目次

• December 2004
  • Dec 31, 2004
  • Dec 30, 2004 (2nd)
  • Dec 30, 2004
  • Dec 28, 2004 (2nd)
  • Dec 28, 2004
  • Dec 26, 2004
  • Dec 25, 2004
  • Dec 24, 2004 (2nd)
  • Dec 24, 2004
  • Dec 23, 2004 (3rd)
  • Dec 23, 2004 (2nd)
  • Dec 23, 2004
  • Dec 22, 2004
  • Dec 21, 2004 (3rd)
  • Dec 21, 2004 (2nd)
  • Dec 21, 2004
  • Dec 20, 2004
  • Dec 19, 2004 (4th)
  • Dec 19, 2004 (3rd)
  • Dec 19, 2004 (2nd)
  • Dec 19, 2004
  • Dec 18, 2004 (4th)
  • Dec 18, 2004 (3rd)
  • Dec 18, 2004 (2nd)
  • Dec 18, 2004
  • Dec 17, 2004 (4th)
  • Dec 17, 2004 (3rd)
  • Dec 17, 2004 (2nd)
  • Dec 17, 2004
  • Dec 16, 2004 (3rd)
  • Dec 16, 2004 (2nd)
  • Dec 16, 2004
  • Dec 15, 2004 (5th)
  • Dec 15, 2004 (4th)
  • Dec 15, 2004 (3rd)
  • Dec 15, 2004 (2nd)
  • Dec 15, 2004
  • Dec 14, 2004 (6th)
  • Dec 14, 2004 (5th)
  • Dec 14, 2004 (4th)
  • Dec 14, 2004 (3rd)
  • Dec 14, 2004 (2nd)
  • Dec 14, 2004
  • Dec 13, 2004 (7th)
  • Dec 13, 2004 (6th)
  • Dec 13, 2004 (5th)
  • Dec 13, 2004 (4th)
  • Dec 13, 2004 (3rd)
  • Dec 13, 2004 (2nd)
  • Dec 13, 2004
  • Dec 12, 2004
  • Dec 11, 2004 (4th)
  • Dec 11, 2004 (3rd)
  • Dec 11, 2004 (2nd)
  • Dec 11, 2004
  • Dec 10, 2004 (4th)
  • Dec 10, 2004 (3rd)
  • Dec 10, 2004 (2nd)
  • Dec 10, 2004
  • Dec 9, 2004 (5th)
  • Dec 9, 2004 (4th)
  • Dec 9, 2004 (3rd)
  • Dec 9, 2004 (2nd)
  • Dec 9, 2004
  • Dec 8, 2004 (4th)
  • Dec 8, 2004 (3rd)
  • Dec 8, 2004 (2nd)
  • Dec 8, 2004
  • Dec 7, 2004 (4th)
  • Dec 7, 2004 (3rd)
  • Dec 7, 2004 (2nd)
  • Dec 7, 2004
  • Dec 6, 2004 (4th)
  • Dec 6, 2004 (3rd)
  • Dec 6, 2004 (2nd)
  • Dec 6, 2004
  • Dec 5, 2004 (4th)
  • Dec 5, 2004 (3rd)
  • Dec 5, 2004 (2nd)
  • Dec 5, 2004
  • Dec 4, 2004 (3rd)
  • Dec 4, 2004 (2nd)
  • Dec 4, 2004
  • Dec 3, 2004 (2nd)
  • Dec 3, 2004
  • Dec 2, 2004 (2nd)
  • Dec 2, 2004
  • Dec 1, 2004
• November 2004
  • Dec 1, 2004 (2nd)
  • Nov 30, 2004 (7th)
  • Nov 30, 2004 (6th)
  • Nov 30, 2004 (5th)
  • Nov 30, 2004 (4th)
  • Nov 30, 2004 (3rd)
  • Nov 30, 2004 (2nd)
  • Nov 30, 2004
  • Nov 29, 2004 (5th)
  • Nov 29, 2004 (4th)
  • Nov 29, 2004 (3rd)
  • Nov 29, 2004 (2nd)
  • Nov 29, 2004
  • Nov 28, 2004 (5th)
  • Nov 28, 2004 (4th)
  • Nov 28, 2004 (3rd)
  • Nov 28, 2004 (2nd)
  • Nov 28, 2004
  • Nov 27, 2004 (4th)
  • Nov 27, 2004 (3rd)
  • Nov 27, 2004 (2nd)
  • Nov 27, 2004
  • Nov 26, 2004
  • Nov 25, 2004 (3rd)
  • Nov 25, 2004 (2nd)
  • Nov 25, 2004
  • Nov 24, 2004 (4th)
  • Nov 24, 2004 (3rd)
  • Nov 24, 2004 (2nd)
  • Nov 24, 2004
  • Nov 23, 2004 (3rd)
  • Nov 23, 2004 (2nd)
  • Nov 23, 2004
  • Nov 22, 2004 (3rd)
  • Nov 22, 2004 (2nd)
  • Nov 22, 2004
  • Nov 20, 2004 (3rd)
  • Nov 20, 2004 (2nd)
  • Nov 20, 2004
  • Nov 19, 2004 (6th)
  • Nov 19, 2004 (5th)
  • Nov 19, 2004 (4th)
  • Nov 19, 2004 (3rd)
  • Nov 19, 2004 (2nd)
  • Nov 19, 2004
  • Nov 18, 2004 (3rd)
  • Nov 18, 2004 (2nd)
  • Nov 18, 2004
  • Nov 17, 2004 (2nd)
  • Nov 17, 2004
  • Nov 16, 2004 (7th)
  • Nov 16, 2004 (6th)
  • Nov 16, 2004 (5th)
  • Nov 16, 2004 (4th)
  • Nov 16, 2004 (3rd)
  • Nov 16, 2004 (2nd)
  • Nov 16, 2004
  • Nov 15, 2004 (4th)
  • Nov 15, 2004 (3rd)
  • Nov 15, 2004 (2nd)
  • Nov 15, 2004
  • Nov 14, 2004 (3rd)
  • Nov 14, 2004 (2nd)
  • Nov 14, 2004
  • Nov 13, 2004 (2nd)
  • Nov 13, 2004
  • Nov 12, 2004
  • Nov 11, 2004 (2nd)
  • Nov 11, 2004
  • Nov 10, 2004 (3rd)
  • Nov 10, 2004 (2nd)
  • Nov 10, 2004
  • Nov 9, 2004 (7th)
  • Nov 9, 2004 (6th)
  • Nov 9, 2004 (5th)
  • Nov 9, 2004 (4th)
  • Nov 9, 2004 (3rd)
  • Nov 9, 2004 (2nd)
  • Nov 9, 2004
  • Nov 8, 2004 (3rd)
  • Nov 8, 2004 (2nd)
  • Nov 8, 2004
  • Nov 7, 2004 (3rd)
  • Nov 7, 2004 (2nd)
  • Nov 7, 2004
  • Nov 6, 2004 (3rd)
  • Nov 6, 2004 (2nd)
  • Nov 6, 2004
  • Nov 5, 2004 (2nd)
  • Nov 5, 2004
  • Nov 4, 2004 (5th)
  • Nov 4, 2004 (4th)
  • Nov 4, 2004 (3rd)
  • Nov 4, 2004 (2nd)
  • Nov 4, 2004
  • Nov 3, 2004 (2nd)
  • Nov 3, 2004
  • Nov 2, 2004
  • Nov 1, 2004
• October 2004
  • Oct 31, 2004 (4th)
  • Oct 31, 2004 (3rd)
  • Oct 31, 2004 (2nd)
  • Oct 31, 2004
  • Oct 30, 2004 (4th)
  • Oct 30, 2004 (3rd)
  • Oct 30, 2004 (2nd)
  • Oct 30, 2004
  • Oct 29, 2004 (2nd)
  • Oct 29, 2004
  • Oct 28, 2004
  • Oct 27, 2004 (3rd)
  • Oct 27, 2004 (2nd)
  • Oct 27, 2004
  • Oct 26, 2004 (2nd)
  • Oct 26, 2004
  • Oct 25, 2004
  • Oct 24, 2004 (5th)
  • Oct 24, 2004 (4th)
  • Oct 24, 2004 (3rd)
  • Oct 24, 2004 (2nd)
  • Oct 24, 2004
  • Oct 23, 2004 (2nd)
  • Oct 23, 2004
  • Oct 22, 2004 (2nd)
  • Oct 22, 2004
  • Oct 20, 2004 (4th)
  • Oct 20, 2004 (3rd)
  • Oct 20, 2004 (2nd)
  • Oct 20, 2004
  • Oct 19, 2004 (3rd)
  • Oct 19, 2004 (2nd)
  • Oct 19, 2004
  • Oct 18, 2004
  • Oct 17, 2004 (2nd)
  • Oct 17, 2004
  • Oct 16, 2004 (2nd)
  • Oct 16, 2004
  • Oct 15, 2004 (2nd)
  • Oct 15, 2004
  • Oct 14, 2004 (3rd)
  • Oct 14, 2004 (2nd)
  • Oct 14, 2004
  • Oct 13, 2004
  • Oct 12, 2004 (3rd)
  • Oct 12, 2004 (2nd)
  • Oct 12, 2004
  • Oct 11, 2004 (4th)
  • Oct 11, 2004 (3rd)
  • Oct 11, 2004 (2nd)
  • Oct 11, 2004
  • Oct 10, 2004
  • Oct 9, 2004
  • Oct 8, 2004 (2nd)
  • Oct 8, 2004
  • Oct 7, 2004
  • Oct 6, 2004 (2nd)
  • Oct 6, 2004
  • Oct 5, 2004 (5th)
  • Oct 5, 2004 (4th)
  • Oct 5, 2004 (3rd)
  • Oct 5, 2004 (2nd)
  • Oct 5, 2004
  • Oct 4, 2004 (2nd)
  • Oct 4, 2004
  • Oct 2, 2004 (4th)
  • Oct 2, 2004 (3rd)
  • Oct 2, 2004 (2nd)
  • Oct 2, 2004
  • Oct 1, 2004
• September 2004
  • Sep 30, 2004 (3rd)
  • Sep 30, 2004 (2nd)
  • Sep 30, 2004
  • Sep 29, 2004
  • Sep 28, 2004 (5th)
  • Sep 28, 2004 (4th)
  • Sep 28, 2004 (3rd)
  • Sep 28, 2004 (2nd)
  • Sep 28, 2004
  • Sep 27, 2004 (5th)
  • Sep 27, 2004 (4th)
  • Sep 27, 2004 (3rd)
  • Sep 27, 2004 (2nd)
  • Sep 27, 2004
  • Sep 26, 2004 (2nd)
  • Sep 26, 2004
  • Sep 25, 2004 (2nd)
  • Sep 25, 2004
  • Sep 24, 2004 (3rd)
  • Sep 24, 2004 (2nd)
  • Sep 24, 2004
  • Sep 23, 2004 (2nd)
  • Sep 23, 2004
  • Sep 22, 2004
  • Sep 21, 2004 (3rd)
  • Sep 21, 2004 (2nd)
  • Sep 21, 2004
  • Sep 20, 2004
  • Sep 19, 2004
  • Sep 18, 2004 (3rd)
  • Sep 18, 2004 (2nd)
  • Sep 18, 2004
  • Sep 17, 2004 (2nd)
  • Sep 17, 2004
  • Sep 16, 2004 (3rd)
  • Sep 16, 2004 (2nd)
  • Sep 16, 2004
  • Sep 14, 2004 (3rd)
  • Sep 14, 2004 (2nd)
  • Sep 14, 2004
  • Sep 13, 2004 (3rd)
  • Sep 13, 2004 (2nd)
  • Sep 13, 2004
  • Sep 12, 2004
  • Sep 11, 2004 (3rd)
  • Sep 11, 2004 (2nd)
  • Sep 11, 2004
  • Sep 10, 2004 (5th)
  • Sep 10, 2004 (4th)
  • Sep 10, 2004 (3rd)
  • Sep 10, 2004 (2nd)
  • Sep 10, 2004
  • Sep 8, 2004 (3rd)
  • Sep 8, 2004 (2nd)
  • Sep 8, 2004
  • Sep 7, 2004 (3rd)
  • Sep 7, 2004 (2nd)
  • Sep 7, 2004
  • Sep 6, 2004 (3rd)
  • Sep 6, 2004 (2nd)
  • Sep 6, 2004
  • Sep 5, 2004
  • Sep 4, 2004 (3rd)
  • Sep 4, 2004 (2nd)
  • Sep 4, 2004
  • Sep 2, 2004
  • Sep 1, 2004 (2nd)
  • Sep 1, 2004
• August 2004
  • Aug 31, 2004 (2nd)
  • Aug 31, 2004
  • Aug 30, 2004
  • Aug 29, 2004 (2nd)
  • Aug 29, 2004
  • Aug 28, 2004 (3rd)
  • Aug 28, 2004 (2nd)
  • Aug 28, 2004
  • Aug 27, 2004 (2nd)
  • Aug 27, 2004
  • Aug 26, 2004 (5th)
  • Aug 26, 2004 (4th)
  • Aug 26, 2004 (3rd)
  • Aug 26, 2004 (2nd)
  • Aug 26, 2004
  • Aug 25, 2004 (5th)
  • Aug 25, 2004 (4th)
  • Aug 25, 2004 (3rd)
  • Aug 25, 2004 (2nd)
  • Aug 25, 2004
  • Aug 24, 2004 (3rd)
  • Aug 24, 2004 (2nd)
  • Aug 24, 2004
  • Aug 23, 2004 (2nd)
  • Aug 23, 2004
  • Aug 22, 2004 (3rd)
  • Aug 22, 2004 (2nd)
  • Aug 22, 2004
  • Aug 21, 2004 (3rd)
  • Aug 21, 2004 (2nd)
  • Aug 21, 2004
  • Aug 20, 2004 (3rd)
  • Aug 20, 2004 (2nd)
  • Aug 20, 2004
  • Aug 19, 2004 (5th)
  • Aug 19, 2004 (4th)
  • Aug 19, 2004 (3rd)
  • Aug 19, 2004 (2nd)
  • Aug 19, 2004
  • Aug 18, 2004 (4th)
  • Aug 18, 2004 (3rd)
  • Aug 18, 2004 (2nd)
  • Aug 18, 2004
  • Aug 17, 2004 (3rd)
  • Aug 17, 2004 (2nd)
  • Aug 17, 2004
  • Aug 16, 2004 (4th)
  • Aug 16, 2004 (3rd)
  • Aug 16, 2004 (2nd)
  • Aug 16, 2004
  • Aug 15, 2004 (4th)
  • Aug 15, 2004 (3rd)
  • Aug 15, 2004 (2nd)
  • Aug 15, 2004
  • Aug 14, 2004 (4th)
  • Aug 14, 2004 (3rd)
  • Aug 14, 2004 (2nd)
  • Aug 14, 2004
  • Aug 13, 2004 (5th)
  • Aug 13, 2004 (4th)
  • Aug 13, 2004 (3rd)
  • Aug 13, 2004 (2nd)
  • Aug 13, 2004
  • Aug 12, 2004 (3rd)
  • Aug 12, 2004 (2nd)
  • Aug 12, 2004
  • Aug 11, 2004 (2nd)
  • Aug 11, 2004
  • Aug 10, 2004
  • Aug 9, 2004 (6th)
  • Aug 9, 2004 (5th)
  • Aug 9, 2004 (4th)
  • Aug 9, 2004 (3rd)
  • Aug 9, 2004 (2nd)
  • Aug 9, 2004
  • Aug 8, 2004
  • Aug 7, 2004 (4th)
  • Aug 7, 2004 (3rd)
  • Aug 7, 2004 (2nd)
  • Aug 7, 2004
  • Aug 6, 2004
  • Aug 5, 2004 (2nd)
  • Aug 5, 2004
  • Aug 4, 2004
  • Aug 3, 2004 (3rd)
  • Aug 3, 2004 (2nd)
  • Aug 3, 2004
  • Aug 2, 2004 (5th)
  • Aug 2, 2004 (4th)
  • Aug 2, 2004 (3rd)
  • Aug 2, 2004 (2nd)
  • Aug 2, 2004
  • Aug 1, 2004 (4th)
  • Aug 1, 2004 (3rd)
  • Aug 1, 2004 (2nd)
  • Aug 1, 2004
• July 2004
• June 2004
• May 2004
• April 2004
• March 2004
• February 2004
• 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.

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>

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.

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