936943<35> · P55

(10146+53)/9 = 11...117<146> : C91 = 2790575263389602709091749210076625621<37> · P54

Feb 13, 2004

By Naoki Yamamoto

(8·10111-71)/9 = 88...881<111> : C91 = 251387268111793279704641072230347489632606863<45> · P46

Feb 12, 2004

By Naoki Yamamoto

(7·10105-43)/9 = 77...773<105> : C92 = 76391818726719666769128900558673<32> · P60

(8·10105-71)/9 = 88...881<105> : C100 = 349476778536336206471041424143<30> · 9731811870711670722256054349377<31> · P40

Feb 7, 2004

By Makoto Kamada

(1023365-7)/3 = 33...331<23365> is probably prime.

(1024253-7)/3 = 33...331<24253> is probably prime.

(1024549-7)/3 = 33...331<24549> is probably prime.

(1025324-7)/3 = 33...331<25324> is probably prime.

Feb 6, 2004

By Makoto Kamada

(1018533-7)/3 = 33...331<18533> is probably prime.

(1022718-7)/3 = 33...331<22718> is probably prime.

Feb 5, 2004

By Makoto Kamada

(108855-7)/3 = 33...331<8855> is probably prime.

(1011245-7)/3 = 33...331<11245> is probably prime.

(1011960-7)/3 = 33...331<11960> is probably prime.

(1012130-7)/3 = 33...331<12130> is probably prime.

Feb 4, 2004

By Makoto Kamada

No PRP was found in sequence (64·10n+53)/9 (20001≤n≤50139).

See also Factorizations of 711...117.

January 2004

Jan 29, 2004

By Makoto Kamada

(4·106923-1)/3 = 133...33<6924> is probably prime.

Jan 27, 2004

By Makoto Kamada

(4·105845-31)/9 = 44...441<5845> is probably prime.

Jan 26, 2004

By Makoto Kamada

(13·104318-1)/3 = 433...33<4319> is probably prime.

(13·104328-1)/3 = 433...33<4329> is probably prime.

(55·103889-1)/9 = 611...11<3890> is probably prime.

(55·104192-1)/9 = 611...11<4193> is probably prime.

(73·103627-1)/9 = 811...11<3628> is probably prime.

(73·103788-1)/9 = 811...11<3789> is probably prime.

(88·103307-7)/9 = 977...77<3308> is probably prime.

(13·104930-1)/3 = 433...33<4931> is probably prime.

Jan 25, 2004

By Makoto Kamada

(8·103395-53)/9 = 88...883<3395> is probably prime.

(8·103882-53)/9 = 88...883<3882> is probably prime.

Jan 20, 2004

By Makoto Kamada

(8·1014602-71)/9 = 88...881<14602> is probably prime.

Jan 19, 2004

By Makoto Kamada

(8·1011091-71)/9 = 88...881<11091> is probably prime.

(4·10551-1)/3 = 133...33<552> is definitely prime.

(4·10989-1)/3 = 133...33<990> is definitely prime.

Jan 18, 2004 (2nd)

Condition of sequence (8·10n-71)/9 = { 1, 81, 881, 8881, 88881, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

105,

107,

110,

111,

112,

120,

123,

125,

126,

127,

130,

131,

133,

138,

143,

146,

147,

150,

(18/150)

Jan 18, 2004

By Makoto Kamada

(8·109507-71)/9 = 88...881<9507> is probably prime.

Jan 16, 2004

By Makoto Kamada

(8·103247-71)/9 = 88...881<3247> is probably prime.

(8·103877-71)/9 = 88...881<3877> is probably prime.

(8·104417-71)/9 = 88...881<4417> is definitely prime.

(8·104417-71)/9 is prime (4417 digits)

Added related link:

WIFC (World Integer Factorization Center) (Hisanori Mishima)

Jan 15, 2004

Condition of sequence (10n+53)/9 = { 7, 17, 117, 1117, 11117, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

115,

116,

117,

119,

120,

123,

124,

126,

133,

134,

139,

140,

144,

146,

147,

148,

149,

150,

(18/150)

Jan 14, 2004

Condition of sequence 5·10n-1 = { 49, 499, 4999, 49999, 499999, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

106,

108,

112,

114,

117,

123,

125,

128,

129,

130,

133,

135,

136,

141,

142,

145,

146,

149,

(18/150)

Jan 11, 2004

Condition of sequence 3·10n-1 = { 29, 299, 2999, 29999, 299999, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

113,

116,

117,

122,

125,

128,

130,

135,

136,

139,

140,

141,

142,

143,

144,

145,

148,

149,

(18/150)