目次

• December 2003
• November 2003
• October 2003
• September 2003
• August 2003
• July 2003
• June 2003
• May 2003
• 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 ((16·10^k-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 ((16·10^k-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.