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News and updates, 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.

Primality testing (10^1314+17)/9 [N-1, Brillhart-Lehmer-Selfridge] Calling Brillhart-Lehmer-Selfridge with factored part 33.43% (10^1314+17)/9 is prime! (0.3062s+0.0258s)

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 27, 2004

The list for composite factors of repunit is available in Factorizations of 11...11 (Repunit). It shows that the smallest composite factor of repunit is C141 in 10³⁹⁶+1.

Dec 26, 2004

By Makoto Kamada / GMP-ECM 5.0.3
(35·10¹⁹⁶-53)/9 = 3(8)₁₉₅3_<197> = 3³ · 13 · 84349 · 461651807 · 446380663993523863_<18> · 18926803629417875634761866211_<29> · C135
C135 = P24 · P111
P24 = 908799301214037157739831_<24>
P111 = 370572601126933505818972951766246195700206529887515200446193569195537707291856741066535946708729578200520407957_<111>
(4·10¹⁹⁸-7)/3 = 1(3)₁₉₇1_<199> = C199
C199 = P26 · C173
P26 = 35433614694519093943915021_<26>
C173 = [37629052097232818667461377267500258556528765122464137560967604709699561844372971913230440011564750950923381136673132384892693048327207884015141809874584076051079951831846111_<173>]
(13·10¹⁵⁵-31)/9 = 1(4)₁₅₄1_<156> = 3 · 11 · 3467296306805827_<16> · C139
C139 = P26 · P113
P26 = 53176083389660692023025181_<26>
P113 = 23739939025715336414882807123530767717941537308874831499933776828542756367871245825790200233389506764457581381871_<113>

Dec 25, 2004

By Makoto Kamada / GMP-ECM 5.0.3
10¹⁹¹-3 = (9)₁₉₀7_<191> = 113 · 2454455881_<10> · C180
C180 = P26 · C155
P26 = 13778267355178489115141197_<26>
C155 = [26168071567655827784668613095752679469186561174274715129360764348641252465542696852075271284487059377732452739736751363821922726151257160699482936406081017_<155>]

Dec 24, 2004 (2nd)

msieve 0.88 was released.
Quadratic Sieve Source Code (jasonp)

Dec 24, 2004

By Makoto Kamada / GMP-ECM 5.0.3
(89·10¹⁸⁷+1)/9 = 9(8)₁₈₆9_<188> = 3 · 11 · 2113 · C184
C184 = P26 · P158
P26 = 53436670079527513453372141_<26>
P158 = 26539618343392390368380352055345120368680743940244939749660016224269777920657790101145291847422912050143063087742829198697524309000191824413799439858404431901_<158>
(17·10¹⁸³-71)/9 = 1(8)₁₈₂1_<184>

= 3⁴ · 11 · 19 · 404051 · 1262581 · C168
C168 = P34 · C134
P34 = 8226908102544685947546600578514601_<34>
C134 = [26585389367622980285597634026808282856915211378205220420001757511984116964702632958717990400249729741198964996462743818335851565740519_<134>]

Dec 23, 2004 (3rd)

By Makoto Kamada / GMP-ECM 5.0.3
(65·10¹⁸⁶+43)/9 = 7(2)₁₈₅7_<187> = 3 · 89 · 4679 · 597347347464359_<15> · 1063097615099489_<16> · 48686557186389825347_<20> · C132
C132 = P29 · C104
P29 = 14690759029212971209960298983_<29>
C104 = [12727794571503673891861633135672096636151861671189328309590168102650816980079545459487050908766251834789_<104>]

Dec 23, 2004 (2nd)

By Wataru Sakai / GMP-ECM
(10¹⁶⁹+53)/9 = (1)₁₆₈7_<169> = 7 · 423599701769_<12> · 1052364121297714227371_<22> · C135
C135 = P35 · C101
P35 = 18307918306050479551975785178628311_<35>
C101 = [19449068501458045327500024953679334708298737317275986294768751101310893283329289738705475713907062479_<101>]
(10¹⁹⁵+71)/9 = (1)₁₉₄9_<195> = 7 · 17 · 23 · 2389 · 12658232542072891_<17> · C172
C172 = P32 · C140
P32 = 54775119319789267517672726665291_<32>
C140 = [24508128083609856106882937213433754990235080308233947248497274818116540519436837105107908460599060015366174127469342984467972328959407611243_<140>]

Dec 23, 2004

By Makoto Kamada / GMP-ECM 5.0.3
(7·10¹³⁵+11)/9 = (7)₁₃₄9_<135> = 311557 · 638558070133433464879_<21> · C109
C109 = P26 · P83
P26 = 57239702533873135368356933_<26>
P83 = 68299928839346941052777163320649254834472709556110044073808899477677543549258602821_<83>

Dec 22, 2004

By Makoto Kamada / GMP-ECM 5.0.3
(34·10¹⁹²-43)/9 = 3(7)₁₉₁3_<193> = 31 · 383 · 2817168331182533_<16> · C174
C174 = P30 · C144
P30 = 303858227491837508671753047587_<30>
C144 = [371699641301045371715009397719700819194689634622987190169463978076986750813314250294469112308304309717672733098887774670224422497803703559243331_<144>]

Dec 21, 2004 (3rd)

By Shusuke Kubota / GGNFS-0.72.6 / 9.27 hours on Celeron 2.5GHz
(7·10¹²⁹+11)/9 = (7)₁₂₈9_<129> = 19 · 29² · 2511503 · 108933706067_<12> · C108
C108 = P43 · P65
P43 = 2283988048706725299301369546639948434838543_<43>
P65 = 77896173863502176571577678368953373896208627033496246039633699907_<65>

Dec 21, 2004 (2nd)

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

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

Dec 21, 2004

By Greg Childers / GGNFS
(64·10¹⁴⁹+53)/9 = 7(1)₁₄₈7_<150> = 3⁴ · 11 · 239 · 3140489951628443_<16> · 92248545285620965837_<20> · C110
C110 = P45 · P65
P45 = 227609230400940542986888598100153182950382309_<45>
P65 = 50642490439835718189428667246630220888405040722636658823591995707_<65>
(28·10¹⁴²+17)/9 = 3(1)₁₄₁3_<143> = 3 · 61 · 397 · 929 · 445940406966740321_<18> · C118
C118 = P42 · P76
P42 = 106540935181710634812146198229680364269369_<42>
P76 = 9702080662448933987065740048827096886400601223981574208001722106465596982803_<76>
(28·10¹⁴⁴+17)/9 = 3(1)₁₄₃3_<145> = 31 · 43 · 283 · 511487 · 38231297339_<11> · 14125658889973_<14> · C110
C110 = P46 · P64
P46 = 5863383766003845426545406587677594940597698973_<46>
P64 = 5091998492558949370668423992575290217029909268874571443087414611_<64>
(28·10¹⁴⁶+17)/9 = 3(1)₁₄₅3_<147> = C147
C147 = P45 · P103
P45 = 215042343423248601224429232591047426278759019_<45>
P103 = 1446743493204865942525593959923268509919858672928989291036331355757624848206979381830636837666024790427_<103>
(28·10¹⁴⁷+17)/9 = 3(1)₁₄₆3_<148> = 11 · 29 · 379 · 362767017637_<12> · 4490115412771_<13> · C119
C119 = P55 · P64
P55 = 3379960048529008835409795832584003030196599486272692489_<55>
P64 = 4674000593576153338391447008543295421946203065781538473141212771_<64>
2·10¹³⁸-9 = 1(9)₁₃₇1_<139> = 7 · 1361 · C135
C135 = P65 · P70
P65 = 28067396514726202523860938206489746457258001501485978553895083833_<65>
P70 = 7479485083314129370275849920397548796557371512278764262868303993853001_<70>
2·10¹⁴⁰-9 = 1(9)₁₃₉1_<141> = 17 · 59113 · C135
C135 = P47 · P89
P47 = 11920269538992421121435956097648950019099811559_<47>
P89 = 16695983163826097420159437859577435460952586279369215627290094387500562238589852030582969_<89>
2·10¹⁴⁴-9 = 1(9)₁₄₃1_<145> = 7 · 47 · 1697 · 4751 · 15421121 · 324513125593_<12> · C117
C117 = P57 · P60
P57 = 573979583578236121980436103332418434430645159014685375809_<57>
P60 = 262495926279377751706900324634363777228196866952780943282841_<60>
2·10¹⁴⁶-9 = 1(9)₁₄₅1_<147> = 1471 · 958054117111388133836953_<24> · C120
C120 = P48 · P72
P48 = 248481397786006983813082785705803914377145937759_<48>
P72 = 571127931149896369612391508288727305834841885540092677990337631749027823_<72>
2·10¹⁴⁸-9 = 1(9)₁₄₇1_<149> = 57431787553239244660626976882036073_<35> · C114
C114 = P45 · P70
P45 = 252248599228180796094726301293542573587723903_<45>
P70 = 1380539695291779642420640847677458347322068680428219755758017617145889_<70>
2·10¹⁵⁰-9 = 1(9)₁₄₉1_<151> = 7² · 313 · 5857 · 19249 · 48073 · C134
C134 = P58 · P77
P58 = 2145366910370960233318195778943906318667242154816224697409_<58>
P77 = 11215105892080335130809942373623305706116017816514634296425819268673685145143_<77>
(16·10¹⁴²-61)/9 = 1(7)₁₄₁1_<143> = 13 · 14011 · 168481 · C132
C132 = P49 · P84
P49 = 3563479047113386761119623011481295788624826790313_<49>
P84 = 162569790755232174632253038467971580277889280486954183359029125576276166458052487149_<84>
(16·10¹⁴³-61)/9 = 1(7)₁₄₂1_<144> = 3 · 11 · 541 · 3777559 · 41314201 · 585278303828958603403_<21> · C105
C105 = P46 · P59
P46 = 6781373468336971839816239803424973990462518899_<46>
P59 = 16075909995899462039765753864202879468478273494535100080009_<59>

Dec 20, 2004

GGNFS-0.72.6 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 19, 2004 (4th)

By Wataru Sakai / GMP-ECM
(10¹⁷⁹+71)/9 = (1)₁₇₈9_<179> = 17 · 43 · C176
C176 = P28 · C148
P28 = 9049402502510222344057348417_<28>
C148 = [1679655468607621721991622154551885402806533022303409245104185450719565742097648958717415511161217486545435460473818370679440714209715530546103064797_<148>]
(10¹⁹³+71)/9 = (1)₁₉₂9_<193> = 3 · 83 · 1431244686853_<13> · 4508363445277_<13> · C165
C165 = P31 · C135
P31 = 1413521664942116360011121415991_<31>
C135 = [489241024496907354315699990163522497568807868639472158427158410636880445374402685926600142762794996201973895068523081010022271307068961_<135>]

Dec 19, 2004 (3rd)

GGNFS-0.72.5 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 19, 2004 (2nd)

By Makoto Kamada / GMP-ECM 5.0.3
(65·10¹⁶⁹+43)/9 = 7(2)₁₆₈7_<170> = 7 · 11 · 23 · 68659 · 4321029614939_<13> · C150
C150 = P27 · P123
P27 = 530897822686884962677615417_<27>
P123 = 258914650400347979772352997931146995187006701423208429518294066462041557386591671044316656361151981352276780780439601952161_<123>

Dec 19, 2004

By Sinkiti Sibata / GGNFS-0.70.1 / 56.62 hours
(16·10¹⁴¹-7)/9 = 1(7)_141<142> = 2700157891_<10> · 723675947437300258661473_<24> · C108
C108 = P40 · P69
P40 = 2059716706349518931454333178468365050321_<40>
P69 = 441709442271126037425440816784629391989083973497442626102237114143659_<69>

Dec 18, 2004 (4th)

GGNFS-0.72.4 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 18, 2004 (3rd)

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

Dec 18, 2004 (2nd)

By Greg Childers / GGNFS
(31·10¹⁴⁹-13)/9 = 3(4)₁₄₈3_<150> = 11 · 109 · C147
C147 = P57 · P90
P57 = 460950251520524706530553225277879860588205486095525504899_<57>
P90 = 623226548022901662551202045361712347011223958350429685982315610317292019855843356086236743_<90>
(29·10¹⁴⁰+7)/9 = 3(2)₁₃₉3_<141> = 778202447329343_<15> · 255634545372895486257701_<24> · C103
C103 = P47 · P57
P47 = 14599358663108219697910971266419485362482734451_<47>
P57 = 110945470430273774745793119192113514201471215817716782511_<57>
(29·10¹⁴²+7)/9 = 3(2)₁₄₁3_<143> = 3² · C142
C142 = P47 · P95
P47 = 72676809139323704052905476303361918607632886971_<47>
P95 = 49262577099619249943533650691225341348077300300841245943490622038640278667808424840167507319957_<95>
(29·10¹⁴⁶+7)/9 = 3(2)₁₄₅3_<147> = 17 · 19 · 31 · 251 · 1546424377213905874648018232119_<31> · C110
C110 = P40 · P71
P40 = 4848526173866663057910655329664036964087_<40>
P71 = 17099331001716948283396379468311539628698618084906876523024979878696657_<71>
(29·10¹⁴⁹+7)/9 = 3(2)₁₄₈3_<150> = 11 · 281 · 293 · 1732331 · C138
C138 = P62 · P76
P62 = 42837029641825804525955562286559217176950686548923355753737357_<62>
P76 = 4794448269214011981143749845644741116116001253418507462237430283225763744863_<76>
(29·10¹⁵⁰+7)/9 = 3(2)₁₄₉3_<151> = 97 · 605486638403_<12> · C137
C137 = P43 · P95
P43 = 4679166340772318350732117004005241862927997_<43>
P95 = 11724942082485353843533433020987100707385825600287806825634979780638923301536053795840228051849_<95>
(64·10¹⁴⁸+53)/9 = 7(1)₁₄₇7_<149> = 19 · 29 · 739 · 1396523 · 1479913 · 51349048391867140770561613_<26> · C106
C106 = P43 · P63
P43 = 9967543258841904417522097714798246109082401_<43>
P63 = 165096026422179072094658317382771330545919884412110764726758719_<63>

Dec 18, 2004

By Makoto Kamada / GMP-ECM 5.0.3
(65·10¹⁵⁴+43)/9 = 7(2)₁₅₃7_<155> = 2903 · C152
C152 = P29 · P123
P29 = 39403853043503858648144059421_<29>
P123 = 631371713196639185248714562919354903977906977865731980463798981070349227815458512741230212303393723150149371924035521455529_<123>

Dec 17, 2004 (4th)

By Makoto Kamada / PFGW v1.2 RC1d
(13·10³⁸⁸³+23)/9 = 144...447_<3884> and (13·10³⁸⁸³+41)/9 = 144...449_<3884> are quasi-repdigit twin PRPs. These twin PRPs are the new record of the largest known quasi-repdigit twin PRPs in our tables.

Dec 17, 2004 (3rd)

355...553 (n≤150) was completed.

Dec 17, 2004 (2nd)

By Greg Childers / GGNFS
(32·10¹⁴⁴-23)/9 = 3(5)₁₄₃3_<145> = 383 · 1867 · 32069 · 491186890889_<12> · 601542130669492044017_<21> · C102
C102 = P49 · P54
P49 = 2823771980123860179925775653461357305045257981711_<49>
P54 = 185838853516964345350674982007227448082307037218837519_<54>

Dec 17, 2004

By Makoto Kamada / GMP-ECM 5.0.3
(67·10¹⁹⁹+23)/9 = 7(4)₁₉₈7_<200> = 7 · 11 · 107 · 127 · 28019 · 31477349 · C182
C182 = P30 · P153
P30 = 392167369159626686630550297457_<30>
P153 = 205698836039776681355251012909841390282900437647629545411809050461810170629288834346279937426562252492963093662881506361037147935518256982678931785012097_<153>
(14·10¹⁷⁸-41)/9 = 1(5)₁₇₇1_<179> = 18077 · 970583 · 1735406205257_<13> · 1745824177303_<13> · C144
C144 = P27 · C117
P27 = 390328319148709270682251559_<27>
C117 = [749712543163762808092051180657424884788820203073702176064721437535025801283241160904783569650296980815170595794069349_<117>]

Dec 16, 2004 (3rd)

GGNFS-0.72.3 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Dec 16, 2004 (2nd)

By Greg Childers / GGNFS
(31·10¹³⁸-13)/9 = 3(4)₁₃₇3_<139> = 401 · 12893 · 12796260241_<11> · 32929379212201443533_<20> · C103
C103 = P48 · P55
P48 = 554633079933542031591579522742284342348517448827_<48>
P55 = 2850679897768946559674743117034328399343889356271523721_<55>
(31·10¹³⁹-13)/9 = 3(4)₁₃₈3_<140> = 3² · 11 · 6701 · 21661 · 544650650153_<12> · C118
C118 = P52 · P67
P52 = 2811507313834452114978909949105462027192928332606231_<52>
P67 = 1565339792198947156697525257721137106919198765964637815049851256959_<67>
(31·10¹⁴⁵-13)/9 = 3(4)₁₄₄3_<146> = 3 · 11 · 487 · C142
C142 = P46 · P96
P46 = 6393603290665443480881234946610729026930442627_<46>
P96 = 335220521651667107218263786787058988531447285220162861949338018864065764032755852659552020024879_<96>
(31·10¹⁴⁷-13)/9 = 3(4)₁₄₆3_<148> = 11 · 71 · 479 · 158838667231_<12> · C131
C131 = P55 · P77
P55 = 3725073438097583761450446773397119494749844316356871593_<55>
P77 = 15561145506225560175962989989424633757984940983855470418315679653575452991279_<77>
(32·10¹⁵⁰-23)/9 = 3(5)₁₄₉3_<151> = 2503 · 870363835261_<12> · C136
C136 = P45 · P91
P45 = 194933845780761498493769886876022080930190049_<45>
P91 = 8372565063096327905371943814043884867748842695140487878773556389068879437910468067490768259_<91>
(64·10¹³⁸+53)/9 = 7(1)₁₃₇7_<139> = 13 · 23 · 419 · 97673 · C129
C129 = P61 · P69
P61 = 1052353020314591008868541069764109032283018939271285517954081_<61>
P69 = 552225267501012347389213738145076502574147575051856567905610514951589_<69>
(64·10¹⁴⁴+53)/9 = 7(1)₁₄₃7_<145> = 13² · C143
C143 = P64 · P80
P64 = 3246208754910879163055187223222904457641401288132318036614219281_<64>
P80 = 12962068590155777291886746877946054984585085319160237158221903879170639247980853_<80>
(64·10¹⁵⁰+53)/9 = 7(1)₁₄₉7_<151> = 13 · 17² · 1637 · 2909 · 146161 · 1680823 · C130
C130 = P59 · P71
P59 = 51282266809016720519204373549550234146821081068719639373219_<59>
P71 = 31548823397773504003120507136102584888224633364181214122391057893172301_<71>

Dec 16, 2004

By Wataru Sakai / GMP-ECM
(10¹⁶⁰+53)/9 = (1)₁₅₉7_<160> = 19 · 197753 · C153
C153 = P29 · P124
P29 = 32153282272391582463785808433_<29>
P124 = 9197197143541566352036992011167749604031684102841422515193498657056297262146411381413519532306022893669673640065317970473607_<124>

Dec 15, 2004 (5th)

By Makoto Kamada / GMP-ECM 5.0.3
(83·10¹⁹⁵+61)/9 = 9(2)₁₉₄9_<196> = 11 · 307 · 311 · C190
C190 = P31 · C160
P31 = 4833547434892721567340970805149_<31>
C160 = [1816678800589205850678424867940972226068049860751790110242961033905951362648474454003602444521902168474105268092631266292494058628857653685711600584129938854943_<160>]

Dec 15, 2004 (4th)

By Greg Childers / GGNFS-0.70.0, GGNFS-0.71.7 / 303 hours (12 days and 15 hours)
(16·10¹⁷⁵-1)/3 = 5(3)_175<176> = C176
C176 = P43 · P134
P43 = 3809865316728652188521021727126618149052923_<43>
P134 = 13998745073520892175014741138026536702111802636628910125487741607654260812520248593507784157795562918507819534511398477530470887314671_<134>

Even though the factor was unfortunately smaller than our hopes, this is the new record of the largest number factored by GGNFS in our tables. Congratulations!

ggnfs.log (edited because of GGNFS problems)[11/23 13:52:13] GGNFS-0.70.0 : makefb [11/23 13:52:38] name: snfs [11/23 13:52:38] n=53333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 (176 digits) [11/23 13:52:38] c0: -1 [11/23 13:52:38] c1: 0 [11/23 13:52:38] c2: 0 [11/23 13:52:38] c3: 0 [11/23 13:52:38] c4: 0 [11/23 13:52:38] c5: 16 [11/23 13:52:38] RFBsize: 751131 (upto 11399989) [11/23 13:52:38] AFBsize: 751173 (upto 11399989) [11/23 13:52:38] maxNumLargeRatPrimes: 3 [11/23 13:52:38] maxLargeRatPrime: 536870912 [11/23 13:52:38] maxNumLargeAlgPrimes: 3 [11/23 13:52:38] maxLargeAlgPrime: 536870912 LatSieveTime: 35763 [11/23 23:48:42] GGNFS-0.70.0 : procrels [11/23 23:53:19] There were 10141/462316 duplicates. [11/23 23:53:19] RelProcTime: 274.3 [11/23 23:53:22] largePrimes: 633678 , relations: 452175 [11/23 23:53:22] reduceRelSets dropped relation-set weight from 32807 to 32807. [11/23 23:53:22] rels:452175, initialFF:0, finalFF:31746 LatSieveTime: 38014 [11/24 10:26:59] GGNFS-0.70.0 : procrels [11/24 10:31:10] There were 21488/551619 duplicates. [11/24 10:31:10] RelProcTime: 247.5 [11/24 10:31:25] largePrimes: 1367170 , relations: 982306 [11/24 10:31:26] reduceRelSets dropped relation-set weight from 74243 to 74243. [11/24 10:31:26] rels:982306, initialFF:0, finalFF:69389 LatSieveTime: 34816 [11/24 20:11:46] GGNFS-0.70.0 : procrels [11/24 20:16:15] There were 28396/579622 duplicates. [11/24 20:16:15] RelProcTime: 251.3 [11/24 20:16:35] largePrimes: 2115734 , relations: 1533532 [11/24 20:16:36] reduceRelSets dropped relation-set weight from 121647 to 121647. [11/24 20:16:36] rels:1533532, initialFF:0, finalFF:109645 LatSieveTime: 37617 [11/25 06:43:38] GGNFS-0.70.0 : procrels [11/25 06:48:24] There were 34592/600484 duplicates. [11/25 06:48:24] RelProcTime: 281.3 [11/25 06:48:52] largePrimes: 2868100 , relations: 2099424 [11/25 06:48:53] reduceRelSets dropped relation-set weight from 174937 to 174937. [11/25 06:48:53] rels:2099424, initialFF:0, finalFF:152509 LatSieveTime: 35298 [11/25 16:37:13] GGNFS-0.70.0 : procrels [11/25 16:42:19] There were 38913/610713 duplicates. [11/25 16:42:19] RelProcTime: 302.9 [11/25 16:42:57] largePrimes: 3610813 , relations: 2671224 [11/25 16:42:59] reduceRelSets dropped relation-set weight from 233492 to 233492. [11/25 16:42:59] rels:2671224, initialFF:0, finalFF:197261 LatSieveTime: 37999 [11/26 03:16:29] GGNFS-0.70.0 : procrels [11/26 03:25:17] There were 42098/622620 duplicates. [11/26 03:25:17] RelProcTime: 494.8 [11/26 03:28:15] largePrimes: 4347528 , relations: 3251746 [11/26 03:28:20] reduceRelSets dropped relation-set weight from 298019 to 298019. [11/26 03:28:20] rels:3251746, initialFF:0, finalFF:244258 LatSieveTime: 35275 [11/26 13:16:23] GGNFS-0.70.0 : procrels [11/26 13:22:57] There were 44884/625667 duplicates. [11/26 13:22:57] RelProcTime: 357.8 [11/26 13:23:52] largePrimes: 5066237 , relations: 3832529 [11/26 13:23:55] reduceRelSets dropped relation-set weight from 368361 to 368361. [11/26 13:23:55] rels:3832529, initialFF:0, finalFF:293080 LatSieveTime: 34869 [11/26 23:05:06] GGNFS-0.70.0 : procrels [11/26 23:11:33] There were 47083/624374 duplicates. [11/26 23:11:33] RelProcTime: 383.7 [11/26 23:12:36] largePrimes: 5764445 , relations: 4409820 [11/26 23:12:41] reduceRelSets dropped relation-set weight from 444664 to 444664. [11/26 23:12:41] rels:4409820, initialFF:0, finalFF:343566 LatSieveTime: 37541 [11/27 09:38:25] GGNFS-0.70.0 : procrels [11/27 09:45:17] There were 49129/624199 duplicates. [11/27 09:45:17] RelProcTime: 408.9 [11/27 09:46:36] largePrimes: 6443200 , relations: 4984890 [11/27 09:46:41] reduceRelSets dropped relation-set weight from 526591 to 526591. [11/27 09:46:41] rels:4984890, initialFF:0, finalFF:395558 LatSieveTime: 34998 [11/27 19:30:02] GGNFS-0.70.0 : procrels [11/27 19:37:23] There were 51084/625667 duplicates. [11/27 19:37:23] RelProcTime: 438.3 [11/27 19:38:45] largePrimes: 7105504 , relations: 5559473 [11/27 19:38:52] reduceRelSets dropped relation-set weight from 615820 to 615820. [11/27 19:38:52] rels:5559473, initialFF:0, finalFF:449902 LatSieveTime: 38202 [11/28 06:15:37] GGNFS-0.70.0 : procrels [11/28 06:23:36] There were 53658/634531 duplicates. [11/28 06:23:36] RelProcTime: 476.4 [11/28 06:25:15] largePrimes: 7758744 , relations: 6140346 [11/28 06:25:23] reduceRelSets dropped relation-set weight from 715106 to 715106. [11/28 06:25:23] rels:6140346, initialFF:0, finalFF:507490 LatSieveTime: 35805 [11/28 16:22:12] GGNFS-0.70.0 : procrels [11/28 16:30:36] There were 55585/639246 duplicates. [11/28 16:30:36] RelProcTime: 500.9 [11/28 16:32:24] largePrimes: 8400501 , relations: 6724007 [11/28 16:32:34] reduceRelSets dropped relation-set weight from 823545 to 823545. [11/28 16:32:34] rels:6724007, initialFF:0, finalFF:567738 LatSieveTime: 15939 [11/28 22:26:36] GGNFS-0.70.0 : procrels [11/28 22:31:51] There were 16027/333645 duplicates. [11/28 22:31:51] RelProcTime: 223.7 [11/28 22:33:55] largePrimes: 8752058 , relations: 7041624 [11/28 22:34:07] reduceRelSets dropped relation-set weight from 898498 to 898498. [11/28 22:34:07] rels:7041624, initialFF:0, finalFF:594868 LatSieveTime: 18088 [11/29 03:35:40] GGNFS-0.70.0 : procrels [11/29 03:42:48] There were 8262/235963 duplicates. [11/29 03:42:48] RelProcTime: 416.1 [11/29 03:51:41] largePrimes: 9003464 , relations: 7269325 [11/29 03:51:54] reduceRelSets dropped relation-set weight from 958277 to 958277. [11/29 03:51:54] rels:7269325, initialFF:0, finalFF:613004 LatSieveTime: 15673 [11/29 08:13:14] GGNFS-0.70.0 : procrels [11/29 08:16:06] There were 8488/239389 duplicates. [11/29 08:16:06] RelProcTime: 170.7 [11/29 08:18:04] largePrimes: 9256309 , relations: 7500226 [11/29 08:18:18] reduceRelSets dropped relation-set weight from 1023363 to 1023362. [11/29 08:18:18] rels:7500226, initialFF:0, finalFF:632194 LatSieveTime: 15686 [11/29 12:39:47] GGNFS-0.70.0 : procrels [11/29 12:43:07] There were 8545/235835 duplicates. [11/29 12:43:07] RelProcTime: 198.8 [11/29 12:45:17] largePrimes: 9501329 , relations: 7727516 [11/29 12:45:33] reduceRelSets dropped relation-set weight from 1091956 to 1091955. [11/29 12:45:33] rels:7727516, initialFF:0, finalFF:652042 LatSieveTime: 16831 [11/29 17:26:07] GGNFS-0.70.0 : procrels [11/29 17:32:30] There were 8564/234252 duplicates. [11/29 17:32:30] RelProcTime: 382.2 [11/29 17:34:41] largePrimes: 9742992 , relations: 7953204 [11/29 17:34:57] reduceRelSets dropped relation-set weight from 1163127 to 1163126. [11/29 17:34:57] rels:7953204, initialFF:0, finalFF:672151 LatSieveTime: 15909 [11/29 22:00:09] GGNFS-0.70.0 : procrels [11/29 22:03:08] There were 8750/234721 duplicates. [11/29 22:03:08] RelProcTime: 178.6 [11/29 22:05:19] largePrimes: 9982336 , relations: 8179175 [11/29 22:05:36] reduceRelSets dropped relation-set weight from 1238436 to 1238435. [11/29 22:05:36] rels:8179175, initialFF:0, finalFF:693137 LatSieveTime: 17930 [11/30 03:04:29] GGNFS-0.70.0 : procrels [11/30 03:13:35] There were 8930/230791 duplicates. [11/30 03:13:35] RelProcTime: 534.2 [11/30 03:24:11] largePrimes: 10215057 , relations: 8401036 [11/30 03:24:25] reduceRelSets dropped relation-set weight from 1315590 to 1315589. [11/30 03:24:26] rels:8401036, initialFF:0, finalFF:714222 LatSieveTime: 15918 [11/30 07:49:51] GGNFS-0.70.0 : procrels [11/30 07:52:52] There were 9539/239721 duplicates. [11/30 07:52:52] RelProcTime: 180.2 [11/30 07:55:10] largePrimes: 10453620 , relations: 8631218 [11/30 07:55:25] reduceRelSets dropped relation-set weight from 1399679 to 1399671. [11/30 07:55:25] rels:8631218, initialFF:0, finalFF:736754 LatSieveTime: 15263 [11/30 12:09:52] GGNFS-0.70.0 : procrels [11/30 12:12:53] There were 9146/230291 duplicates. [11/30 12:12:53] RelProcTime: 180.7 [11/30 12:15:16] largePrimes: 10681393 , relations: 8852363 [11/30 12:15:33] reduceRelSets dropped relation-set weight from 1485330 to 1485300. [11/30 12:15:33] rels:8852363, initialFF:0, finalFF:759300 LatSieveTime: 16603 [11/30 16:52:20] GGNFS-0.70.0 : procrels [11/30 16:55:43] There were 9593/232143 duplicates. [11/30 16:55:43] RelProcTime: 200.6 [11/30 16:58:27] largePrimes: 10907631 , relations: 9074913 [11/30 16:58:48] reduceRelSets dropped relation-set weight from 1575637 to 1575598. [11/30 16:58:48] rels:9074913, initialFF:0, finalFF:782612 LatSieveTime: 16006 [11/30 21:25:37] GGNFS-0.70.0 : procrels [11/30 21:28:48] There were 9561/231338 duplicates. [11/30 21:28:48] RelProcTime: 190.7 [11/30 21:31:23] largePrimes: 11131848 , relations: 9296690 [11/30 21:31:42] reduceRelSets dropped relation-set weight from 1668747 to 1668695. [11/30 21:31:42] rels:9296690, initialFF:0, finalFF:806396 LatSieveTime: 18411 [12/01 02:38:37] GGNFS-0.70.0 : procrels [12/01 02:41:57] There were 9925/235063 duplicates. [12/01 02:41:57] RelProcTime: 197.7 [12/01 02:44:43] largePrimes: 11356498 , relations: 9521828 [12/01 02:45:06] reduceRelSets dropped relation-set weight from 1768513 to 1768444. [12/01 02:45:06] rels:9521828, initialFF:0, finalFF:831270 LatSieveTime: 15513 [12/01 07:03:43] GGNFS-0.70.0 : procrels [12/01 07:07:01] There were 10112/232186 duplicates. [12/01 07:07:01] RelProcTime: 197.3 [12/01 07:09:46] largePrimes: 11576617 , relations: 9743902 [12/01 07:10:07] reduceRelSets dropped relation-set weight from 1871179 to 1871096. [12/01 07:10:08] rels:9743902, initialFF:0, finalFF:856509 LatSieveTime: 16904 [12/01 11:51:57] GGNFS-0.70.0 : procrels [12/01 11:58:54] There were 10487/234815 duplicates. [12/01 11:58:55] RelProcTime: 289.3 [12/01 12:07:40] largePrimes: 11796464 , relations: 9968230 [12/01 12:09:14] reduceRelSets dropped relation-set weight from 1979490 to 1979423. [12/01 12:09:14] rels:9968230, initialFF:0, finalFF:882943 LatSieveTime: 15738 [12/01 16:31:36] GGNFS-0.70.0 : procrels [12/01 16:35:11] There were 10595/232597 duplicates. [12/01 16:35:11] RelProcTime: 214.9 [12/01 16:38:27] largePrimes: 12012081 , relations: 10190232 [12/01 16:38:50] reduceRelSets dropped relation-set weight from 2091865 to 2091557. [12/01 16:38:50] rels:10190232, initialFF:0, finalFF:909780 LatSieveTime: 15849 [12/01 21:03:03] GGNFS-0.70.0 : procrels [12/01 21:06:35] There were 10579/231759 duplicates. [12/01 21:06:35] RelProcTime: 211.7 [12/01 21:09:57] largePrimes: 12224466 , relations: 10411412 [12/01 21:10:21] reduceRelSets dropped relation-set weight from 2207637 to 2207210. [12/01 21:10:21] rels:10411412, initialFF:0, finalFF:937211 LatSieveTime: 18291 [12/02 02:15:16] GGNFS-0.70.0 : procrels [12/02 02:18:58] There were 10608/230396 duplicates. [12/02 02:18:58] RelProcTime: 218.6 [12/02 02:22:26] largePrimes: 12434530 , relations: 10631200 [12/02 02:22:52] reduceRelSets dropped relation-set weight from 2326522 to 2325901. [12/02 02:22:52] rels:10631200, initialFF:0, finalFF:964946 LatSieveTime: 15731 [12/02 06:45:09] GGNFS-0.70.0 : procrels [12/02 06:48:45] There were 11114/232152 duplicates. [12/02 06:48:46] RelProcTime: 216.4 [12/02 06:52:23] largePrimes: 12643680 , relations: 10852238 [12/02 06:52:51] reduceRelSets dropped relation-set weight from 2452438 to 2451757. [12/02 06:52:51] rels:10852238, initialFF:0, finalFF:994044 LatSieveTime: 15271 [12/02 11:07:26] GGNFS-0.70.0 : procrels [12/02 11:11:05] There were 10927/225327 duplicates. [12/02 11:11:05] RelProcTime: 218.2 [12/02 11:14:48] largePrimes: 12844313 , relations: 11066638 [12/02 11:15:21] reduceRelSets dropped relation-set weight from 2578246 to 2576939. [12/02 11:15:21] rels:11066638, initialFF:0, finalFF:1022502 LatSieveTime: 15483 [12/02 15:33:27] GGNFS-0.70.0 : procrels [12/02 15:37:11] There were 11092/225788 duplicates. [12/02 15:37:11] RelProcTime: 223.4 [12/02 15:40:56] largePrimes: 13043965 , relations: 11281334 [12/02 15:41:30] reduceRelSets dropped relation-set weight from 2709969 to 2708358. [12/02 15:41:30] rels:11281334, initialFF:0, finalFF:1051960 LatSieveTime: 16128 [12/02 20:10:22] GGNFS-0.70.0 : procrels [12/02 20:14:06] There were 11366/228972 duplicates. [12/02 20:14:06] RelProcTime: 223.5 [12/02 20:18:00] largePrimes: 13244537 , relations: 11498940 [12/02 20:18:36] reduceRelSets dropped relation-set weight from 2848876 to 2846194. [12/02 20:18:36] rels:11498940, initialFF:0, finalFF:1082590 LatSieveTime: 18425 [12/03 01:25:45] GGNFS-0.70.0 : procrels [12/03 01:29:37] There were 11636/230056 duplicates. [12/03 01:29:37] RelProcTime: 229.9 [12/03 01:33:43] largePrimes: 13444481 , relations: 11717360 [12/03 01:34:27] reduceRelSets dropped relation-set weight from 2992092 to 2988600. [12/03 01:34:27] rels:11717360, initialFF:0, finalFF:1113766 LatSieveTime: 15326 [12/03 05:49:57] GGNFS-0.70.0 : procrels [12/03 05:53:41] There were 11555/224036 duplicates. [12/03 05:53:41] RelProcTime: 223.7 [12/03 05:57:57] largePrimes: 13636912 , relations: 11929841 [12/03 05:58:35] reduceRelSets dropped relation-set weight from 3136950 to 3132879. [12/03 05:58:35] rels:11929841, initialFF:0, finalFF:1145098 LatSieveTime: 16011 [12/03 10:25:29] GGNFS-0.70.0 : procrels [12/03 10:29:20] There were 12248/234010 duplicates. [12/03 10:29:20] RelProcTime: 230.5 [12/03 10:33:29] largePrimes: 13836056 , relations: 12151603 [12/03 10:34:09] reduceRelSets dropped relation-set weight from 3294208 to 3290036. [12/03 10:34:09] rels:12151603, initialFF:0, finalFF:1178843 LatSieveTime: 16102 [12/03 15:02:34] GGNFS-0.70.0 : procrels [12/03 15:06:32] There were 12121/230190 duplicates. [12/03 15:06:32] RelProcTime: 237.3 [12/03 15:10:46] largePrimes: 14029999 , relations: 12369672 [12/03 15:11:30] reduceRelSets dropped relation-set weight from 3454479 to 3449089. [12/03 15:11:30] rels:12369672, initialFF:0, finalFF:1212783 LatSieveTime: 15276 [12/03 19:26:12] GGNFS-0.70.0 : procrels [12/03 19:30:05] There were 11633/219421 duplicates. [12/03 19:30:05] RelProcTime: 232.3 [12/03 19:34:28] largePrimes: 14214114 , relations: 12577460 [12/03 19:35:15] reduceRelSets dropped relation-set weight from 3612809 to 3605178. [12/03 19:35:15] rels:12577460, initialFF:0, finalFF:1245483 LatSieveTime: 15178 [12/03 23:48:16] GGNFS-0.70.0 : procrels [12/03 23:52:14] There were 11858/220278 duplicates. [12/03 23:52:14] RelProcTime: 237.3 [12/03 23:56:40] largePrimes: 14397110 , relations: 12785880 [12/03 23:57:29] reduceRelSets dropped relation-set weight from 3775133 to 3765795. [12/03 23:57:29] rels:12785880, initialFF:0, finalFF:1279004 LatSieveTime: 18225 [12/04 05:01:19] GGNFS-0.70.0 : procrels [12/04 05:05:20] There were 12282/223248 duplicates. [12/04 05:05:20] RelProcTime: 240.0 [12/04 05:09:52] largePrimes: 14580559 , relations: 12996846 [12/04 05:10:46] reduceRelSets dropped relation-set weight from 3945548 to 3935357. [12/04 05:10:46] rels:12996846, initialFF:0, finalFF:1313921 LatSieveTime: 15434 [12/04 09:28:04] GGNFS-0.70.0 : procrels [12/04 09:36:52] There were 12097/220677 duplicates. [12/04 09:36:52] RelProcTime: 263.1 [12/04 09:42:38] largePrimes: 14760972 , relations: 13205426 [12/04 09:43:34] reduceRelSets dropped relation-set weight from 4115846 to 4105184. [12/04 09:43:34] rels:13205426, initialFF:0, finalFF:1348784 LatSieveTime: 15785 [12/04 14:06:42] GGNFS-0.70.0 : procrels [12/04 14:11:09] There were 12602/227926 duplicates. [12/04 14:11:09] RelProcTime: 266.2 [12/04 14:16:48] largePrimes: 14945744 , relations: 13420750 [12/04 14:17:46] reduceRelSets dropped relation-set weight from 4299857 to 4286490. [12/04 14:17:47] rels:13420750, initialFF:0, finalFF:1385476 LatSieveTime: 15349 [12/04 18:33:42] GGNFS-0.70.0 : procrels [12/04 18:38:11] There were 12570/221067 duplicates. [12/04 18:38:11] RelProcTime: 267.9 [12/04 18:43:51] largePrimes: 15123370 , relations: 13629247 [12/04 18:44:59] reduceRelSets dropped relation-set weight from 4480104 to 4465840. [12/04 18:44:59] rels:13629247, initialFF:0, finalFF:1421952 LatSieveTime: 15363 [12/04 23:01:05] GGNFS-0.70.0 : procrels [12/04 23:05:49] There were 12779/220704 duplicates. [12/04 23:05:49] RelProcTime: 283.8 [12/04 23:11:37] largePrimes: 15299043 , relations: 13837172 [12/04 23:12:40] reduceRelSets dropped relation-set weight from 4666009 to 4650467. [12/04 23:12:40] rels:13837172, initialFF:0, finalFF:1458975 LatSieveTime: 18118 [12/05 04:14:42] GGNFS-0.70.0 : procrels [12/05 04:19:20] There were 12837/220759 duplicates. [12/05 04:19:20] RelProcTime: 276.3 [12/05 04:25:22] largePrimes: 15473353 , relations: 14045094 [12/05 04:26:37] reduceRelSets dropped relation-set weight from 4857381 to 4839907. [12/05 04:26:37] rels:14045094, initialFF:0, finalFF:1496836 LatSieveTime: 15440 [12/05 08:44:02] GGNFS-0.70.0 : procrels [12/05 08:48:40] There were 12834/220193 duplicates. [12/05 08:48:40] RelProcTime: 277.5 [12/05 08:54:35] largePrimes: 15646132 , relations: 14252453 [12/05 08:55:48] reduceRelSets dropped relation-set weight from 5054621 to 5032363. [12/05 09:02:22] rels:14252453, initialFF:0, finalFF:1535134 [12/05 09:02:22] depinf file written. Run matsolve. LatSieveTime: 15444 [12/05 13:19:55] GGNFS-0.70.0 : procrels [12/05 13:24:30] There were 13089/219069 duplicates. [12/05 13:24:30] RelProcTime: 274.8 [12/05 13:30:33] largePrimes: 15816589 , relations: 14458433 [12/05 13:31:49] reduceRelSets dropped relation-set weight from 5258364 to 5233514. [12/05 13:38:22] rels:14458433, initialFF:0, finalFF:1574218 [12/05 13:38:22] depinf file written. Run matsolve. LatSieveTime: 15222 [12/05 17:52:13] GGNFS-0.70.0 : procrels [12/05 17:56:52] There were 12979/215925 duplicates. [12/05 17:56:52] RelProcTime: 278.4 [12/05 18:03:10] largePrimes: 15983252 , relations: 14661379 [12/05 18:04:27] reduceRelSets dropped relation-set weight from 5465174 to 5434200. [12/05 18:11:18] rels:14661379, initialFF:0, finalFF:1613288 [12/05 18:11:18] depinf file written. Run matsolve. LatSieveTime: 15255 [12/05 22:25:40] GGNFS-0.70.0 : procrels [12/05 22:30:19] There were 13081/216392 duplicates. [12/05 22:30:19] RelProcTime: 277.4 [12/05 22:36:32] largePrimes: 16149465 , relations: 14864690 [12/05 22:37:54] reduceRelSets dropped relation-set weight from 5672938 to 5640767. [12/05 22:45:29] rels:14864690, initialFF:0, finalFF:1653042 [12/05 22:45:29] depinf file written. Run matsolve. ... snip while problems are solved ... [12/14 06:46:41] GGNFS-0.71.7 : matsolve [12/14 06:46:49] Pruning matrix with wt=0.250 [12/14 06:46:49] Initial matrix is 1003962 x 1172266 with sparse part having weight 89183263. [12/14 06:46:49] (total weight is 152592774) [12/14 06:57:57] Matrix pruned to 932322 x 1032323 with weight 67286075. [12/14 18:22:28] BLanczosTime: 41071.3 [12/14 18:22:28] GGNFS-0.71.7 : sqrt [12/14 18:22:30] bmultiplier=8 [12/14 18:34:36] From dependence 0, sqrt obtained: [12/14 18:34:36] r1=3809865316728652188521021727126618149052923 (pp43) [12/14 18:34:36] r2=13998745073520892175014741138026536702111802636628910125487741607654260812520248593507784157795562918507819534511398477530470887314671 (pp134) [12/14 18:34:36] (pp=probable prime, c=composite) [12/14 18:34:36] sqrtTime: 727.3

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>]