Table of contents

  1. December 2003
  2. November 2003
  3. October 2003
  4. September 2003
  5. August 2003
  6. July 2003
  7. June 2003
  8. May 2003
  9. April 2003

December 2003

Dec 26, 2003 (2nd)

Condition of sequence (7·10n-43)/9 = { 3, 73, 773, 7773, 77773, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

105,

106,

114,

117,

119,

120,

122,

130,

131,

133,

137,

139,

141,

143,

145,

146,

148,

(17/150)

Dec 26, 2003

By Makoto Kamada

(7·104494-43)/9 = 77...773<4494> is probably prime.

(7·10383-43)/9 = 77...773<383> is definitely prime.

Dec 19, 2003

By Robert Backstrom

(52·10119-7)/9 / 89 / 6547 / p11 / p13 = c92 = 8479592619703354082297012972049944781917<40> · p52

Dec 18, 2003

By Robert Backstrom

(2·10118-17)/3 / p30 = c89 = 128862634771682035176637827911843449<36> · p54

(2·10119-17)/3 / 7 / 23 / 113 / 179 = c113 = 157024241265230756802160557744587682501673<42> · p72

Dec 17, 2003

By Robert Backstrom

(2·10114-17)/3 / 937 / 1442143 / 4604309 = c99 = 34095162056777834071230050180190307803510297577<47> · p52

(2·10116-17)/3 / 359 / 17957 / 51095069 = c102 = 109605072684735772888299028780527623414486567<45> · p58

(2·10117-17)/3 / 19 / 254824649 / p14 = c94 = 41228988172363672704926930235352621<35> · p59

Dec 16, 2003

Condition of sequence (2·10n+61)/9 = { 9, 29, 229, 2229, 22229, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

106,

109,

118,

120,

121,

123,

124,

125,

127,

130,

133,

136,

140,

142,

143,

145,

147,

(17/150)

Dec 15, 2003

Condition of sequence (52·10n-7)/9 = { 57, 577, 5777, 57777, 577777, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

119,

120,

122,

131,

133,

134,

137,

138,

139,

140,

144,

146,

149,

150,

(14/150)

Dec 14, 2003

Condition of sequence (2·10n-17)/3 = { 1, 61, 661, 6661, 66661, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

114,

116,

117,

118,

119,

127,

129,

132,

136,

137,

138,

144,

145,

147,

148,

150,

(16/150)

Dec 13, 2003

By Robert Backstrom

(19·10133-1)/9 / 32 / 72 / 193 / 257 / p26 = c101 = 31730260191554454705277152906949623766469777177<47> · p55

Dec 12, 2003

By Robert Backstrom

(19·10123-1)/9 / 1721 / 495797 = c115 = 4410902396712067680758090011068891021640711626659006237<55> · p60

Dec 11, 2003

By Robert Backstrom

(19·10136-1)/9 / 3 / 2539 / 3851 / p26 = c104 = 513601376061672883842767390669497<33> · 41912584787806197984964451447711989<35> · p37

Dec 10, 2003

By Robert Backstrom

(19·10131-1)/9 / 113 / 2531 / p11 / p11 = c106 = 500543932286794368034008215537074340475299<42> · p64

(19·10135-1)/9 / 691 / p14 / p22 = c98 = 539174554013026944765855678379<30> · p68

Dec 9, 2003

By Robert Backstrom

(19·10129-1)/9 / 1733 / p22 = c105 = 11730675224777369340662624085358439<35> · p71

(19·10132-1)/9 / 22859 / p28 = c101 = 17615934918098592313822835788081<32> · p70

Dec 7, 2003

By Robert Backstrom

(19·10113-1)/9 = c114 = 1136618745395201361989589826146142199191<40> · p75

(10118+71)/9 / 32 / 1151 / 6073 = c110 = 452998278768228589918517038670507<33> · p77

(19·10126-1)/9 = c127 = 1085586821944623873258448972960300144037<40> · p88

(19·10117-1)/9 / 227 / p13 = c102 = 3228603551096156029806074486994564644929<40> · p63

Dec 6, 2003

By Robert Backstrom

(19·10112-1)/9 : c108 = 109174735427764361215292162709625511<36> · 138661547990392980374543093364946273<36> · p38

Dec 5, 2003

By Robert Backstrom

(10138+71)/9 : c109 = 408287153725627590310462551061<30> · 773434418357099924006939896057111<33> · p47

(10131+71)/9 : c107 = 8597277713777376058924466679339241186763<40> · p67

(10127+71)/9 : c120 = 717787056455060146823203463159005488018911211175169242819<57> · p63

(10141+71)/9 : c106 = 933229737170954225910080587831<30> · p76

(10145+71)/9 : c131 = 40479256610920802498530867222267697<35> · p96

Dec 4, 2003 (2nd)

Condition of sequence (19·10n-1)/9 = { 21, 211, 2111, 21111, 211111, ... } was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

112,

113,

117,

123,

126,

129,

131,

132,

133,

135,

136,

137,

138,

140,

141,

146,

(16/150)

Dec 4, 2003

By Robert Backstrom

(10116+71)/9 : c112 = 838513452265118808271358599905282737069130720672715931<54> · p58

(10136+71)/9 : c94 = 1008522659585686791509357769319047928771648621<46> · p49

Dec 3, 2003

By Robert Backstrom

(10101+71)/9 : c101 = 989695116849902014398434139994927<33> · p68

(10107+71)/9 : c92 = 3561680165295406930096617902894103654165726629<46> · p47

(10103+71)/9 : c100 = 170871005289556522957138395311995912579<39> · p62

November 2003

Nov 30, 2003

Condition of sequence 9, 19, 119, 1119, 11119, ... (10n+71)/9 was extended to n≤150.

Following numbers have not factorized yet. Probably these numbers still have small factors.

n=

101,

103,

107,

116,

118,

127,

131,

133,

134,

136,

138,

140,

141,

144,

145,

146,

148,

(17/150)

Nov 23, 2003

By Robert Backstrom

(5·10138-41)/9 : C138 = 70203345773723679414392944782899031985178687<44> · P94

Nov 21, 2003

By Robert Backstrom

(8·10138-17)/9 : C136 = 5357895340167768341368325953524194627712611<43> · P93

Nov 17, 2003 (2nd)

Robert Backstrom found a 64-digit factor from (4·10137+23)/9 by NFSX v1.8.

(4·10137+23)/9 = 13 · 17 · 71 · 48353 · C128

C128 = P64 · P65

P64 = 3873427810897206492826803544173207904097049309161228410649094089<64>

P65 = 15123348794966710220577957154576315517166316170179252829192622901<65>

Nov 17, 2003

By Robert Backstrom

(4·10137+23)/9 : C128 = 3873427810897206492826803544173207904097049309161228410649094089<64> · P65

Nov 16, 2003

By Robert Backstrom

(64·10214+53)/9 : C168 = 7311969362974857810620083837519730350559033<43> · P125

Nov 13, 2003

By Robert Backstrom

(5·10138+13)/9 : C137 =7647544151363873634070411291659818767261<40> · P97

Nov 12, 2003

By Robert Backstrom

(10138+11)/3 : C127 = 5300870924121769684515930051058370530883329<43> · P84

Nov 8, 2003

By Robert Backstrom

(5·10137+13)/9 : C132 = 7095315152292414030130087418393276413489710291869<49> · P83

Nov 7, 2003

By Robert Backstrom

(64·10194+53)/9 : C165 = 126060699027366262149334756818570062113<39> · P127

Nov 6, 2003

By Robert Backstrom

(10136+11)/3 : C133 = 1040616808341821000485160672452764460456393379251<49> · P85

Nov 5, 2003 (2nd)

Sequence 533...33 ((16·10n-1)/3, n≤150) is completed.

Nov 5, 2003

By Robert Backstrom

(16·10135-1)/3 : C136 = 79431269265529626757374388885181713949272333<44> · 2142756986346820652432437301693228248213010293<46> · P47

(25·10135-1)/3 : C127 = 72913600388893044344495502023289197969598960346408033006289<59> · P68

Nov 3, 2003

By Robert Backstrom

(10134+11)/3 : C112 = 6588981070346533729358741268938426706209671<43> · P69

(10135-7)/3 : C125 = 141364859961875308600170986493309798460087<42> · P84

Nov 1, 2003

By Robert Backstrom

(8·10134-17)/9 : C128 = 72534183378848867710699827397259500930478306505663631<53> · P75

(5·10133-41)/9 : C133 = 755384514012002121120867489031925730659<39> · P94

October 2003

Oct 31, 2003 (2nd)

A 58-digit factor from (8·10141-17)/9 was found by Robert Backstrom using GMP-ECM 5.0c. This is a new record of largest known factor found by the elliptic curve method. Congratulations!!

GMP-ECM 5.0 [powered by GMP 4.1.2] [ECM]
Input number is
17837657355451922652810408444172047764808329085628834562349057700991
285509358864423437663868837774542492041869 (110 digits)
Using B1=3897500, B2=5831973006, polynomial Dickson(12), sigma=2735675386
Step 1 took 61120ms
Step 2 took 51050ms
********** Factor found in step 2:
3213162276640339413566047915418064969550383692549981333701
Found probable prime factor of 58 digits:
3213162276640339413566047915418064969550383692549981333701
Probable prime cofactor
5551433702907422298841863964693267244613910158966569 has 52 digits

See also

ECMNET (Paul Zimmermann)

Oct 31, 2003

By Robert Backstrom

(2·10147-11)/9 : C145 = 218458756433618805480126903986087<33> · P112

(4·10149+23)/9 : C145 = 119221957896880184054806821523081<33> · P113

(8·10141-17)/9 : C141 = 49832154030989267740867384231123<32> · 5551433702907422298841863964693267244613910158966569<52> · 3213162276640339413566047915418064969550383692549981333701<58>

Oct 29, 2003

Tetsuya Kobayashi reported. GMP-ECM B1=11000000 5500times for (16·10206-61)/9 finished. However, the prime factor was not found. Log file is available at http://members.at.infoseek.co.jp/~satoshi_hmny/171.206.zip.

Oct 28, 2003

By Robert Backstrom

(4·10137-1)/3 : C102 = 21810955337479286395064319825795834179522402279<47> · P55

9·10141-1 : C142 = 3088098192434236868514129081431<31> · P112

Oct 27, 2003

By Robert Backstrom

(4·10133+23)/9 : C131 = 6764350390863059925436511862677086220783892751<46> · P86

Oct 26, 2003

By Robert Backstrom

(10133+11)/3 : C131 = 2886709058094502986252293643786525612424666837924303<52> · P79

(5·10141-41)/9 : C140 = 597904737277458425760135737388503<33> · 800072387234248260558900034990633<33> · P74

Oct 25, 2003

By Robert Backstrom

(10140-7)/3 : C138 = 102812003407969205835154954321343069716429<42> · P97

Oct 24, 2003

By Robert Backstrom

(4·10131-1)/3 : C118 = 36221582685652932788594570800544098201743843677<47> · P72

10137-9 : C137 = 5165311746933052842465538744631<31> · P107

Oct 22, 2003

By Robert Backstrom

(5·10132+13)/9 : C102 = 4074220013086644289540449801737500982772443<43> · P59

Oct 21, 2003

By Robert Backstrom

(8·10143-17)/9 : C130 = 191487754485401761868598938072597<33> · 94867828833140499200211307524647727692672202209<47> · P51

8·10131-1 : C113 = 55184314154163867404343729437330341621784519<44> · P69

Oct 20, 2003

By Robert Backstrom

(71·10137-17)/9 : C105 = 479118047340424200448510695121253185739186089<45> · P60

8·10130-1 : C101 = 2283800845342290599281799116344340478326176593<46> · P56

Oct 18, 2003 (2nd)

Robert Backstrom found 59-digits factor of (5·10130+13)/9 by NFSX v1.8.

(5·10130+13)/9 = C130 = P59 · P72

P59 = 44808955029945007565499273431574530907671133211043949553229<59>

P72 = 123983153631743455790444991479946015511764203465409640937103549203831033<72>

See also 55...557.

Oct 18, 2003

By Robert Backstrom

(5·10130+13)/9 : C130 = 44808955029945007565499273431574530907671133211043949553229<59> · P72

Oct 17, 2003

By Robert Backstrom

9·10139-1 : C129 = 1576375569625015882582733569<28> · P102

Oct 16, 2003

By Robert Backstrom

(16·10215-61)/9 : C126 = 2642243356116844953643918897797407<34> · 4330859096168901897940963503386710819148959<43> · P50

(4·10141-1)/3 : C127 = 323021939072650534602020754397<30> · 302430522769765368386663720809027<33> · P65

Oct 15, 2003

By Robert Backstrom

(5·10150-41)/9 C125 = 490441118971293564217225327589<30> · P95

(5·10150+13)/9 C121 = 877147777675210067870037603912262351<36> · P85

Oct 14, 2003

By Robert Backstrom

(8·10123-17)/9 : C120 = 33234363699498984164234544173233706039<38> · P82

Oct 13, 2003

By Robert Backstrom

(8·10133-17)/9 : C121 = 13476291399345038508660026880850215830179<41> · P81

(8·10120-17)/9 : C107 = 1553782571566811545980850336630792267720690901<46> · P62

(8·10122-17)/9 : C102 = 4651129696094685712162426266825197639720411<43> · P59

(16·10139-1)/3 : C123 = 2713984231399921612698367200678239<34> · P90

(10138-7)/3 : C123 = 9966499855598431385427869723465563<34> · P89

(5·10147-41)/9 : C123 = 14089208459643190583637217041341<32> · P91

Oct 12, 2003

By Robert Backstrom

(8·10103-17)/9 : C98 = 22597320485551835403553961780765417537<38> · P60

(4·10131+23)/9 : C126 = 20426924713689289932026769612825914663<38> · P88

(8·10106-17)/9 : C106 = 1261660972086485864661721724784731807<37> · P70

(8·10128-17)/9 : C113 = 10927808425024913074695044852579<32> · P82

(8·10119-17)/9 : C113 = 299999069421527844113664020937884337059777<42> · P71

(10139+17)/9 : C121 = 700622813289580301050586529689<30> · P91

Oct 11, 2003

By Robert Backstrom

(8·10136-17)/9 : C89 = 271667204945646081053311900993567523872793<42> · P47

(4·10130+23)/9 : C130 = 8883006716943893644475417909344907<34> · P96

(5·10129-41)/9 : C124 = 1203572887256093821567298121809<31> · P94

Oct 10, 2003

By Robert Backstrom

(25·10127-1)/3 : C109 = 1235940471684380184027674194121487343602244799<46> · P64

(10134+17)/9 : C126 = 39222209065718302209209849<26> · 18325537995917379232027777402253<32> · P69

(10132+17)/9 : C130 = 863066058253783849268374572901662957863<39> · P91

8·10134-1 : C135 = 22687636885581412690987724364313<32> · 45383414450456616414537904444367<32> · P72

Oct 9, 2003

By Robert Backstrom

(10128+11)/3 : C118 = 475154870115229177076020587081234400726663632120047<51> · P67

(2·10128-11)/9 : C108 = 2000281379456033788037758300154874752260789206492659<52> · P57

10149-9 : C120 = 9406652544628197783013757175083<31> · 17015077596097981289004980562402392680515791<44> · P46

(10131-7)/3 : C121 = 4080171962202943804051748180804443<34> · 2025791268522142950892771678633795935911<40> · P48

Oct 8, 2003 (2nd)

Condition of sequence 88...887 was extended to n≤150.

Oct 8, 2003

By Robert Backstrom

(4·10145+23)/9 : C116 = 212094783166834350629892681988789255277<39> · P77

(10127+11)/3 : C105 = 91899360402884286142571830565519052633291571739<47> · P58

10147-9 : C119 = 1989051072783415478046060199<28> · P91

Oct 7, 2003

By Robert Backstrom

(5·10133+13)/9 : C115 = 64688581837212633639151014380577852253<38> · P77

(5·10127+13)/9 : C110 = 80334165764761388909669144443097479783<38> · P72

(2·10127-11)/9 : C122 = 36134697911413711828412466517304805121853464321<47> · P76

Oct 6, 2003

By Robert Backstrom

(64·10127-1)/9 : C112 = 436936959074491582487456428199<30> · 96143216326452043974615531085458506053<38> · P45

(4·10126+23)/9 : C120 = 150120037922403471536713775953886401041222117107<48> · P72

(16·10125-1)/3 : C116 = 222180014867413479466529<24> · 47788838989857151781847282291827916769<38> · P55

(2·10142-11)/9 : C113 = 164316964756186302158333349418739689<36> · P78

(2·10137-11)/9 : C112 = 46420799539183752235420713661145631161807899<44> · P68

(10146+11)/3 : C115 = 123699608781625830643193667765233<33> · P83

(4·10140+23)/9 : C115 = 952940642357627103757683958791274463<36> · P79

Oct 5, 2003

By Robert Backstrom

10145-9 : C108 = 362929801125787433471130910799<30> · 162964976215164129227941885578492094157<39> · P40

(2·10148-11)/9 : C108 = 2182492353788207197335578479737599<34> · 7485554533105775050813272783812837<34> · P41

(5·10129+13)/9 : C107 = 14162525773428600972717169870939897<35> · P73

10125-9 : C115 = 239025992477781293791695002659636001203014815071<48> · P67

(10140+11)/3 : C109 = 73054262997832424364871827629<29> · P80

8·10140-1 : C110 = 3443842139270242346445128879641<31> · 1284088379384936105787261115435555419481<40> · P40

(5·10142-41)/9 : C96 = 2788441012637861496953961166768132782840324817<46> · P51

(10128-7)/3 : C111 = 67475659878131825628043479039601<32> · P79

Oct 4, 2003

By Robert Backstrom

(10144+11)/3 : C106 = 103473305782388149019921363043601487<36> · P71

(10130+11)/3 : C107 = 83778394948959259217609627119<29> · P78

(5·10123-41)/9 : C99 = 519372493798066849955094878935951137403427449<45> · P54

(4·10124+23)/9 : C111 = 22388822797986383630299651141233757<35> · 77469452047874751157203011774981771<35> · P42

(4·10127-1)/3 : C108 = 2247838055920049612696156407806157<34> · 1076997096198551882473001011983734401<37> · P38

(25·10149-1)/3 : C105 = 2994541463358736681453602854782190039<37> · P68

Oct 3, 2003

By Robert Backstrom

(4·10129-1)/3 : C100 = 87543999811629418720135732349233999<35> · P65

8·10124-1 : C107 = 103664942350385134585704120704881<33> · 15433616177086530544791352956393457<35> · P41

(2·10135-11)/9 : C101 = 475900693439438622159972488667266705611<39> · P62

(4·10120+23)/9 : C117 = 165872452147028862235165595802809771100097<42> · P76

Oct 2, 2003

By Robert Backstrom

(16·10123-1)/3 : C122 = 7882317739705350072729039107931745687698173<43> · P79

8·10112-1 : C111 = 10422340853038410236015043584682186702615256189871<50> · P62

Oct 1, 2003

By Robert Backstrom

(23·10138+1)/3 : C131 = 6792867609382640846012633657297930367246491<43> · P88

(10136+17)/9 : C89 = 9351141344184190892402836872032757137633719<43> · P46

(4·10118+23)/9 : C91 = 260320995139728525049660224279457187<36> · P56

(4·10114+23)/9 : C102 = 425390831411115278470313909736884176526672760838939<51> · P52

(5·10128+13)/9 : C96 = 168436772342433789693726559258523243<36> · P61

(5·10131-41)/9 : C96 = 5879352501828639437450714642003<31> · P65

September 2003

Sep 30, 2003

Condition of sequence 44...447 was extended to n≤150.

Sep 26, 2003

Sequence 66...667 ((2·10n+1)/3, n≤150) is completed. Many large prime factors in the sequence were found by Tetsuya Kobayashi.

Sep 22, 2003

Condition of sequence 55...557 was extended to n≤150.

Sep 21, 2003

Condition of sequence 22...221 was extended to n≤150.

Sep 19, 2003

Condition of sequence 799...99 was extended to n≤150.

Sep 18, 2003

Condition of sequence 33...337 was extended to n≤150.

Sep 17, 2003

Condition of sequence 55...551 was extended to n≤150.

Sep 16, 2003

Condition of sequence 133...33 was extended to n≤150.

Condition of sequence 33...331 was extended to n≤150.

Condition of sequence 11...113 was extended to n≤150.

Condition of sequence 833...33 was extended to n≤150.

Sep 15, 2003

Condition of sequence 899...99 was extended to n≤150.

Condition of sequence 99...991 was extended to n≤150.

Sep 12, 2003

Condition of sequence 711...11 was extended to n≤150.

Condition of sequence 533...33 was extended to n≤150.

Sep 4, 2003

Front page was updated.

Sep 3, 2003

(2·102566-11)/9 is prime (2566 digits)

August 2003

Aug 22, 2003

Plateau and depression numbers (n≤130) is completed.

Aug 18, 2003

(7·102065-61)/9 is prime (2065 digits)

101657-9 is prime (1657 digits)

Aug 17, 2003

Primality proving program based on Pocklington's theorem version 0.2.1 is available.

(2·101364+1)/3 is prime (1364 digits)

(2·10875+1)/3 is prime (875 digits)

(2·101204+1)/3 is prime (1204 digits)

(4·102080-31)/9 is prime (2080 digits)

July 2003

Jul 8, 2003

Sequence 533...33 ((16·10k-1)/3, n≤110) is completed.

Jul 7, 2003

Sequence 77...779 ((7·10n+11)/9, n≤110) is completed.

Sequence 11...117 ((10n+53)/9, n≤110) is completed.

Robert Backstrom found 58-digits factor of 8·10136-3 by NFSX v1.8.

8·10136-3 = C137 = P58 · P80

P58 = 1217797251394238108616742402333715863565219418129129381047<58>

P80 = 65692380162961593262803328038291158319994419810107776881488006468756954660207851<80>

See also 799...997.

Jul 4, 2003

Sequence 33...337 ((10n+11)/3, n≤110) is completed.

Jul 3, 2003

Sequence 33...331 ((10n-7)/3, n≤110) is completed.

Sequence 299...99 (3·10n-1, n≤110) is completed.

Jul 1, 2003

Robert Backstrom found 44-digits factor of (4·10136-7)/3 by NFSX v1.8.

(4·10136-7)/3 = C137 = P44 · P93

P44 = 33900308806686259998523282961567274561330131<44>

P93 = 393310084853963331624828154111527695354295203527368422183511981871474871658216313458331267201<93>

See also 133...331.

Sequence 899...99 (9·10n-1, n≤110) is completed.

June 2003

Jun 29, 2003

Sequence 44...449 ((4·10n+41)/9, n≤110) is completed.

Sequence 711...11 ((64·10n-1)/9, n≤110) is completed.

Sequence 811...11 ((73·10n-1)/9, n≤110) is completed.

Jun 14, 2003

Sequence 299...99 (3·10n-1, n≤100) is completed.

Jun 13, 2003

Sequence 88...887 ((8·10n-17)/9, n≤100) is completed.

Sequence 233...33 ((7·10n-1)/3, n≤100) is completed.

Sequence 733...33 ((22·10n-1)/3, n≤100) is completed.

Sequence 577...77 ((52·10n-7)/9, n≤100) is completed.

Jun 12, 2003

Sequence 899...99 (9·10n-1, n≤100) is completed.

Sequence 211...11 ((19·10n-1)/9, n≤100) is completed.

Sequence 811...11 ((73·10n-1)/9, n≤100) is completed.

Sequence 66...661 ((2·10n-17)/3, n≤100) is completed.

Sequence 77...779 ((7·10n+11)/9, n≤100) is completed.

Sequence 911...11 ((82·10n-1)/9, n≤100) is completed.

Jun 11, 2003

Sequence 44...441 ((4·10n-31)/9, n≤100) is completed.

Sequence 22...223 ((2·10n+7)/9, n≤100) is completed.

Jun 10, 2003

Sequence 33...337 ((10n+11)/3, n≤100) is completed.

Sequence 611...11 ((55·10n-1)/9, n≤100) is completed.

Jun 9, 2003

Sequence 55...553 ((5·10n-23)/9, n≤100) is completed.

Jun 8, 2003

Sequence 977...77 ((88·10n-7)/9, n≤100) is completed.

Sequence 877...77 ((79·10n-7)/9, n≤100) is completed.

Jun 7, 2003

Sequence 411...11 ((37·10n-1)/9, n≤100) is completed.

Sequence 44...449 ((4·10n+41)/9, n≤100) is completed.

Jun 5, 2003

Sequence 533...33 ((16·10k-1)/3, n≤100) is completed.

Jun 4, 2003

Robert Backstrom found 58-digits factor of 2·10116-9 by NFSX v1.8.

2·10116-9 = C117 = P58 · P60

P58 = 1300077873236814617625875427828886902290588172083356016807<58>

P60 = 153836938630497839571709555448490510158389234978218219454513<60>

See also 199...991.

Sequence 88...881 ((8·10n-71)/9, n≤100) is completed.

Jun 3, 2003

Sequence 833...33 ((25·10n-1)/3, n≤100) is completed.

Jun 2, 2003

Sequence 11...119 ((10n+71)/9, n≤100) is completed.

Sequence 77...773 ((7·10n-43)/9, n≤100) is completed.

Sequence 177...77 ((16·10n-7)/9, n≤100) is completed.

May 2003

May 29, 2003

Sequence 99...991 (10n-9, n≤100) is completed.

May 28, 2003

Sequence 88...889 ((8·10n+1)/9, n≤150) is completed. Many large prime factors in the sequence were found by Tetsuya Kobayashi.

May 26, 2003

Sequence 599...99 (6·10n-1, n≤100) is completed.

May 25, 2003

Sequence 477...77 ((43·10n-7)/9, n≤100) is completed.

Sequence 511...11 ((46·10n-1)/9, n≤100) is completed.

Sequence 55...559 ((5·10n+31)/9, n≤100) is completed.

May 22, 2003

Tetsuya Kobayashi found 67-digits factor of (8·10137+1)/9 by NFSX 1.8. The factorization required about 72~73 hours by Athlon 950MHz for square root phase and Pentium4 2.26GHz for other stages.

(8·10137+1)/9 = C137 = P67 · P71

P67 = 4437288481554696424422856887148473496376331762236461989508296410243<67>

P71 = 20032253764520808344662115277305517886662723403005271772453535967903123<71>

See also 88...889.

May 21, 2003

Sequence 44...447 ((4·10n+23)/9, n≤100) is completed.

May 20, 2003

Sequence 99...997 (10n-3, n≤100) is completed.

May 13, 2003

Sequence 311...11 ((28·10n-1)/9, n≤100) is completed.

May 10, 2003

Sequence 677...77 ((61·10n-7)/9, n≤100) is completed.

Sequence 77...771 ((7·10n-61)/9, n≤100) is completed.

Sequence 11...117 ((10n+53)/9, n≤100) is completed.

May 9, 2003

Sequence 22...229 ((2·10n+61)/9, n≤100) is completed.

Sequence 55...551 ((5·10n-41)/9, n≤100) is completed.

Sequence 377...77 ((34·10n-7)/9, n≤100) is completed.

Sequence 433...33 ((13·10n-1)/3, n≤100) is completed.

Sequence 44...443 ((4·10n-13)/9, n≤100) is completed.

Sequence 499...99 (5·10n-1, n≤100) is completed.

Sequence 55...557 ((5·10n+13)/9, n≤100) is completed.

May 8, 2003

Sequence 133...33 ((4·10n-1)/3, n≤100) is completed.

Sequence 22...227 ((2·10n+43)/9, n≤100) is completed.

May 7, 2003

Sequence 33...331 ((10n-7)/3, n≤100) is completed.

May 4, 2003

Sequence 11...113 ((10n+17)/9, n≤100) and 22...221 ((2·10n-11)/9, n≤100) are completed.

May 3, 2003

Robert Backstrom found 55-digits factor of (28·10121+17)/9 by NFSX v1.8.

(28·10121+17)/9 = 32 · 11 · 2884725140574578047751739139603605911742922913348638439<55> · 108937119577495706512863268091410957711158118577124848292522656933<66>

See also 311...113.

May 1, 2003

Sequence 799...99 (8·10n-1, n≤100) is completed.

April 2003

Apr 29, 2003

Factorization pages were renewed.

Factorizations of near-repdigit numbers composed of all the same digit except either first digit or last digit (xyy...yy and xx...xxy) are available.