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STUDIO KAMADA

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News and updates, August 2004

Aug 31, 2004 (2nd)

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

Aug 31, 2004

By Greg Childers / GGNFS
(5·10¹⁴⁴-23)/9 = 55...553_<144> = 3155473 · C138
C138 = P61 · P77
P61 = 3457898337391254117443536803587089986426888551811788124829981_<61>
P77 = 50915592927019281212453401230452149699776576675503934503083410807471594464581_<77>
(5·10¹⁵⁰-23)/9 = 55...553_<150> = 3124063013_<10> · C141
C141 = P34 · P108
P34 = 1261351634852468232589667781970541_<34>
P108 = 140984554188332077855633489967688233437420652572411041963485055154719514641574805797228505081879605516177441_<108>

Aug 30, 2004

By Wataru Sakai / GMP-ECM
(5·10¹³⁶+31)/9 = 55...559_<136> = 3² · 19 · 14621 · 18405487608033979_<17> · C114
C114 = P29 · P85
P29 = 22941531353226945978587822711_<29>
P85 = 5262408723788222083958932368465628124821942929809754825892965345331732331829246044221_<85>
(88·10¹²⁵-7)/9 = 977...77_<126> = 103 · 1104638413_<10> · 783570542195239159_<18> · C98
C98 = P33 · P65
P33 = 583194596093677893676999249215487_<33>
P65 = 18805773661709255464759023344806978999117917846849495140292588971_<65>
(88·10¹³⁴-7)/9 = 977...77_<135> = 109 · 2269471297_<10> · 279911946799_<12> · 856899311599_<12> · C101
C101 = P26 · P75
P26 = 49976932281996619715258291_<26>
P75 = 329737352937526175571243655849882152236634405766781729375262653015197094839_<75>

Aug 29, 2004 (2nd)

By Greg Childers / GGNFS
(5·10¹⁴³-23)/9 = 55...553_<143> = 587 · 5969437 · 363320389 · C125
C125 = P41 · P84
P41 = 96315368735175588476997855956059367718617_<41>
P84 = 453075583452401617266699849132802617393128642784210542825421600112582684159010445899_<84>

Aug 29, 2004

By Makoto Kamada / PFGW
10²⁶⁷¹⁸-10⁸⁹⁰⁶-1 is near-repdigit prime. (26718 digits)
10³⁰⁵⁰⁴-10¹⁰¹⁶⁸-1 is near-repdigit prime. (30504 digits)

Aug 28, 2004 (3rd)

By Naoki Yamamoto / GMP-ECM, PPSIQS 1.1
(4·10¹³⁹-13)/9 = 44...443_<139> = 3 · 347 · 9066214008695924081_<19> · C117
C117 = P35 · P39 · P43
P35 = 62758738670313835736654307681801469_<35>
P39 = 860577449091221010153116454199427374951_<39>
P43 = 8719199566569262614948284612004217364358257_<43>

Aug 28, 2004 (2nd)

By Greg Childers / GGNFS
(5·10¹⁴²-23)/9 = 55...553_<142> = 3 · 17 · C141
C141 = P50 · P91
P50 = 67446337988576193814235887298581645667909842134703_<50>
P91 = 1615098241391384562749769450064252517974558843846458794999503329618544609394159962629906901_<91>

Aug 28, 2004

By Sander Hoogendoorn / GGNFS
(34·10¹²¹-7)/9 = 377...77_<122> = 37 · 59 · C119
C119 = P43 · P76
P43 = 2885175855914863701516781901606315598600683_<43>
P76 = 5998054156309717055110960940861832877646996441285735446346101979722675862293_<76>

Aug 27, 2004 (2nd)

Factor table of 122...223 is available.

Aug 27, 2004

By Greg Childers / GGNFS
(5·10¹³³-23)/9 = 55...553_<133> = 3 · 73 · 79 · 199 · 1505173 · C121
C121 = P44 · P77
P44 = 46723373906581656680817154017202356736601543_<44>
P77 = 22944711285892422900279830474026033242608228109256425452324948591607523522873_<77>
(5·10¹⁴¹-23)/9 = 55...553_<141> = 7 · 73 · 747982158741485693_<18> · C121
C121 = P55 · P66
P55 = 2337328675718309158903020591142384471616803828915676963_<55>
P66 = 621864218337745482757167500083886259558150403580690738504658519097_<66>

Aug 26, 2004 (5th)

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

Aug 26, 2004 (4th)

By Chris Monico / GGNFS
2·10¹³²-1 = 199...99_<133> = 383 · 6784703 · 40846423 · 295764098205281929_<18> · C98
C98 = P36 · P63
P36 = 157992194582767457565322208346460391_<36>
P63 = 403241538412822815665069568615264515364295352454530261564930183_<63>

Aug 26, 2004 (3rd)

By Wataru Sakai / GMP-ECM
(34·10¹³⁷-7)/9 = 377...77_<138> = 50406390252637_<14> · C124
C124 = P32 · C93
P32 = 34685456789003348824526610617033_<32>
C93 = [216074437871417469140229483512985570728754485831228584104580782638769496740849010032758535037_<93>]

Aug 26, 2004 (2nd)

By Greg Childers / GGNFS
(7·10¹¹⁸-61)/9 = 77...771_<118> = 3217 · 25297654516081_<14> · C101
C101 = P38 · P64
P38 = 15532685161648299645436808908256508059_<38>
P64 = 6152869061347022773120137671779564447700348458674270239224253297_<64>
(7·10¹²⁴-61)/9 = 77...771_<124> = 23 · 148573 · C118
C118 = P37 · P82
P37 = 1729703780752569274687317509531141257_<37>
P82 = 1315879336314025102410131461657237752084658495968833748838537800733316050062033257_<82>
(5·10¹²⁷-23)/9 = 55...553_<127> = 3 · 177544559 · C119
C119 = P53 · P66
P53 = 57735393220072586184214785431113466220986058930404477_<53>
P66 = 180657811404142454615368294277776931300547360361648960048421496457_<66>
(5·10¹³⁰-23)/9 = 55...553_<130> = 3³ · 4049 · 57753354473_<11> · C114
C114 = P38 · P77
P38 = 19960569960792207752495397053020759637_<38>
P77 = 44082457912202275382610636840555331907749721721065039824037003201618677031711_<77>

Aug 26, 2004

By Sander Hoogendoorn / GGNFS
3·10¹³⁰-1 = 299...99_<131> = C131
C131 = P42 · P90
P42 = 176410843726584853883407743387462128062837_<42>
P90 = 170057573368314684049302929168844425493413216950195208787238174395441995530703625941928227_<90>

Aug 25, 2004 (5th)

By Wataru Sakai / GMP-ECM
(5·10¹⁴⁷+31)/9 = 55...559_<147> = 13 · 29 · 129119 · 8232703 · 4452154780181895301_<19> · C114
C114 = P28 · C87
P28 = 1479486472724455175482176443_<28>
C87 = [210461319855963603918690047463997122821686720568503127833902340218293951960145917799017_<87>]

Aug 25, 2004 (4th)

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

Aug 25, 2004 (3rd)

By Naoki Yamamoto / GMP-ECM
(4·10¹³³-13)/9 = 44...443_<133> = 3² · 881 · C129
C129 = P32 · C97
P32 = 88443650427428754868785226431323_<32>
C97 = [6337710609168435045816071777774001848170814820004013594434185050821845551425814831622495237307529_<97>]

Aug 25, 2004 (2nd)

By Greg Childers / GGNFS
(2·10¹⁵⁰+43)/9 = 22...227_<150> = 3671 · C146
C146 = P42 · P105
P42 = 157565285946882496580150516924132711926663_<42>
P105 = 384186906691672283239484922312826833955667843655411472913536560158364186826432903253690140355517421267699_<105>
(5·10¹²⁶-23)/9 = 55...553_<126> = 17 · 2423 · C122
C122 = P60 · P62
P60 = 699371641821031509426181243514691610033944032212980992934229_<60>
P62 = 19284888882897143716756472125298651081954215492789755961542427_<62>

Aug 25, 2004

By Sander Hoogendoorn / GGNFS
3·10¹²⁵-1 = 299...99_<126> = 7 · 3599650081_<10> · 31612646761_<11> · C105
C105 = P46 · P59
P46 = 3876544332029444008036492867365402990466431683_<46>
P59 = 97153246083586305759374376504412500632762391535023918322219_<59>

Aug 24, 2004 (3rd)

By Sander Hoogendoorn
(55·10²⁷⁷⁹-1)/9 is prime.

Aug 24, 2004 (2nd)

GGNFS 0.53.3 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Aug 24, 2004

By Sander Hoogendoorn / GGNFS 0.53.0 with getdeps 0.50.2-k1
5·10¹³³-1 = 499...99_<134> = 7 · 71 · 219487417057_<12> · 2348810983951_<13> · C108
C108 = P38 · P71
P38 = 15643468407459141953163921151000061497_<38>
P71 = 12474492012328826373816556204599871102049686859053368900342040470592073_<71>

Aug 23, 2004 (2nd)

Condition of the sequence 10ⁿ-3 = { 7, 97, 997, 9997, 99997, ... } was extended to n≤150.
Following numbers were not factorized. These numbers might have small factors. You should run GMP-ECM (B1≥1000000) first.
n= 141, 146, 147, 148, 149, (5/150)

Aug 23, 2004

By Greg Childers / GGNFS 0.53.2
(2·10¹⁴⁶+43)/9 = 22...227_<146> = 3² · 29 · C143
C143 = P43 · P101
P43 = 3364565907180457097034187412279371804597387_<43>
P101 = 25305675747513146684875882899371352586297206368096475611848955976490346440281246471121840525358003461_<101>

Aug 22, 2004 (3rd)

By Naoki Yamamoto / GGNFS 0.50.2
(4·10¹²⁸-13)/9 = 44...443_<128> = 23 · 43 · 512412863 · C116
C116 = P51 · P66
P51 = 333206455823654062100588260759434130906808772074837_<51>
P66 = 263201136283162454275794566273264043568002234611743477143224398277_<66>

Aug 22, 2004 (2nd)

GGNFS 0.53.2 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Aug 22, 2004

By Naoki Yamamoto / GGNFS 0.50.2, PPSIQS 1.1
(4·10¹²⁹-13)/9 = 44...443_<129> = 229 · C127
C127 = P32 · P41 · P55
P32 = 20990037785105128323588237213979_<32>
P41 = 54502554364749898092285546838629172994617_<41>
P55 = 1696492415514857958127622430338131526395673614569962069_<55>

Aug 21, 2004 (3rd)

By Naoki Yamamoto / GGNFS 0.50.2
(4·10¹²⁴-13)/9 = 44...443_<124> = 3² · 26459 · 1045621041241625955707_<22> · C98
C98 = P35 · P63
P35 = 30367480109022487445766221681028821_<35>
P63 = 587784969575581161395939998890201991302322526714771636885549999_<63>

Aug 21, 2004 (2nd)

By Makoto Kamada
I clearly should have tried GMP-ECM more.

Results of GGNFS 0.53.0

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

Aug 21, 2004

By Greg Childers / GMP-ECM
(34·10¹³¹-7)/9 = 377...77_<132> = 19 · 67601 · C126
C126 = P28 · P98
P28 = 6288769795552204180769775851_<28>
P98 = 46769635893058267878190776473401799344503349258949702146522667174623480094831320247302033067906033_<98>

Aug 20, 2004 (3rd)

By Chris Monico / GGNFS
2·10¹³⁷-1 = 199...99_<138> = 107933154040501_<15> · C124
C124 = P59 · P66
P59 = 11254877967108971721971687364747575335643268954022536802019_<59>
P66 = 164639613139898133672159836253458304835231081639583063417570849921_<66>

Aug 20, 2004 (2nd)

By Naoki Yamamoto / GGNFS 0.50.2
(4·10¹²⁵-13)/9 = 44...443_<125> = 7 · 93377 · 240860290487_<12> · C108
C108 = P31 · P78
P31 = 1061760791562605750846153441939_<31>
P78 = 265881203190276539563970491198910438199516859054681554008060898087257465997209_<78>

Aug 20, 2004

By Greg Childers / GMP-ECM
(34·10¹³²-7)/9 = 377...77_<133> = 3² · 1867 · 1748743559555400006807950141_<28> · C102
C102 = P28 · P74
P28 = 7254004109979341312421744721_<28>
P74 = 17723343506004936697214614039918927960791058454059566778726810617202213319_<74>
(34·10¹³⁹-7)/9 = 377...77_<140> = 37 · 1586537 · 2330145454548179_<16> · C117
C117 = P31 · P87
P31 = 1619770177395862286483247847039_<31>
P87 = 170509290882093697207008859530456309564425733897850238400787099667581196837729899566793_<87>

Aug 19, 2004 (5th)

By Wataru Sakai / GMP-ECM
(34·10¹²⁹-7)/9 = 377...77_<130> = 3 · 277 · 15811637 · 19183430041663_<14> · C107
C107 = P32 · P75
P32 = 30113967432941796834668647331809_<32>
P75 = 497696182350347055977921428273088348975758183194450101962994877260301281773_<75>

Aug 19, 2004 (4th)

By Chris Monico / GGNFS
2·10¹⁴⁰-1 = 199..99_<141> = 89 · 68567 · 411986842103_<12> · 78243273145651897_<17> · C106
C106 = P41 · P65
P41 = 45790969898680950598430026489151331148057_<41>
P65 = 22203152531205841279242744607049040699497136455068620741800643479_<65>

Aug 19, 2004 (3rd)

By Naoki Yamamoto / GGNFS 0.50.2
(4·10¹²⁰-13)/9 = 44...443_<120> = 17 · 29 · 1951 · C114
C114 = P48 · P67
P48 = 126278279929905556957812282763062906900442138493_<48>
P67 = 3659187263304819072653186507809952999110494563658336236607612963757_<67>
(4·10¹¹⁸-13)/9 = 44...443_<118> = 3 · 269389 · 4143961337_<10> · C103
C103 = P39 · P64
P39 = 775433748534841428512105225274185871533_<39>
P64 = 1711417528326269878672672868878672958755897011537865961679653449_<64>

Aug 19, 2004 (2nd)

By Makoto Kamada

Results of GGNFS 0.53.0

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

Aug 19, 2004

By Greg Childers / GGNFS-0.52.1
(2·10¹⁴⁵+43)/9 = 22...227_<145> = 7 · 239 · 197558191 · 30733767413_<11> · 1064894417201_<13> · C111
C111 = P40 · P71
P40 = 7548491687442602199312838584500034844247_<40>
P71 = 27215353068933707944920442554488103229476570627617679875175622257104599_<71>
By Greg Childers / GMP-ECM, PPSIQS
(4·10¹²⁶-13)/9 = 44...443_<126> = 181 · 1783981 · 2187208687_<10> · C108
C108 = P33 · P33 · P44
P33 = 145119096374045890132496165483233_<33>
P33 = 379384042130033365903045831353401_<33>
P44 = 11430226472250843355124233756188951341826253_<44>

Aug 18, 2004 (4th)

By Chris Monico / GMP-ECM
2·10¹⁴²-1 = 199...99_<143> = 7 · 9554829631_<10> · 4356731702671_<13> · 3357467657868616871_<19> · C101
C101 = P34 · P67
P34 = 2187736421927986737235449390719177_<34>
P67 = 9344183469892461100358281997257285354029613953632153751125132345671_<67>

Aug 18, 2004 (3rd)

By Naoki Yamamoto / PPSIQS 1.1
(7·10¹³⁷+11)/9 = 77...779_<137> = 13 · 1039 · 408241 · 26181751369_<11> · 3425292729398808720905941333_<28> · C90
C90 = P32 · P58
P32 = 22056639529761150661156954369573_<32>
P58 = 7130898895763021156191882973421912329046913869904778581777_<58>

Aug 18, 2004 (2nd)

By Chris Monico / GGNFS
2·10¹⁴³-1 = 199...99_<144> = 644351574301_<12> · C132
C132 = P39 · P94
P39 = 107281422616573668503595416894220191851_<39>
P94 = 2893227456310286462832991811810130099788185702416662782780831395802057171334344263213571023649_<94>

Aug 18, 2004

By Makoto Kamada
Results of GGNFS 0.53.0.

Results of GGNFS 0.53.0 on Pentium 4 3.06GHz + Windows XP + Cygwin

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

Aug 17, 2004 (3rd)

By Greg Childers
(2·10¹⁴²+43)/9 = 22...227_<142> = C142
C142 = P44 · P98
P44 = 85575960030413375991725497538275202907116371_<44>
P98 = 25967832805293130914623433239564146332704548526760355957782902914023432604012069669809063815161537_<98>

Aug 17, 2004 (2nd)

By Naoki Yamamoto / PPSIQS 1.1
(4·10¹³⁵-13)/9 = 44...443_<135> = 487 · 84319 · 124557435973_<12> · 2797096370368950528020003_<25> · C92
C92 = P43 · P49
P43 = 3501974296552962694014683900191202199676961_<43>
P49 = 8871009204635018234101741616969553488078528522909_<49>
By Naoki Yamamoto / GMP-ECM
(7·10¹³⁷+11)/9 = 77...779_<137> = 13 · 1039 · 408241 · 26181751369_<11> · C117
C117 = P28 · C90
P28 = 3425292729398808720905941333_<28>
C90 = [157283666467016791459278588493585530666059307917051439689052861990003340364439962061071221_<90>]

Aug 17, 2004

GGNFS-0.53.0 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Aug 16, 2004 (4th)

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

Aug 16, 2004 (3rd)

By Greg Childers / GMP-ECM
(8·10¹²⁴-53)/9 = 88...883_<124> = 3 · 7³ · 17 · 1003295831_<10> · C111
C111 = P33 · P78
P33 = 533252834868991076123023980274187_<33>
P78 = 949775583879503059080554641404277630343016126240250646001790651451482941038323_<78>
By Greg Childers / GMP-ECM, PPSIQS
(8·10¹⁵⁰-53)/9 = 88...883_<150> = 61 · 173 · 5911811 · 3977381638220226078712047067_<28> · C112
C112 = P31 · P36 · P47
P31 = 1262586736045044638972457650263_<31>
P36 = 180055297964424173888575711364616079_<36>
P47 = 15757474264116676493899622251753222363620467539_<47>
By Greg Childers / GGNFS-0.52.1
(2·10¹³⁹+43)/9 = 22...227_<139> = 7² · 163 · 1237 · 333292525991_<12> · C120
C120 = P45 · P76
P45 = 250032617848968707843053187291507341768566071_<45>
P76 = 2699055776113772740729745272715963145141623773257945023853997234998414725053_<76>
(2·10¹⁴⁰+43)/9 = 22...227_<140> = 3 · 31 · 1069 · 8964601 · 30421352050471_<14> · 285569714646679_<15> · C100
C100 = P37 · P64
P37 = 1537826626889528440102962149670111199_<37>
P64 = 1866370374076115987720915143645308809137896395487265990911695741_<64>

Aug 16, 2004 (2nd)

By Chris Monico / GGNFS-0.52.2
2·10¹⁴⁴-1 = 199...99_<145> = 31 · 9804138075439_<13> · C130
C130 = P35 · P96
P35 = 13854961586932530041353553255527433_<35>
P96 = 474956195168874037512374864466717106402173543729681853735275008639338252700754042774999705598967_<96>

Aug 16, 2004

By Sander Hoogendoorn / ggnfs-0.50.2-k1
(8·10¹¹⁶-53)/9 = 88...883_<116> = 367 · 9043 · 95090691059444371_<17> · C93
C93 = P32 · P61
P32 = 70432600953289405607699156781551_<32>
P61 = 3999052930997618606487937766796750548209350357198059429827483_<61>

Aug 15, 2004 (4th)

By Naoki Yamamoto / GGNFS 0.50.2
(16·10¹¹⁷-7)/9 = 177...77_<118> = 197 · 1210163 · 2294141 · C103
C103 = P34 · P69
P34 = 3366193491864394615092466070341489_<34>
P69 = 965624317230638336861113164255644815470547736072360700302995506212843_<69>

Aug 15, 2004 (3rd)

By Naoki Yamamoto / GGNFS 0.50.2, PPSIQS 1.1
(13·10¹³⁴-1)/3 = 433...33_<135> = 199 · 7177 · C129
C129 = P39 · P43 · P48
P39 = 310443695806204825883048853941991091621_<39>
P43 = 5785687201900892982007414968214381142462459_<43>
P48 = 168922803190060510326666688051641536230900596989_<48>
By Naoki Yamamoto / PPSIQS 1.1
(46·10¹⁴⁸-1)/9 = 511...11_<149> = 3² · 193 · 359 · 40430864797_<11> · 22431655423337_<14> · 1251360360918225535713445002829_<31> · C89
C89 = P38 · P52
P38 = 42057935411015848231340866859995766233_<38>
P52 = 1717182112351141063777768046172842443193154091976929_<52>

Aug 15, 2004 (2nd)

By Chris Monico / GGNFS
2·10¹⁴⁸-1 = 199...99_<149> = 7 · C148
C148 = P54 · P95
P54 = 117070574659995165200777586374365068986623688168229103_<54>
P95 = 24405303086969361747536590638875719351910103103955718453805022842339158858638099335114643253319_<95>

Aug 15, 2004

By Greg Childers / GGNFS-0.52.1
(2·10¹²⁸+43)/9 = 22...227_<128> = 3² · 331 · 12541 · C120
C120 = P58 · P63
P58 = 1000344265034890698594181838433694614479773335378392497189_<58>
P63 = 594614271324990197436080568035620507861369527178899595166636737_<63>
(2·10¹²⁹+43)/9 = 22...227_<129> = 139 · 6133 · 71363 · 39741047095727_<14> · C104
C104 = P47 · P58
P47 = 20258864215419377654796177065819979543859152227_<47>
P58 = 4537035977305463554114827190992685878369459699025736038723_<58>
(2·10¹³²+43)/9 = 22...227_<132> = 17 · 25163 · C126
C126 = P60 · P67
P60 = 196959804603855884145383854955199894753944509737958282726147_<60>
P67 = 2637536889245416809305135888586468429618408002108774236518191211971_<67>
(2·10¹³³+43)/9 = 22...227_<133> = 7 · 59 · 113 · C128
C128 = P36 · P38 · P56
P36 = 266826656904029035443015530298752551_<36>
P38 = 15777624776497722546638020690112501273_<38>
P56 = 11310665340782789985942630553853205383547938874605745521_<56>
(2·10¹³⁵+43)/9 = 22...227_<135> = 109 · 24889 · 18963649 · 6013186489_<10> · 310929595079563_<15> · C97
C97 = P35 · P62
P35 = 49324426672587319939477856618057831_<35>
P62 = 46838486383247495945892705345162490638183050272054527763817419_<62>

Aug 14, 2004 (4th)

By Tetsuya Kobayashi / GMP-ECM 5.0.3
(82·10¹³⁹-1)/9 = 911...11_<140> = 7² · 13 · 22745010213596190913_<20> · 39018381622916411765473_<23> · C96
C96 = P27 · P69
P27 = 672037649153157760391664637_<27>
P69 = 239818630401442350150517403201814834134176811816856060030914476606831_<69>
(46·10¹³⁵-1)/9 = 511...11_<136> = 479 · C134
C134 = P29 · C105
P29 = 46154078138132146557551248199_<29>
C105 = [231190363516601815875245621524025323063245909981915517274853408346607442950108028978835915150679748856991_<105>]
(52·10¹³³-7)/9 = 577...77_<134> = 3² · 53 · C132
C132 = P27 · P105
P27 = 507161535575400433388365477_<27>
P105 = 238833997115881069691548632721734130353784577435020569573433120826879103881898021999882972026521882938113_<105>
5·10¹⁴⁶-1 = 499...99_<147> = 1324743175841_<13> · 41231655271646690609789_<23> · C112
C112 = P33 · P80
P33 = 491797844488087910675065491701111_<33>
P80 = 18613194785067937897308160940271109215879924182776436506899598937897470234894541_<80>
(8·10¹⁵⁰-71)/9 = 88...881_<150> = 7 · 39119 · 74975514714601_<14> · 3953010438312526830606053_<25> · C107
C107 = P30 · P32 · P46
P30 = 278093556698362052053293534853_<30>
P32 = 20097196725658504721430579226829_<32>
P46 = 1959692207996245702222602127514306060796873037_<46>
(37·10¹⁴⁸-1)/9 = 411...11_<149> = 7 · 351343 · 15715685701_<11> · C133
C133 = P35 · P98
P35 = 21065758028443297907249484416012389_<35>
P98 = 50491636065502153240509298781996095334209499692636542105438958927122662225516148030340946437926599_<98>
3·10¹⁴⁴-1 = 299...99_<145> = 114960971 · 2213287753_<10> · C128
C128 = P30 · P99
P30 = 108090137887270909297090797793_<30>
P99 = 109080439628348269202774046214310086366771298172396864071466868126105645656536199141927505676107861_<99>
(28·10¹⁴⁰-1)/9 = 311...11_<141> = C141
C141 = P32 · P110
P32 = 28061244394528078097445236936881_<32>
P110 = 11086860822600495496089798493845024271017940020968874041788390705256335001099077800139750826481064002684323831_<110>
(46·10¹²⁹-1)/9 = 511...11_<130> = 17 · 19 · 82240334137855241_<17> · C111
C111 = P34 · P34 · P44
P34 = 2674032226448216912556195682541261_<34>
P34 = 4058621363993797320237221962751579_<34>
P44 = 17728939570931867503068789999212267866115483_<44>
(46·10¹⁴⁸-1)/9 = 511...11_<149> = 3² · 193 · 359 · 40430864797_<11> · 22431655423337_<14> · C119
C119 = P31 · C89
P31 = 1251360360918225535713445002829_<31>
C89 = [72221134370216050511886139455047439541624002248961467278999502369658735430252413113238457_<89>]
(73·10¹²³-1)/9 = 811...11_<124> = 29 · 2927 · 144100861 · C111
C111 = P32 · C80
P32 = 63833739956555856215699127353593_<32>
C80 = [10388258895723777777326223736958021452464103794984537490479460124159085376982729_<80>]
(73·10¹²⁹-1)/9 = 811...11_<130> = 809 · 9723253213_<10> · C118
C118 = P27 · P91
P27 = 848035601727306124412985569_<27>
P91 = 1215923209499907110359099149008584747886873725147568593926890646948761420775922583207060507_<91>
(73·10¹³⁴-1)/9 = 811...11_<135> = 13881683 · C128
C128 = P30 · C99
P30 = 269001190545339915526867145161_<30>
C99 = [217212105758048703274010767129432057546261389285898400665761853003366980068691694075671343515862997_<99>]
(73·10¹⁴³-1)/9 = 811...11_<144> = 7 · 582319 · 223470319 · C129
C129 = P29 · P101
P29 = 56223336320445107851116811063_<29>
P101 = 15837436546409483213789519639504868703318612432957682219628275351899328538773456582356006613264313511_<101>
(73·10¹⁴⁷-1)/9 = 811...11_<148> = 4159 · 17747 · 1166927 · C134
C134 = P31 · P104
P31 = 5211981027531516487669631329999_<31>
P104 = 18068411228607373367533120273425957835243258126098442269324290869126076885106512239894555942041618508259_<104>
(43·10¹²⁴-7)/9 = 477...77_<125> = 4219 · 1850749 · C115
C115 = P31 · P85
P31 = 1829658182397745082611987252939_<31>
P85 = 3344251535561118609019392015412413893530067677471043320719122483668509889510526481053_<85>
By Makoto Kamada / PPSIQS 1.1
(73·10¹²³-1)/9 = 811...11_<124> = 29 · 2927 · 144100861 · 63833739956555856215699127353593_<32> · C80
C80 = P38 · P42
P38 = 16851944024522236784620221321632467021_<38>
P42 = 616442760586388278887103869502804909104749_<42>

Aug 14, 2004 (3rd)

By Naoki Yamamoto / GMP-ECM
(88·10¹⁴⁵-7)/9 = 977...77_<146> = 197 · 16937 · 2652168012682425937332375349_<28> · C113
C113 = P29 · P85
P29 = 10494560093981267791683167017_<29>
P85 = 1052863760281934042939222037220079887789397898463048988151570459130673394086322002521_<85>

Aug 14, 2004 (2nd)

By Naoki Yamamoto / GGNFS 0.50.2
(2·10¹²⁹-17)/3 = 66...661_<129> = 56149 · 269195509511_<12> · C113
C113 = P46 · P67
P46 = 5850093849009154750695732932179251467340256621_<46>
P67 = 7539387594423886122474188626010642810713734707297642446847656344419_<67>

Aug 14, 2004

By Wataru Sakai / GMP-ECM
(88·10¹⁴⁵-7)/9 = 977...77_<146> = 197 · 16937 · C140
C140 = P28 · C113
P28 = 2652168012682425937332375349_<28>
C113 = [11049342003053844732883196766217892563493538977511315244647157237917799253367565480991912205020696144074738049857_<113>]

Aug 13, 2004 (5th)

By Naoki Yamamoto / GGNFS 0.50.2
(88·10¹¹⁶-7)/9 = 977...77_<117> = 624278792959867_<15> · C103
C103 = P33 · P70
P33 = 740524292869073229988058449820401_<33>
P70 = 2115057948046324213103243818118224005976352820802067289787971722593331_<70>

Aug 13, 2004 (4th)

By Chris Monico / GGNFS
2·10¹⁴⁹-1 = 199...99_<150> = 59 · 8885059 · C141
C141 = P31 · P111
P31 = 1493309014925537823429198505631_<31>
P111 = 255486514302691494846148453167109949281503703507120073976338942411963652635881540252707023179121976597815727409_<111>

Aug 13, 2004 (3rd)

By Greg Childers / GGNFS
(2·10¹¹⁷+43)/9 = 22...227_<117> = 239 · 1327 · 3119 · C108 = P46 · P63
P46 = 1602380498589551460844803694041803071803326713_<46>
P63 = 140196650172888378636539392161737752562515331031081392670520997_<63>

Aug 13, 2004 (2nd)

By Naoki Yamamoto / GGNFS-0.50.2
(5·10¹¹⁷+31)/9 = 55...559_<117> = 13 · 519917644084338582319771_<24> · C92
C92 = P45 · P48
P45 = 346062737628772422538383221785890093185552101_<45>
P48 = 237517026412700840486947528737713794462517971333_<48>
(5·10¹⁴⁶+31)/9 = 55...559_<146> = 3243941 · 1398873744713_<13> · 695031043209532567098808030379149_<33> · C95
C95 = P35 · P60
P35 = 39503056720157868435026638079206339_<35>
P60 = 445903749438031877158379025823963572610293551734734557460293_<60>

Aug 13, 2004

GGNFS-0.52.2 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Aug 12, 2004 (3rd)

By Wataru Sakai / GMP-ECM
(88·10¹¹⁹-7)/9 = 977...77_<120> = 315303250430129350630357_<24> · C97
C97 = P33 · P65
P33 = 152458436617826712499433931140047_<33>
P65 = 20340435765872929924195496749772356003903484474400699753398423363_<65>

Aug 12, 2004 (2nd)

By Naoki Yamamoto / GGNFS 0.50.2
(16·10¹⁵⁴-61)/9 = 177...771_<155> = 13² · 127 · C150
C150 = P40 · P111
P40 = 3733121936303998720580918507923629269009_<40>
P111 = 221878321587930532169969709902563560847331538413982435341417449466367100689787271320174821863118816102475066813_<111>
(5·10¹¹³+31)/9 = 55...559_<113> = 7² · C112
C112 = P41 · P71
P41 = 43720746141733364946107849658114339806371_<41>
P71 = 25932467950045189401837833609812116498751235726707090602373851852516221_<71>
By Naoki Yamamoto / GMP-ECM
(5·10¹²⁹+31)/9 = 55...559_<129> = 13 · 43 · 1272231689_<10> · 11160255697127399_<17> · C101
C101 = P35 · P67
P35 = 17321531270228804971420531802867243_<35>
P67 = 4041001865615899813621236180480845269006050736592447296930252650437_<67>

Aug 12, 2004

GGNFS-0.52.1 was released.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Aug 11, 2004 (2nd)

By Sander Hoogendoorn / ggnfs-0.50.2-k1
(5·10¹¹⁶+31)/9 = 55...559_<116> = 17² · 3679800784648829_<16> · C98
C98 = P32 · P67
P32 = 44334860269035801667552039407673_<32>
P67 = 1178311185643301456111174295447537534022224985031162773715621064043_<67>

Aug 11, 2004

GGNFS-0.52.0 was released. This version includes ggnfs-0.50.2-k1.
GGNFS - A Number Field Sieve implementation (Chris Monico)

Aug 10, 2004

By Wataru Sakai / GMP-ECM
(5·10¹²³+31)/9 = 55...559_<123> = 13 · 229 · 6661 · 10949 · 3361177 · 2619474031_<10> · C96
C96 = P32 · P65
P32 = 18272483111100886415621718646609_<32>
P65 = 15904928508226266154222347295244079475097632916793327874442395241_<65>

Aug 9, 2004 (6th)

(Aug 11, 2004) ggnfs-0.50.2-k1 is included to GGNFS-0.52.0.
ggnfs-0.50.2-k1 was released. This patch accelerates getdeps of GGNFS 0.50.2. In getdeps.c, makeMasterIndex() calls fread() and fwrite() over and over, so this routine takes long wasting time especially on Cygwin. The same is looked about addNewRelations3(). ggnfs-0.50.2-k1 changes the function to take not wasting time but large memory. Changes will be included in GGNFS in the future.

ggnfs-0.50.2-k1.txt***** Speed up GGNFS ***** Patch name: ggnfs-0.50.2-k1 Author: Makoto Kamada ( m_kamada@nifty.com ) Requirements: GGNFS 0.50.2 Cygwin only? Large memory (over 256MB? free) How to install: (1) Download source codes of GGNFS 0.50.2 from http://www.math.ttu.edu/~cmonico/software/ggnfs/devel/ggnfs-0.50.2.tar.gz and expand them to current directory, if necessary. tar zxf ggnfs-0.50.2.tar.gz (2) Enter ggnfs directory. cd ggnfs (3) Apply patch. patch -p0 < ../ggnfs-0.50.2-k1.patch (4) Compile GGNFS. make Changes: Aug 8, 2004 ggnfs-0.50.2-k1 * Speed up addNewRelations3() and makeMasterIndex() in getdeps.c by reducing fgets(), fread(), fwrite() and clock(). * Delete .type directives in assembly codes, since latest Cygwin environment brings not a warning but an error on them.

Some results of ggnfs-0.50.2-k1

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

Aug 9, 2004 (5th)

Condition of the sequence (8·10ⁿ-53)/9 = { 3, 83, 883, 8883, 88883, ... } was extended to n≤150.
Following numbers were not factorized. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.
n= 116, 117, 118, 122, 124, 125, 126, 129, 130, 132, 135, 136, 139, 142, 143, 144, 146, 148, 149, 150, (20/150)

Aug 9, 2004 (4th)

Condition of the sequence (4·10ⁿ-13)/9 = { 3, 43, 443, 4443, 44443, ... } was extended to n≤150.
Following numbers were not factorized. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.
n= 118, 120, 124, 125, 126, 127, 128, 129, 133, 135, 136, 137, 139, 141, 143, 144, 146, 147, 149, 150, (20/150)

Aug 9, 2004 (3rd)

By Naoki Yamamoto / PPSIQS 1.1
(88·10¹⁴²-7)/9 = 977...77_<143> = 17 · 21491 · 12889824783089_<14> · 299476320250181152930460992793_<30> · C95
C95 = P47 · P49
P47 = 13245760762206208300793072742910185771632215651_<47>
P49 = 5234174633003279598976699261396818482965422304033_<49>

Aug 9, 2004 (2nd)

By Naoki Yamamoto / GGNFS-0.50.2
(5·10¹²⁸+31)/9 = 55...559_<128> = C128
C128 = P32 · P97
P32 = 38269214212140348621764618632681_<32>
P97 = 1451703587316704504219071457325686645925023851742369363924810363182131249318712352433397460201039_<97>

Aug 9, 2004

Condition of the sequence (34·10ⁿ-7)/9 = { 37, 377, 3777, 37777, 377777, ... } was extended to n≤150.
Following numbers were not factorized. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.
n= 121, 123, 124, 127, 128, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 142, 143, 147, 149, 150, (20/150)

Aug 8, 2004

By Naoki Yamamoto / GGNFS-0.50.2
(5·10¹⁴⁸+31)/9 = 55...559_<148> = 3 · 17 · C147
C147 = P44 · P103
P44 = 48927720345537554079204669065308406118675509_<44>
P103 = 2226395611819538088138623926667538986963803982837221614882581319995207895365189900082209127633525519401_<103>

Aug 7, 2004 (4th)

By Wataru Sakai / GMP-ECM
(5·10¹⁴⁶+31)/9 = 55...559_<146> = 3243941 · 1398873744713_<13> · C128
C128 = P33 · P95
P33 = 695031043209532567098808030379149_<33>
C95 = [17614561105781635495651811321705417120485475600235294076950813661998769837908505718148946397327_<95>]

Aug 7, 2004 (3rd)

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

Aug 7, 2004 (2nd)

By Sander Hoogendoorn
5·10¹³⁵-1 = 499...99_<136> = C136
C136 = P60 · P77
P60 = 269003202410838504214036520941412612134351136344950318928159_<60>
P77 = 18587139317262429780586757996354609670472835010983311369908899791500395369761_<77>

Aug 7, 2004

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

Aug 6, 2004

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

Aug 5, 2004 (2nd)

By Sander Hoogendoorn / GGNFS-0.42.0
5·10¹³⁰-1 = 499...99_<131> = 739 · 1129 · 1779149 · 37524595431275311_<17> · C102
C102 = P40 · P63
P40 = 7628309663740789043344274685157484199841_<40>
P63 = 117672497216416907975811138393270288338026728779873725975710671_<63>

Aug 5, 2004

By Wataru Sakai / GMP-ECM
(79·10¹²⁶-7)/9 = 877...77_<127> = 337 · 4721 · 73637 · 119869 · 7474153 · 1022663261_<10> · C95
C95 = P32 · P64
P32 = 20934653464832126854449165578597_<32>
P64 = 3906225375647472141875367898907852805403416735828228781396251017_<64>

Aug 4, 2004

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

Aug 3, 2004 (3rd)

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

Aug 3, 2004 (2nd)

Condition of the sequence (88·10ⁿ-7)/9 = { 97, 977, 9777, 97777, 977777, ... } was extended to n≤150.
Following numbers were not factorized. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.
n= 116, 119, 121, 122, 125, 127, 128, 130, 132, 134, 137, 138, 141, 142, 143, 144, 145, 146, 149, 150, (20/150)

Aug 3, 2004

Condition of the sequence (5·10ⁿ+31)/9 = { 9, 59, 559, 5559, 55559, ... } was extended to n≤150.
Following numbers were not factorized. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.
n= 113, 116, 117, 123, 126, 128, 129, 130, 132, 134, 135, 136, 137, 139, 140, 142, 146, 147, 148, 150, (20/150)

Aug 2, 2004 (5th)

By Naoki Yamamoto / GGNFS-0.50.2
(4·10¹¹⁶+41)/9 = 44...449_<116> = 7 · 337 · 2039 · 26753002217_<11> · C99
C99 = P38 · P61
P38 = 44794759861299396985200448488293440259_<38>
P61 = 7710323090519545020480623649489753373694054004099076008805283_<61>
By Naoki Yamamoto / PPSIQS 1.1
(37·10¹⁴⁷-1)/9 = 411...11_<148> = 23 · 61 · 257 · 14065141 · 2002045231_<10> · 16106441408411_<14> · 3574843806050081_<16> · C97
C97 = P34 · P63
P34 = 8382239055754299828581187813116803_<34>
P63 = 838945471965205785933350926848623267517006821503864790379243727_<63>

Aug 2, 2004 (4th)

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

Aug 2, 2004 (3rd)

By Naoki Yamamoto / GGNFS-0.50.2
(7·10¹²⁹-1)/3 = 233...33_<130> = 460973 · 2805891978037_<13> · 5542822167307_<13> · C99
C99 = P45 · P54
P45 = 496581743478488996713861801354111444216964147_<45>
P54 = 655403347174745853386934264992436518045116721863278677_<54>
(7·10¹¹³+11)/9 = 77...779_<113> = 13 · 41 · 317 · 4049231 · 659079229 · C93
C93 = P33 · P60
P33 = 507527545879734298342291428748409_<33>
P60 = 339859381634013658446000254171861064394439537000913446780329_<60>
(7·10¹¹⁵+11)/9 = 77...779_<115> = 3 · 43 · 23561 · 2182451195879_<13> · C97
C97 = P48 · P49
P48 = 204630175486239665441834420067922388530171436419_<48>
P49 = 5730043032793768756673983042924268914827505976591_<49>

Aug 2, 2004 (2nd)

By Chris Monico / GGNFS
2·10¹⁵⁰-1 = 199...99_<151> = 17 · 336263 · 6516017 · 11385821807_<11> · C127
C127 = P38 · P89
P38 = 55120529024967151191001971500609072753_<38>
P89 = 85554335523575100570067317351631393271852473171138400561538366131132422284355387689070967_<89>

Aug 2, 2004

By Wataru Sakai / GMP-ECM
(79·10¹³⁵-7)/9 = 877...77_<136> = 67 · C135
C135 = P32 · P104
P32 = 11929546337170934826957294007451_<32>
P104 = 10982111550657510700513355288216179071140051766262673835508750420486872948294203183491129951906834483681_<104>
(7·10¹³¹-61)/9 = 77...771_<131> = 67 · 617 · 1823 · 310621183 · 48346728036539_<14> · C101
C101 = P37 · P65
P37 = 6853714382111772333567001250060157467_<37>
P65 = 10027316802528728876840365539723496805982556831028807023311815417_<65>

Aug 1, 2004 (4th)

By Naoki Yamamoto / GGNFS-0.50.2
(7·10¹⁴⁴-1)/3 = 233...33_<145> = C145
C145 = P47 · P98
P47 = 37466137662297732968966339042619987350087992783_<47>
P98 = 62278459401524391449909039884972845130019000157718994827933933144917142216395425263726960259325851_<98>

Aug 1, 2004 (3rd)

By Sander Hoogendoorn / NFSX 1.8
(79·10¹¹⁹-7)/9 = 877...77_<120> = 173 · 223 · 3221 · 91757 · 1074533 · C101
C101 = P33 · P69
P33 = 156477338651555641824995709430741_<33>
P69 = 457859759985964363716052010340892271341496432063774626160703756819043_<69>
By Sander Hoogendoorn / GGNFS-0.42.0
5·10¹²⁵-1 = 499...99_<126> = 31 · 992445257 · C116
C116 = P35 · C81
P35 = 36167938192618912257635160348826241_<35>
C81 = [449343018205749408245949108992786992858072894255838328977051237721820163447966617_<81>]
By Makoto Kamada / PPSIQS 1.1
5·10¹²⁵-1 = 499...99_<126> = 31 · 992445257 · 36167938192618912257635160348826241_<35> · C81
C81 = P36 · P45
P36 = 541041326367575421678108269681570849_<36>
P45 = 830515149780762684023194221858216749394061433_<45>

Aug 1, 2004 (2nd)

Condition of the sequence (7·10ⁿ+11)/9 = { 9, 79, 779, 7779, 77779, ... } was extended to n≤150.
Following numbers were not factorized. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.
n= 113, 115, 117, 119, 122, 123, 124, 126, 129, 133, 134, 135, 137, 139, 141, 142, 143, 145, 147, 148, (20/150)

Aug 1, 2004

Condition of the sequence (4·10ⁿ+41)/9 = { 9, 49, 449, 4449, 44449, ... } was extended to n≤150.
Following numbers were not factorized yet. These numbers may have small factors. You should run GMP-ECM (B1≥1000000) first.
n= 116, 119, 122, 123, 125, 126, 129, 130, 131, 132, 133, 135, 140, 142, 143, 145, 147, 148, 149, 150, (20/150)