Old log (2000)


Dec. 29, 2000

by me,

p(7837), 
56216371746883303451161702528753955107985829671734435535424146882768265505553176495859=
1028293865615697013325277987361256053 * 54669558602514291476184577824843542244086554760903

p(7956), 
34961227275223342221801934768421347084904248636796566671115934050413830311412680209133=
101845618049428241034747522903619757 * 343276696089720609735683001973463166562121394088769

p(9230), 
1652720603051914135598271814846864177296996200854336501542674609912416061498566622680357213610733181349=
6262158187090416816462485279 * 263921886620340521719766584470244632803529309148950451392733882662822726331

Dec. 28, 2000

News !

partition number 6000 series are completely factored by me (Dec. 28, 2000).

p(6743), 
35529201486434241296399052282920132184452311233483962914126977269616408643847501937323=
73025838178109318512507901725543 * 486529184365934422177204710866710154828968642166034461

p(6745), 
36645640135481565522440650617684875083999454685354806065395535243089899513008872052043=
890474948523683079906851715479945684862047 * 41152915302374660505044641136680280657016469

p(6761), 
11571667005155889158227306901848159553919687739436995401589302267337212655942777349413=
555127843307657569762138564709888821 * 20845048838133583026052682873610544020318754043953

p(6776), 
133114231269956133579208576725379774194201159373233698595934828042472441544942828091021=
143359340259591787539165318523162169108153 * 928535462209270446911927574465053717209687157

p(6838), 
10208815095447066067877759678945248298411456500685333375368329084856324148917269175111=
141006332552005006682546258315419279523 * 72399692344894649207809303630600300863224230157

p(6860), 
10596013741519053941463239875344969535427664232884750641598745063730896834033848245159=
64453826409669726685385623741029414612343 * 164396969610005654798934307765161740425432913

p(6924), 
6557312124184481831132391323952135495283430672139759860238231429548668304556324534949=
149334639109542179512729868510406641 * 43910188307847746570548587103254027054773370687989

p(6941), 
334665563709308243597777901932065814084038232911572689748480233967509067744266403095773=
39788007610374957017690077638779690681 * 8411216942213568627041419431758249543650558379333

p(6973), 
21795930733626894614957503921087021205034934970012615535087331363890598510125138291900761=
45414436544857955245529171364484151 * 479933967959682559518553805883051478708967388870160111

p(6993), 
687033501648151703101219644854006020730836797245584459174347276037740613628809945943053=
63689773369073305124118668093351327 * 10787187099361916509695558692602322083912610980361939

p(6995), 
3795826710033647859914432701828156774724911791873866074823464095020760138055802502899=
689629406958558725572472041200484813 * 5504154364260958830334865323526892979528044479423

p(7621), 
22144119801240821545088115250123485105949045133193900684584897096591662869469558943933=
217241197684053220807325087442211 * 101933335100860245037741626826375434669999360843014303

p(7706), 
2141437757282983294969083370277303480567196513587754197147610549736314261726284407385893969=
838476928901425257713934676463 * 2553961454954641199435770710546147669027615176421133067273663

p(9812), 
3367804789167624632224083617335410367908282967697622212265402131923591137808870812075676571246147=
285929105286980919171704682799349 * 11778460908299038302982251436786559131792094820707551902913666903

Dec. 25, 2000

By Sean Irvine (Dec. 23, 2000),

Webmind NZ is pleased to announce the factorization of 95!-1.
Four prime factors 97, 14983, 405048793, and 13952770586273
were already known.

We used Jens Franke's implementation of the double-prime
variation of the multiple polynomial quadratic sieve to split
the remaining 121 digit composite into 59 and 63 digit primes:

12567987371175933926362928813184833422003421176616583508547 *
100068035001280028333231951900141716704950608273071023642271803

The sieving was performed using idle CPU time on a cluster of
thirty-two 560-600 MHz Pentium III machines running Linux.  Sieving
started on 3 November and completed 22 December (please note sieving
was not continuous throughout this period).  The factor base consisted
of 254130 elements.

95!-1 was the only number of the form n!-1 with n <= 100 which had not
yet been factored.

95: 97.14983.405048793.13952770586273.
    12567987371175933926362928813184833422003421176616583508547.P63

Sean Irvine
Webmind NZ


By Sean Irvine (Dec. 22, 2000),

p9696 C103 = 
313552623423778502672305470036759636521 (p39) *
24112885321931232237616394159912332978829060304937459219317739967 (p65)

p9771 C101 =
9964971636581329433700823370506222673947 (p40) *
9565272885432880680528959366405808089466487000915406459543587 (p61)

p9891 C94 =
3073860785996525012797182719292824689861 (p40) *
936379709535260776678453469126231166078365649278190761 (p55)

p9897 C97 =
10000693297939775938637021972128668583 (p38) *
196720573359165066115085030145675897978646097639973535085267 (p60)

p9908 C96 =
250930386500787573289342576381636751186105155067 (p48) *
1590852908261481884656171329113467046831952944677 (p49)

Dec. 16, 2000

By Sean Irvine (Dec. 16, 2000),

p9945 C102 =
31790189231754048351860377481672777424361 (p41) *
5780083744077728066213990667169120894720169375428490564066983 (p61)


By Jens Franke (Dec. 15, 2000),

"I have factored the following partition numbers by MPQS with two large
 primes and verified primality of the factors assuming the GRH:

p8259.c93: 529401449942746605301497114292293806716592501 380492222048660380282594271463136776086900466659
p8362.c93: 12195793848253577819122925788582633931 78664496611926998956814497902041052174165383691488136821
p8754.c92: 5151688177635857678912503818235886686823 3032388115884072091455916610364157194514148368128493
p8802.c90: 4590564852952453595226137935112467 75218389340453252611643579202113531979414980761661607659
p8879.c90: 913987869667069151023068369094727 173141865965923268356769407733334798412976603317647304801
p8905.c94: 1517396339989194856346975362077365535618961 2027624075929717725597877040781411759946890671223827
p8925.c95: 536285950841283318072131739942959581243 95555345436271880610676461198746125357195425792754647991
p8949.c95: 3166663604871842410593187557877 15614985112307323324350744063805323638329679528546358886122010187
p8964: 371344882639832391625615504303 5148398494673211557872801805098496749626838480271776898911263329 

 This takes indeed much less than 30 hours on 800 MHz AMD athlon machines,
 even for numbers in the 90 digits range:

franke@pc1:/home/franke/partitionen > l p8259.c93.mpqs-fb p8259.c93.ff
-rw-r--r--   1 franke   users     8110605 Dec 14 15:16 p8259.c93.ff
-rw-r--r--   1 franke   users      465499 Dec 14 02:08 p8259.c93.mpqs-fb
franke@pc2:/home/franke/p9510 > l *.c93.mpqs-fb *.c93.ff
-rw-r--r--   1 franke   users     8481332 Dec 14 14:29 p8362.c93.ff
-rw-r--r--   1 franke   users      497584 Dec 14 02:11 p8362.c93.mpqs-fb

 I am working on the remaining c93 and c85 in the 8000-9000 range, but this
 may take some time since the c85 are running on an old 200 MHz Pentium MMX,
 so it takes 12-20 hours to factor them."


by me,

partition numbers

p(6804), 
2710460519127986267440130935021801765356255814007252077915316840068570748541377002229=
290178747905781158197474099324428917 * 9340658262155201905322123746295376404471302071937

p(6845), 
2498489060706541379140843608634647993317899323048748846713520583449683064272354074453=
685328438940902964967351468719131 * 3645681280303603938841966896042672947603698557053263

p(7606), 
3134953590115714433507734848270879853886137192601925788071937957871879661987844984563=
26582193000837877001647445125942382513 * 117934347629516494591874646691049236552077882851

p(8366), 
27256946446392613405775993326983999037454674727032893760937802849434016424144161861813017=
56111385895196666143263677357 * 485764983550796680601726108412796530884639520657055224820381

Dec. 14, 2000

Announcement.
I will go to Frankfurt for business trip from 17 to 24 December, 
so last update before departure will be 16 December,
and next update after arrival will be 25 December.

by me,

partition numbers

p(6728), 
2402901828026645652835614578171535413644346788036136137289052781226381622937835569549= P40 * P45
9035272407242946853956090173070578650657 * 265946804891063060703096815112251455172005357

p(7404), 
2422548565977058966035016803854638330400580612456973897890274848243373711971966089713= P34 * P51
4412439567151253746332241974909677 * 549027024417945205991341183835935981223032506386069

p(7619), 
1141174513402993514058690556817053247545350529506416026531909201736900781420662847409= P37 * P48
2977792079441517880396433684936359003 * 383228406469876743978808751343006309837820856803

p(7985), 
1400630445313336838147699878541314772416009208090111748383548246092374001548532051481= P41 * P44
16585621259752101381745600206855906725227 * 84448476386724840644145896468359691390955403

p(8698), 
228249217568691875785083259546843628370708962374431412538798004875945100503271793176941=
369016405295778076458860951809 * 618534065946859624127124840029192419869740370163796208749

Dec. 13, 2000

By Sean Irvine (Dec. 12, 2000),

p9858 C103 =
1459761899902929776764062680006003922079 (p40) *
1238718923813785950224667977215050817149639723715074029336198813 (p64)

p9960 C96 =
24966650628701354639660226518022986963 (p38) *
6563023687088619195317636642937982801873818648056891019029 (p58)


By Jens Franke (Dec. 11, 2000),

"It should take much less than 30 hours on an Athlon machine, which has a larger
 L1 cache. I obtained the following factorizations in about 24 hours on four
 AMD Athlon 800MHz machines, all by MPQS with two large primes and testing
 for primality assuming the truth of GRH:"

p8886: 3129227441393615698832661477081023 40636381573725136043689599730169468177355077028464364587 
p8934: 2076307180633183477578080071760699760701 1274014912216308998646828283856377923916869299191351 
p8952: 69819755026212836800190845982621 3541177739355249229995696567050804625614134705617452732923 
p8982: 91339543924899359924356543104359 4304640080831138476160869943876533982696838309532153814356157
p8983: 731949744512793443341191216707259169 15696247246181802242427549122442049855162115647523825614889 
p8987: 91210834490114965605775717072499 511198153034607082891797638295102990442575461854778238809


by me, 

p(8186)
11336057864217288905518044816195179730734931410397346082921784963952076656246000367423=
318227963588951188839456715709 * 35622444163517484684547523466457556693155539233690699947

Dec. 12, 2000

By Jens Franke

(Dec. 11, 2000),
p(7948),
389706234224581236769974621186712241 * 2396546509690898434772028203042295773316925087067

(Dec. 10, 2000),
p(8751),
4417659037907298945352048902366578807 * 490171976190880547750808449907255753722670832081


by me,

j(tau) 576,
573764956057511049630242612407960160224072145968868918095979173410656130682902278085809=
21643497086557773262555748652352507567524481 * 26509808177619406150402397622782754893847089

j(tau) 609,
23180299270231028044555066750137178426142274084030268579819610140997029176666531779823269=
266877813613696567526959204607920052659273 * 86857348523486931419054827074025895486498166653

j(tau) 676,
24713974872548781026714997679193619028206213255695017299769141337023355843869406454967=
4934255900299801618183214165792467 * 5008652848962936599554543474558938293611335639487501

j(tau) 715,
8314922568721855334429669345416906346274245199064784976713275017774733925987910393487=
34501460147427272292185160507563 * 241002048411620282743841442154127589332266947634258349

j(tau) 723,
1499338706750440267878468577499749752813207166612040496940264312520551619629517685059623=
371399997412513209265895644399166080612079 * 4036991699504854509021277196002064917772491337

j(tau) 901,
18494505556887397453829726413165132248911156454706633977375869991991407955723799811413923=
11194920902917267278253162413340021 * 1652044325928907867457421785683004162125604770979380663

p(7948), 
933949115435703912214649698936554819547755810288573976385745843232636412842399687147=
389706234224581236769974621186712241 * 2396546509690898434772028203042295773316925087067

p(8031), 
414989333506957787462763444211621261583292705468619475128121322861886693536841234596241=
148496135479904607886796472499 * 2794613692577317242171815659834260943527378496487824281259

p(8395), 
1034879541564560024627752217976822089841557582780416458226455072935115730420503942927427=
389674262293256586919296169 * 2180195511639979642112903279 * 1218127193146698943305411625219877

Dec. 09, 2000

By Sean Irvine (Dec. 08, 2000),

p9036 C86 =
10454537769748107209959314903511349 (p35) *
1307843996689531347557563031839925739250978784877037 (p52)

p9212 C85 =
187620204590705005304585400713189270041 (p39) *
47971631882468654221609551172668451254153115271 (p47)

p9225 C85 =
41881703230076090191994351608846204049 (p38) *
24088308421475038191708250677673287559714116347 (p47)

p9291 C84 =
869408418852778492647393279713713397 (p36) *
740425921360558407230752483817952020316029832001 (p48)

p9376 C86 =
2286238282016499154952468327 (p28) *
18813193204060376939986636532555186388746324782629744879443 (p59)

p9455 C92 =
117556569127796524179929013310798051 (p36) *
101705053925540550644944871787764194038428575119096153667 (p57)

p9507 C86 =
1900565456773351079799497399417 (p31) *
45788365903514780911655769750193431573179541588074169589 (p56)

p9510 C84 =
148049671293698791076249331097198366137487 (p42) *
4962942259306976351825129944197302475762467 (p43)

p9532 C91 =
3990932844020385216248800178739673717 (p37) *
2086038054466947875234526438987861008158113944035531373 (p55)

p9550 C93 =
3564069077143965284373853921343357833011022117 (p46) *
53951715717235195680752619445358118176789960663 (p47)

p9556 C85 =
57459612661831591731594602374834966201 (p38) *
21988828881945354942571468392165248930685102017 (p47)

p9626 C91 =
1532346632198528094731740259078753 (p34) *
6179108910056908250471860683777480037998586488190963306171 (p58)

p9659 C91 =
115498200186685135102374508933 (p30) *
31139535421201366834937802794838961172435900006624399201337451 (p62)

p9704 C91 =
158661904953187944127625264937015843874134887 (p45) *
6584606063562190035197813503428443543711779139 (p46)

p9744 C84 =
374188620801311937334639261985861 (p33) *
2368759783861098368870116760779995111197521259060351 (p52)

p9753 C91 =
9760267649959042149567706010665541 (p34) *
325346593763814171912407404014615580498959869103801312413 (p57)

p9785 C90 =
113248485271207050117351770773441239971 (p39) *
2914967843219248296115288590164017446445824656573381 (p52)

p9879 C90 =
91547434491264102198409833730995106859759 (p41) *
1170152861227613616935504803423997068523461940173 (p49)

p9971 C96 =
1108091673443737143530874173624982720872278129 (p46) *
144455410259294007980874687337264768128061684025423 (p51)

p9977 C105 =
785629176695451977174787275952276513133 (p39) *
135231308158490344806745031915203510020345074012266953232230119011 (p66)

p9986 C99 =
280276033271806100169306414459966979 (p36) *
1720093620238492128305725141971937699292096366329045567235029973 (p64)


By Jens Franke

(Dec. 07, 2000),
p(8853)
6611255988737908142954389189697573 *
149308745971386422996914851034020713859066804576829

p(9510)
148049671293698791076249331097198366137487 *
4962942259306976351825129944197302475762467

(Dec. 06, 2000),
p(9744)
374188620801311937334639261985861 *
2368759783861098368870116760779995111197521259060351

Dec. 03, 2000

Announcement.
I will go to Sydney for business trip from 3 to 8 December, 
so next update will be 9 December.


By Sean Irvine (Dec. 02, 2000),

p9085 C87 =
186085392581681410226855545306835141 (p36) *
848567435116444182346269975390379324912207229022289 (p51)

p9296 C92 =
400871401141915328244097913 (p27) *
56949946918614012108803240719369263190941587845124911127045168213 (p65)

p9458 C87 =
426553514928127696042627041029085051432361 (p42) *
251288726029256924323620015515205868405438627 (p45)

Above with Franke MPQS

p9993 C104 =
142979915182068538847412577488583418161 (p39) *
596368990215138100747330159110113287283481499181848497127276028029 (p66)

This one with ECM

Dec. 02, 2000

By Sean Irvine (Dec. 01, 2000),

p9075 C91 =
2113542254993233428157013688491 (p31) *
2297246139284277854960744977049978119871730457315660812052987 (p61)

p9249 C92 =
252245695763749340424957306227471 (p33) *
72014918391213182557308814333331446961027781596301303470471 (p59)

p9886 C88 =
765723211972085494587766563099151289 (p36) *
6836762766550822374650660998851399948288874844835317 (p52)


by me,

partition numbers

p(8958), p(9843)

Dec. 01, 2000

By Sean Irvine (Nov. 30, 2000),

p9078 C89 =
5945036654663959402099594807731528411548173 (p43) *
7730128725134070513258849886222868617199569097 (p46)

p9425 C88 =
10280759152397055093658120230265739549 (p38) *
182760899793203556966251125657634999728372894111339 (p51)

p9468 C88 =
24776662893515107374642690719093 (p32) *
106748533446650081009419324038411270660885101235029588581 (p57)

p9558 C89 =
23014417973022673436367417872895442451 (p38) *
519715094228664110859650220474981524882351496715121 (p51)

p9562 C90 =
3072221450900132302537649550122815215401723 (p43) *
62830550744819140762101466808729623291582569949 (p47)

p9639 C90 =
3206672680977387523366001063891345507 (p37) *
121810559116794435801562195140949892079469171152290633 (p54)

p9827 C89 =
13778915791264531846815391262904173647579 (p41) *
2870619640353476331985010110737179733551227209713 (p49)

p9855 C89 =
15091092439475036937474512185537824904693 (p41) *
762951382006301851307362910645000422947817132453 (p48)


by me,

partition numbers

p(6672), p(7439), p(7736), p(8196), p(9456), p(9518), p(9910)

Nov. 29, 2000

By Sean Irvine (Nov. 28, 2000),

p9302 C91 =
14260061467219967267087856274049 (p32) *
278259382075304752066763828482172507640709564736829427415611 (p60)

p9345 C88 =
1107896575381976947057366282707052410793 (p40) *
2344264793858981117866052036917033143415834883041 (p49)

p9912 C88 =
18859509217389126801004585676101 (p32) *
67243767891641907497159146850684758248438014339847699851 (p56)

p9072 C91 =
5430291406152805108289716333 (p28) *
1943901739765358468006865909299 (p31) *
528553178048887126535681759102629 (p33)

!89 C102 =
43112211272595213190525330079771712162300433866613 (p50) *
14180452233818404486915332467491442751546749488738297 (p53)


by me,

partition numbers

p(7112), p(7460)

Nov. 28, 2000

by me,

j(tau) 683 :
1627768660021756912355208668627944494216498937266153022866920612737035969875804400265719453123408188719600149244274411 (c118)=
424284069632555496031978253 (p27) *
3836506662697612474586056001679489246111863358865171278426651849602420187738340891656188887 (c91)

partition numbers

p(7324), p(7394), p(8029), p(8124), p(8554), p(8956)

Nov. 27, 2000

By Sean Irvine (Nov. 26, 2000),

p9124 C89 =
5130226026248296722556013055424641682192541 (p43) *
3352955073013615856302566544297958405161549567 (p46)

p9231 C89 =
754435899236717096401154615404013287 (p36) *
32418002441582580115730704793350362736737644695149883 (p53)

Nov. 26, 2000

By Sean Irvine (Nov. 25, 2000),

K90 C90 =
802504996595176662674088395794121 (p33) *
233558960892208590935329723962111393859513806965750639987 (p57)

p9177 C90 =
3956108593673586187321101130173060211481317 (p43) *
45170927181612601667902327878941196539988790117 (p47)

p9278 C90 =
2763553254955661015704488686011 (p31) *
241852314220968098682145011870350047098253713397021749670867 (p60)

p9320 C90 =
7631854522766782544490926474077198755188417 (p43) *
93593940769303535182872846558383330180669178983 (p47)

p9365 C90 =
12324628355069131714744254142687 (p32) *
23662724370673458094707417533920194008888237840010611624641 (p59)

p9530 C90 =
2478813809213122033306396801232915651 (p37) *
67017414766561715242437884962563482729441044961188477 (p53)

p9995 C106 =
2072539152752191745937956922843419265765025912097003 (p52) *
606473763543420251327080468741989326389283761346497337 (p54)

All done with Franke MPQS.


by me

#Pn+1 (100)
1636655366414096892380162499048371108725451466971057839593134713308932037459199104274153962037354873904980584959283486624454456507196358123903940584922018957634845653348571883401364480675357068187008850917585973324429 (c217)=
1783414933249556329882751243 (p28) * 
917708681193978138569199419642245119158602028208765174903613850189362922941897451819412486696821176845019482594542548111554506169777391742241512884602021652459570045945834629722235925864903 (c189)

partition numbers

p(6785), p(6809), p(7284), p(8610), p(9237), p(9359), p(9790), p(9930)

Nov. 24, 2000

By Sean Irvine (Nov. 23, 2000),

p9030 C89 =
18636972810130878249759416855643441737 (p38) *
1880320634991673318116803431641523598854366735650589 (p52)

p9031 C91 =
12768945382530060400731694046839 (p32) *
155686832801837851476632691734853725782954702835659233552677 (p60)


by me,

partition numbers

p(7192), p(7504), p(8138), p(8866), p(9117), p(9546), p(9737)

Nov. 21, 2000

By Sean Irvine (Nov. 20, 2000),

p9021 C90 =
182649200244298699880192335470090364129997 (p42) *
717932614876089962240406765508303295604620285419 (p49)

p9920 C85 =
25460220270371156592633273108131 (p32) *
77865376191717381547209893229073500360695895174690697 (p53)

p9983 C97 =
4828142967921926324051071840849 (p31) *
321706704372423841211910886656191241624590016830232057867484576439 (p66)


by me,

partition numbers

p(6824), p(6972), p(6988), p(7264), p(7442), 
p(8094), p(8161), p(8242), p(8522), p(9430), p(9542), p(9789)

Nov. 19, 2000

By Sean Irvine (Nov. 17, 2000),
Wolestenholm 3 series has completed.

W3,89 C104 =
2522194953575142105469424111502257 (p34) *
11150491599980503413116586241550686635117248974249887752804972119299797 (p71)

W3,98 C101 =
11534976112274236655481585776961398451391689446513 (p50) *
2246121955806004324623812398830703095223957944788711 (p52)

p9926 C85 =
5232165295565478847463762632279801 (p34) *
1677126825613756474138372137451519620363838045039597 (p52)


by me,

#Pn+1 (110) :
924011560340338903482995761763615732936715286457857416450581971796190593053424553371463950977622446181900109942734863043574806280513880105071581914595279692891591950154654251209554593566457298037978399034139812864285621285565390100910503786939 (c243)=
16441081297983673247170201 (p26) *
56201386246636908371605125768092209673161443376712890449642206877573342052095851227130351526002397871930984670332020138103545437466551138291683770237980632450856781949183731413177365808821850250331112848813349951329139 (c218)

partition numbers

p(6938), p(6955), p(7966)

Nov. 16, 2000

By Sean Irvine 
(Nov. 14, 2000),
W1,273 C99 =
313755919544329211796637217449289370431405803757 (p48) *
514063898765428427119117827981165558484256889602731 (p51)

(Nov. 13, 2000),
W3,81 C99 =
603979549293587780456571159952633079 (p36) *
589902674597939620091087289334437015709964883356745103059865931 (p63)

(Nov. 12, 2000),
PI Pn + NextPrime : n=64 : C100
13380709033365884759607400778414262611 (p38) *
84972002823006334706844059181786972806779543486195005306529273 (p62)


by me,

PI Pn - NextPrime : n=76
26175713492731890518147712100294806186694531805724597010927741031380956218891845960133002058352870455601816189579821216476577840789 (c131)=
2744881585572136016775491 (p25) *
9536190424504557457424559891996712529337950671153442927207611167824407606054351671676084392773716049547079 (c106)

#Pn-1 (106) :
95742699051984414970338740432881117876916477609246776542787841768229770178460433682434112156739192455496532885614832756445450827338000146159956383098788719508862425473200434595728432060738781305385640725021059967739 (c215)=
171608868874990994549 (p21) *
557912301850369265900420970551293076861649757331267727368246429685095529598040931995253362245834394040625733931517822921736277008299513617066704478399243492943710077343828702061819111913120187311 (c195)

#Pn-1 (108) :
2170087856633587896901876852969280495478913529812958790434450586578706484069963241100175308200190392307665157596300128558892410005749954118446263172768551737389451795532935126841088616961643467566659116734998124276293732699889577 (c229)=
31961871189065801 (p17) *
67896145497763530913276984700373324460200904437421143838824944020174962351716638363505858307751324168730815064754795642537951024769562793167459854361011194785234164905290268096517095065833085264369508247051002977 (c212)

#Pn-1 (110) :
349845741451052114085585150546240244792466946089686923418381980043887892182309159606013344817546345883717957390182499817396797234062647157371099596157959425597124565656989775469407123030770131387244865511499396900821658217380233882405851 (c237)=
185809449979049590103 (p21) *
1882819961473961437594903762732330699326524603214391279346549710553151838784757165116377395134328001183617207793381776232644616998470660753904786656871842359841902308484554477441212383043974192553975577783556167634717 (c217)

partition numbers

p(6933), p(6987), 
p(7477), p(7774), p(7930), p(7957), p(7999), 
p(8013), p(8140), p(8294), p(8399), p(8476), p(8595), p(8793), 
p(9222), p(9247), p(9450), p(9606), p(9615), p(9634), p(9747), p(9969)

Nov. 11, 2000

By Sean Irvine (Nov. 10, 2000),

!81 C95 =
547158369378792474020049955239655247093 (p39) *
100982862603667765481873145905514816457950125773806528289 (p57)


by me,

PI Pn + NextPrime : n=87 : 
165842249118486908743128824570397569115549898825115077650049102238002017975051691588755915124881651201381934889603624234010805277915279739563652561830772064662053 (c162)=
11470929868563791878003989427 (p29) *
14457611633820497587636793346521911993838270775869086646328497155838176525055172190176328389797888404885148650630724585074859027607239 (p134)

#Pn+1 (104) : 42822585820480483171767933459157775680598131049564497549694135624320906262255801202444785888461616224817576052099186224693181127544726289805493823925324280799396954314388961776314496933733856652712446114449593042886199830273 (c224)=
74764332127349806087 (p20) *
572767583177746341947685609742977699331140457856005061894641086655437930646164501952497642251496456876854115185089288529777783870211429010473496422737492248454639289347559781078111873811647748323450436279 (c204)

j(tau) 560 : 5441424144161474611524507829153407316004679634485449010561670610958487342217655934727273973923381456624647 (c106)=
5995828606700706786873264775901 (p31) *
907534971576797386795717632043041225134850832582849266125141173214676087347 (p75)

partition numbers

p(7173), p(7360), 
p(8018), p(8347), p(8593), p(8984), 
p(9024), p(9051), p(9055), p(9441), p(9453), p(9610), 

Nov. 08, 2000

By Sean Irvine 
(Nov. 07, 2000),

W1,248 C99 =
14363223123854881036206805242656579362775893 (p44) *
30032342460773033411700418120159094542066072575244009159 (p56)

[Franke MPQS]

(Nov. 06, 2000),

p9922 C89 =
9316996074386332796541511453 (p28) *
1271851186154520414246400156820745828411195829555147187554069 (p61)


by me,

#pn-1 (104)
38005007758652123795104911652935645397842745588748137850270967745857256553887404636014254072964330391842732819079235357139323589229798047236171078403574797936433775247713261911815150133124976259945476367803317046722815438773269 (c227)=
83295975985520577647 *
456264631142068280635149470296338272998297727045651116330095720003168554609779860631656465366388908341572163262862343999068790882429783992493316696324491256484019430760989330923526904249175324519012493994427 (c207)

partition number

p(8315), p(8449), p(8801), p(9123), p(9129),
p(9163), p(9213), p(9307), p(9369), p(9381),
p(9415), p(9536), p(9654), p(9655), p(9684), p(9748)

Nov. 03, 2000

By Sean Irvine (Nov. 02, 2000),

p(9951) C92 = 
46727728787615485451022094959279467 (p35) *
901043085743879651594930960945066095441213999686786550331 (p57)


by me,

partition number

p(7589), 
p(8057), p(8160), p(8508), p(8553), p(8559), 
p(9119), p(9135), p(9186), p(9351), p(9424), 
p(9509), p(9534), p(9738), p(9745), p(9881)

Nov. 01, 2000

by me,

partition number

p(6659), p(6701), p(6704), 
p(7051), p(7126), p(7296), p(7550), p(7818), p(7902), p(7947), 
p(8272), 
p(9191), p(9372), p(9442), p(9611), p(9932)

Oct. 30, 2000

by me,

partition number

p(6802), p(6843), 
p(7335), p(7657), p(7714), p(7875), p(7886), p(7963), 
p(8086), p(8154), p(8304), p(8339), p(8624), p(8988), 
p(9037), p(9330), p(9487), p(9593), p(9683), 
p(9799), p(9900), p(9946), 

Oct. 25, 2000

By Sean Irvine (Oct. 24, 2000),

W1,276 C98 =
3674439172613281466837490715556096609462404159589 (p49) *
9828556774768457171964908347968551714477348248021 (p49)

by me,

partition number

p(9540), p(9816)

Oct. 23, 2000

by me,

partition number

p(8467), p(8703), p(8705), p(9416), p(9493), p(9717), p(9762)

Oct. 19, 2000

By Sean Irvine (Oct. 17, 18, 2000),

p(9956) C85 =
8844780862031597857359349476105206341 (p37) *
729258050486203338251602661444017069655720254583 (p48)

p(9961) C91 =
809120180732771762645293794655027282153 (p39) *
6327790792095695494779907710122523353871627522628159 (p52)

p(9991) C84 =
4731543571743170402464569182696906746109 (p40) *
131337724912560442265361975177366128108718361 (p45)


by me,

partition number

p(7202), p(8048), p(8204), p(8451), p(8615), p(8872),
p(9053), p(9260), p(9523), p(9918)

Oct. 14, 2000

By Sean Irvine (Oct. 13, 2000),

p(9966) C87 =
1084375633163750031763613397559 (p31) *
225267882224422818315399657415229909400592974485523282043 (p57)


by me,

partition number

p(8989), p(9331), p(9555), p(9617), p(9828)

Oct. 12, 2000

By Sean Irvine (Oct. 11,10, 2000),

p(9990) C87 =
185751014140552240545529894780058477 (p36) *
2193700529733069341509403454850614832906400474184701 (p52)

p(9972) C86 =
31679569248070435479942829075419196861 (p38) *
1286861202869511720025888614792817584862606559269 (p49)

[Magma MPQS]


by me,

partition number

p(8481), p(9410), p(9751), p(9860), p(9878)

Oct. 09, 2000

by me,

partition number

p(6984), p(7993), p(8321), p(8914), p(9149), p(9254), p(9495), p(9868), p(9905)

Oct. 04, 2000

By Sean Irvine (Oct. 03, 2000),

p(7125) C90 =
308148538182059097468272109830919613949 (p39) *
705833757102594837332923447272540703696618141174669 (p51)


by me,

partition number

p(8479), p(9166), p(9268), p(9553)

Oct. 03, 2000

by me,

partition number

p(8244), p(8377), p(8478), p(8482), p(8500), p(8852), p(9707)

Sep. 27, 2000

By Sean Irvine (Sep. 25, 2000),

!78 C96 =
1660093562046267501593751931921562727211 (p40) *
280918230091725759285687637445386162596500070641808398011 (p57)


by me,

partition number

p(7523), p(8007), p(8475), p(8566), p(9190)

Sep. 25, 2000

by me,

partition number

p(8051), p(8053), p(8355), p(9698), p(9862)

Sep. 22, 2000

By Sean Irvine (Sep. 22, 2000),

W3,75 C93 =
252767720013033789205145714760268651 (p36) *
1000278187805158348550428345729743357126110419928362860727 (p58)

(Sep. 21, 2000),

p(7025) C88 =
465199804727627036677142351471088618158917 (p42) *
10321238645681518955496151687998495554242237363 (p47)
[Magma MPQS]

p(7091) C88 =
5340409122154054069383121823 (p28) *
221788558352153570561337456018668259886982035834610707325771 (p60)
[Magma MPQS]


by me,

partition number

p(8103), p(8621), p(8911), p(9155), p(9273), p(9943)

Sep. 20, 2000

By Sean Irvine (Sep. 19, 2000),

p(9988) C90 =
17877400376349764103021839766250736879899 (p41) *
32934698208846674659653470628100029900904655992247 (p50)
[Magma MPQS 83 hours]

by me,

partition number

p(7322), p(8380), p(8564)

Sep. 19, 2000

By Sean Irvine (Sep. 18, 2000),

W1,234 C97 =
1108158589204565962523131545545429581067 (p40) *
6141796769290976063185350430788762121815135627747265978849 (p58)
[Magma MPQS 79 hours]

j(418) C90 =
3405960006576059399332514199444820099 (p37) *
150359205420147104556345100588630746421904798529296707 (p54)
[Magma MPQS 67 hours]


by me,

partition number

p(9563), p(9939)

Sep. 18, 2000


by me,

partition number

p(8372), p(8742), p(8786), p(8846), p(8980), p(9033), p(9271), p(9863)

Sep. 15, 2000

By Sean Irvine (Sep. 15, 2000),

W1,304 C89 =
1978011657402113560344891596477 (p31) *
24857999219736574034958739052588802259066863824906380081841 (p59)
[Magma MPQS 17 hours]

(Sep. 14, 2000),

j(580) C86 =
1060557084701459271543854387784660639689 (p40) *
53801208085484232618938183530939654885181935441 (p47)
[Magma MPQS 30 hours]

j(581) C85 =
2688753257754085094107707764456764247 (p37) *
1513621905461039085253901824815680727916217889101 (p49)
[Magma MPQS 21 hours]


By Lorenzo Allegrucci (Sep. 13, 2000),

p6629:c83 =
38653445744129039215041272014456731051354952628605562376164063976956582330067334427
probable prime factor: 349098444341315943083675727331932041 (36 digits)
probable prime factor: 110723626446004154154805529816378587191284988547 (48 digits)


by me,

partition number

p(8407), p(8919), p(9605), p(9726), p(9958)

Sep. 14, 2000

News !

The new version of PPMPQS (ver. 2.70) programmed by Mr. Tomabechi has launched !
It is available on Windows and also on Linux.
Please try and enjoy !

Index page written in Japanese has been totally updated.

Sep. 12, 2000

News !

j(tau) 300 series are completely factored by Sean Irvine (Sep. 11, 2000).

By Sean Irvine (Sep. 11, 2000),

j(374) C96 =
784420051610136999240009577773876043934559449 (p45) *
1010262186381920771113967398696328612649392629610959 (p52)
[Magma MPQS 40 hours on 6 processors]

This completes the j 300-400 range.

j(421) C87 = 
13540593752388721938342082266048083009 (p38) *
10730995759894411665611735098288817482051981585973 (p50)
[Magma MPQS 27 hours]

j(430) C86 =
4478173417063480677384008619416930873753 (p40) *
14798714076151280656410904551592239175336320739 (p47)
[Magma MPQS 31 hours]

j(474) C87 =
5239629318438509883898317346133 (p31) *
30722185077736798924360559772821010397346756060706043523 (p56)
[Magma MPQS 31 hours]

j(492) C88 =
139332955618017994198147171317090281 (p36) *
33816549725582703787393084429649479581932905217124917 (p53)
[Magma MPQS 44 hours]

j(525) C87 =
23170372493130903292138545731773432762939 (p41) *
10176009342435094825162979874849425761360188637 (p47)
[Magma MPQS 31 hours]

j(566) C86 =
152179143562705329846059669835550960421 (p39) *
154953353346169289729892079492190949757799612921 (p48)
[Magma MPQS 23 hours]

p(9994) C89 =
795589550925945444488401269042237677 (p36) *
18653830787147825568727781468726665015616191548037303 (p53)
[Magma MPQS 17 hours, 3 processors]

Sep. 11, 2000

By Sean Irvine (Sep. 07, 2000),

#P69- C88 =
27913736083844472670791119867911 (p32) *
36386551051452777251003904141705029067927819723770646317 (p56)

by me,

partition number

p(8255), p(8504), p(9765)

Sep. 07, 2000

By Sean Irvine (Sep. 06, 2000),

by Magma MPQS

j(378) C86 =
383229197998819348626860456417603 (p33) *
141796715025451857459163506310974397086532410643578907 (p54)

j(380) C91 =
46660993666775372164624832559096745271 (p38) *
53086855489485190740538275221812666628385715765467539 (p53)


by me,

partition number

p(9917)

Sep. 06, 2000

By Sean Irvine (Sep. 05, 2000),

by Magma MPQS

W1,271 C93 = 
30840751607342204400044368477206041 (p35) *
26621353634403841330986612359444346510529421255573160731711 (p59)

!72 C87 = 
341086547294560600305675163 (p27) *
943195139017508539644251509788538096666396126273786377581417 (p60)

!82 C87 = 
888134632633709185290177617531213 (p33) *
312904082008989245602276155905499346652812245706552001 (p54)

j(313) C86 = 
278363102549760913061757708332828267943973 (p42) *
151145345596723742200179248596676604062198069 (p45)

j(344) C85 = 
562082270439106832225124045073798163 (p36) *
8299200016593958251063227795776084874419702718473 (p49)

j(368) C88 = 
4326478704922360202620123571598029 (p34) *
309741209507136353653029298495342615883764987464947699 (p54)

p(6649) C84 = 
11370130007491134052931634416793067 (p35) *
12448837642546656969097120144409231866603789802299 (p50)


by me,

partition number

p(7767), p(7987), p(8305)

Sep. 03, 2000

By Lorenzo Allegrucci (Sep. 01, 2000),

p6508:c83 =
27775764255417593196894515224980033337624326373636880300691532364893367392672490911
probable prime factor: 14583554420969830481965915279163 (32 digits)
probable prime factor: 1904594960435609561668532839153847119652900244546797 (52 digits)

p6568:c82 =
2695109974713373209337935260399387382673547613429148272982601454242516151134255771
probable prime factor: 24595936750252042690479073061446699 (35 digits)
probable prime factor: 109575414918309851603906229985870777950232648529 (48 digits)


by me,

partition number

p(7095), p(7866), p(8043), p(8122), p(8619), p(9344), p(9586)

Sep. 01, 2000

By Sean Irvine (Aug. 31, 2000),

W1,257 C93 = 
818824131288395174486486931698236354321855657 (p45) *
588867010301983664655911869831705147666808208263 (p48) [Magma MPQS]

W1,324 C93 = 
421045101551675499437360089 (p27) *
2027940337302788552955799760502231221493867342962222268443036294209 (p67)


By Lorenzo Allegrucci (Aug. 31, 2000),

After 127 curves run, 
p(6476) : 27547205825365146462281863161447210912928116023002292859179424634010060494971444721 (83digits)
1416671733830733741131223813015583 (p34) *
19445016913605288131546716681039839498280487983087 (p50)


by me,

partition number

p(8367), p(9180), p(9335)

Aug. 31, 2000

By Lorenzo Allegrucci (Aug. 30, 2000),

p6387:c85 =
2408808191892077765238938259221299921796192824522959537488479785054665584522101654041
probable prime factor: 282397839787851651494200082238005327191553 (42 digits)
probable prime factor: 8529839299414149504930772348273231141327897 (43 digits)

p6430:c82 =
2155257316935481513752964855113970425350161795073655001102707219028637998647505163
probable prime factor: 182275254594231082254932425395031 (33 digits)
probable prime factor: 11824190407707126558127129875774096694015239940973 (50 digits)

(Aug. 28, 2000),
p6663:c81 =
103205127555806237132468934798207214537505030542676098937286251735808734836731671
probable prime factor: 2539680984755680940555269184447 (31 digits)
probable prime factor: 40637043855228392579311536467902460706129048052393 (50 digits)


By Sean Irvine (Aug. 30, 2000),

W1,274 C94 =
1208280234770123639161045560863077929467 (p40) *
2436571937273339727119951469270392112756049792049101979 (p55)

Aug. 29, 2000

By Lorenzo Allegrucci (Aug. 28, 2000),

"1h, 58m for my MPQS to break the cofactor of p6427

c81 =
228807064456081565269163801884172952947680237190341470690641587676633342512791089
probable prime factor: 20945055164819545781142854735645198738593 (41 digits)
probable prime factor: 10924156687846702810579216629902443126673 (41 digits)

 How beautiful primes !"

p6339 = 2.3.3.5.c83
c83 =
12463881331914600264912022715310834871327175040403507519457385513219572075752504259 =
1689098453793184631559095802821827 (34 digits)
7379014114852001272275021523551811931034652431617 (49 digits)


by me,

partition number

p(9488), p(9848)

Aug. 28, 2000

By Lorenzo Allegrucci (Aug. 26, 2000),

p6280 = c84 =
436735170883829206872574126693737544348277580409575241811976917342060341283507064683 =
27907004516436377952143099749717208596229 (41 digits)
15649661382560978823998955331390679560388527 (44 digits)


By Sean Irvine (Aug. 26, 2000),

W4,71 C89 = 
143321079907405000447907814947483 (p33) *
377297418991860509691002545184260467815302597446333979973 (p57)

W1,348 C91 = 
7094238456474417074502626789116222649 (p37) *
627181357485754864333747373180857335281727551621450413 (p54)

by me,

partition number

p(9195)

Aug. 26, 2000

By Lorenzo Allegrucci (Aug. 22, 24, 25 2000),

p6228 = 2.3.7.37.c81
c81 =
121930615316755497988987313821876696958781172687829681547356613109643233200408079 =
5482765114073857563795494150587445776087 (p40) *
22238890920891087380632327536255280935817 (p41)

p6201 = 2.c83
c83 =
61325515918937040651097024781979738310263578097785926744566602704900988457583580357 =
53795732734405811397189314165069 p(32) *
1139969897272455057891007382593324046178974863019353 p(52)

p6184 = 5.11.c82
c82 =
1694990310934387925836887912626177280006573217702290400313385465568132947049082527 =
44488136668464104429446376906737 (p32) *
38099827007047928163449245408697947008028273526671 (p50)


By Sean Irvine (Aug. 24, 2000),

W2,155 C93 = 
1720608167723729894235025890365809470299213021 (p46) *
385800040917037380193401849474414322127625599029 (p48)
[Magma MPQS 83 hours]


by me,

partition number

p(8271), p(8985), p(9126)

Aug. 22, 2000

By Lorenzo Allegrucci (Aug. 21, 2000),

p(6157) = 2.11.c82 =
2738729138919029704253489572431904701076632943949779058468910377327936806375891103 =
42987588105958625048344667630594029 (p35) *
63709765064474671057810679281510995062500770107 (p47)


By Sean Irvine (Aug. 21, 2000),
(Using Magma MPQS)

W1,285 C92 = 981287002468353896697722535285593108093.P53
W1,320 C87 = 29492569461444800997714841174395858397.P50


by me,

partition number
p(9131)

Aug. 21, 2000

By Lorenzo Allegrucci (Aug. 15, 2000),

p(6121) = 2.2.5.c82 =
1680955917251413120660610292463689639840776985609619808808979823004259787374407083 =
312695418065619558549019212841 *
5375697308422543743153832174351343649264653617354163

By me,

partition number

p(8050), p(8067), p(8083), p(8163), p(8264),
p(8466), p(8599), p(8645), p(8744), p(8940), 
p(9092), p(9106), p(9266), p(9703), p(9728)

Aug. 15, 2000

By Tetsuya Kobayashi (Aug. 13, 2000),

PI Pn - NextPrime : n=57 : 192229 * 4474741 * 8850559 * 40235377102122950297181190344218600420563 * 3814688413548089734125036007609141611913380445223 (p49)


By Lorenzo Allegrucci (Aug. 08, 2000),

p(6086) = 2^3 * 3^2 * c81

c81 =
264361779623153204152529925789604368707826849909457214701370936795137285519564751 =
11690823562985893872194337803898640613 * 
22612759332040924636928110621003125770571427


By me,

partition number

p(8065), p(8711)

Aug. 07, 2000

By Lorenzo Allegrucci (Aug. 02, 2000),

partition number

p(6711) = 2 * 7 * 7 * 54323 * c80

73179466870915712190828150668078009438832014555895161910724242019813171126537541 =
140624089277310500651431778357850303223 (p38) *
520390690151286308924147668405849455599267 (p42)

By me,

partition number

p(6664), p(6711), p(7207), p(7295),
p(8071), p(8078), p(8222), p(8252), p(8387), 
p(9100), p(9948), p(10000)

Jul. 31, 2000

j(tau) 511 : 11604649876729011351706790599217874435642048190993847354654040438841484501122721405518193066439239946163051270300813289 (c119)=
141701699947191320281163597 (p27) *
81894923498121576080722406610426784583366937167314385102643495711686230122433762823652666637 (p92)

j(tau) 559 : 4501550542324163239003706605028003355022643309751309279121573522497796659652708321964975195687201 (c97)=
712676363642937314846821273 (p27) *
6316402187542611928961184993927630639465742898341092725508832216833737 (p70)

partition number

p(7089), p(8037), p(8507), p(8755), p(8881), 
p(9107), p(9176), p(9198), p(9591), p(9982)

Jul. 24, 2000

j(tau) 812 : 304566139107255907879498324583369827504760784372862518924263128659083177053892210387438242238858261516695923462939524881447430872995014048327 (c141)=
6429557541445460715588428267 (p28) *
47369688682929942917762477506115562623161728201037272201172197559253167341283307136857702499752259785138624796181 (c113)

partition number

p(6111), p(6456), p(6714),
p(7163), p(7365), p(7635), p(7754), p(7928), 

Jul. 17, 2000

j(tau) 871 : 1922100338268332612501677604214402019375722107410256518462502569902003601788948018473349655432159583913975581174244764447058695959 (c130)=
13563002523503748090176059 (p26) *
141716432990222133429613442411927182366778984858285750949844416016676048833092397463196480372360695846101 (c105)

partition number

p(7682), p(7792), 
p(8352), p(8414), p(8587), p(8678), p(8822), 
p(9073), p(9121)

Jul. 10, 2000

partition number

p(6051), p(7116), 
p(8112), p(8330), p(8528), p(8569), p(8574), p(8647), p(8666), 
p(9128), p(9519), p(9670), p(9963)

Jul. 3, 2000

partition number

p(6702), 
p(7269), p(7381), 
p(8490), p(8494), p(8694), p(8725), 
p(9256), p(9559), p(9782), p(9925)

Jun. 26, 2000

j(tau) 723 : 2816703438085758007348406745403929513196253827187358952791277915823985971922355343421175812636664814566170418233199 (c115)=
1878630509173260831432014713 (p28) *
1499338706750440267878468577499749752813207166612040496940264312520551619629517685059623 (c88)

j(tau) 835 : 38835901755617443289994541426794923454443811285156088509836668429739753923101207694375164110875648583056653531943648815197935902696539290831 (c140)=
2185821087461536145037061160207 (p31) *
17767191458802704027515561416704499134653430028210847421100896821993220894381028623143584888647707287932372033 (c110)

j(tau) 857 : 1448437323949159588647197025048897232790586196829560377999323766677002136689248134548312034579215411735570909931412280880843622909953853171853 (c142)=
431287820318867790039985368289 (p30) *
3358400714581445343668420508311543850141888100440600586834181894305615730027081623838841913388762335047775282477 (c112)

partition number

p(6910), p(6958), 
p(8080), p(8111), p(8157), p(8436), p(8561), p(8618), p(8884),
p(9196), p(9385), p(9399), p(9443), p(9807), p(9808), p(9899)

Jun. 19, 2000

PI Pn - NextPrime : n=69 :
289502027296977600921755794484965093268075686283329114952409552677911275196394160943681723027348943210419172494266377167 (c120)=
285031428189231310091745105743741 (p33) *
1015684583051586425869206984659817521450418658049087388627028688660294310611164138633787 (c88)

j(tau) 394 : 3559247070810282801700879372317659789462449951134415517753569993671407417330428972331411417 (c91)=
338760958646814453345897887715427 (p33) *
10506662529908247634984098911636650211727998882313202644371 (p59)

j(tau) 454 : 17933429772866503773733847486388372454611069468721592412864596585575971929898551015689 (c86)=
132654323775582701399959303 (p27) *
135189183906325550503242734678602811636871197264599424273263 (p60)

j(tau) 718 : 8471504737514329477606439802380666885910953591670730432816458656394863163757740530480614979445333361243970290201 (c112)=
68502663971763633870025501271 (p29) *
123666792593733731456089417589865878824933958231574592688596145392677267796873154831 (p84)


partition number

p(6399), p(7229), 
p(8017), p(8183), p(8513), p(8675), p(8696),
p(8716), p(8748), p(8833), p(8947), p(8985),
p(9099), p(9102), p(9148), p(9193), p(9541),

Jun. 12, 2000

j(tau) 657 : 39461310212075585312341462328440384222228841385895515818608963632717556184791157370378796637 (c92)=
101916804240363593043269036168929001 (p36) *
387191400929417576609738620591532594073767861129404023637 (p57)

partition number

p(6679),
p(7445), p(7758), p(7793), 
p(8162), p(8316), p(8691),
p(9008), p(9012), p(9142), p(9321), p(9671), p(9788), p(9963)

Jun. 05, 2000

j(tau) 588 : 3829433161283203275715476259680466240257159914219977368196957399305363354231173454231243789341499732239124864844530893 (c118)=
7351532234186072141418038153 (p28) *
520902723309242282582207845451963793471512874840970567472659505852817721081831438537388581 (p90)

j(tau) 682 : 5765336868216632777645860365423649390094587597454700026647467198872965356910017681674344452224347784087 (c103)=
153264220922405520631647233 (p27) *
40696516965747611290778790546341580641 (p38) *
924329182839672202742336162694391167479 (p39)


partition number

p(7896),
p(8144), p(8212), p(8581), p(8633), p(8892), p(8922), 
p(9009), p(9462), p(9633), p(9892), p(9992)

May. 30, 2000

partition number p(n) : n=8001 to 10000 are added.

By Tetsuya Kobayashi ("Hamayan") (May 29, 2000)

Wol2(148) : 149 * 132044977 * 16161203558366750221121587 * 5923442769373245169148572285453 * 1158740261210815830120173302351743969293320436367394711 (p55)
Wol2(195) : 4007 * 1128644983808809609189 * 90929047927095235887737 * 21550415707234381953073165168859 * 30910439606880741734566811699484190549 * 220573516062896217345366361820950413265827615485501 (p51)

May. 15, 2000

partition number

p(6295), p(6546), p(6810), p(6895), p(7118), p(7478), p(7629), p(7831)

May. 08, 2000

partition number

p(6072), p(6135), p(6343), p(6675), p(7704)

May. 01, 2000

j(tau) 578 : 8573052796814692272916011350264206414541945859575331785656218468372619233059155825573801856555728466092060613661143309482427 (c124)=
30660312288806698203385062040681 (p32) *
279614007713303567616042687668719228613814852705185082371349402336207499049388102395060852867 (p93)

j(tau) 668 : 651510817645578486765500565400285575798383046482700819354309037664278004711109261125870108158158148236273122913051699880467271 (c126)=
1491340001617283746955978999 (p28) *
436862698605983574945159994357234837239301497586162770932714461224708547283596099496034769345223729 (p99)

j(tau) 679 : 434147604997140460128166339004295383117038914444139300560435375211965839200510011930421 (c87)=
466171938811251693446464253 (p27) *
931303600350175598153008570646369152079786244705723380156057 (p60)

partition number

p(6312), p(6593), p(6689), p(6857),
p(7200), p(7274), p(7312), p(7383), p(7503)

Apr. 24, 2000

j(tau) 901 : 1527995257709640262841062537090216683340401682751250272381236866679480987968240721235691799406138763940713378395542678637 (c121)=
82618875806637135425994427116719 (p32) *
18494505556887397453829726413165132248911156454706633977375869991991407955723799811413923 (c89)

partition number

p(6489), p(6960), 
p(7079), p(7239), p(7288), p(7316), p(7520), p(7731), p(7778), p(7996),

Apr. 17, 2000

j(tau) 676 : 7120642882568167231880174511656371811035634902052885279070914495533382706024905367528063361254395530002700602913 (c112)=
288122121969035045556337639 (p27) *
24713974872548781026714997679193619028206213255695017299769141337023355843869406454967 (c86)

j(tau) 762 : 4391235333959625058056019523481527103118193665317259132522660326754705723287369465857982979098460609846334557932944082788499171887 (c130)=
26089233078716539265075233 (p26) *
168315999198227563770401685016026771098514914328107382595572276079726703172811921149235289072499635906639 (p105)

j(tau) 776 : 1556884904998476350557080620071736898906819709910674498516630426018294362961518143070657327938122782166026523314468887299597256029343190946799 (c142)=
5348562397872270331891021 (p25) *
291084741877149267583179968519759520005144831934722411164475489383251357977495869562662504544228090248144968109029419 (c117)

j(tau) 907 : 50531507167773806210502939544269069898316928859697318128118653570358573359787958866102942907421262985489733133281 (c113)=
32802091897021901515262387 (p26) *
1540496481944237112789891784125558108098026491281251615479551102603740137661811866036763 (p88)

j(tau) 940 : 165478527720494339769751690739058253735625550792788345857050637875995883406733783746619383234722250749017378847656789167 (c120)=
858004646629143142041257701656415069429 (p39) * 
4112054645314965395202476473925233947301 (p40) *
46902191014686168947428624709052996420823 (p41)

partition number

p(6141), p(6205), p(6324), p(6519), p(6959), p(6970),
p(7056), p(7060), p(7198), p(7270), p(7349), p(7372), p(7490), p(7658), p(7830), 

Apr. 10, 2000

Wol1(255) : 80541843759695619953958042854211904988176810888887323141862700913051394415047792956254583909 (c92)=
42026920200826160611761287647 (p29) *
1320441948895147791734332512991 (p31) * 
1451358460539140599171997975879717 (p34)

Wol1(320) : 4014558756707711497942213051859459098550345410098980610984854789671301013872393876793371119244239643550417640207961 (c115)=
8489039904794192280516571723 (p28) *
472910812262819748605373020917018503915170947604911008900637142542944524843413588243307 (c87)

partition number

p(6009), p(6226), p(6604), 
p(7211), p(7251), p(7279), p(7393), p(7401), p(7613), p(7757), p(7981), 

Apr. 03, 2000

partition number

p(6731), p(7062), p(7081), p(7266), p(7463), p(7579), p(7662), p(7785)

Mar. 27, 2000

partition number

p(6639), p(7289), p(7631)

Mar. 20, 2000

partition number

p(7071), p(7143), p(7212), p(7275), p(7334),
p(7400), p(7426), p(7690), p(7789), p(7924), p(7969)

Mar. 13, 2000

partition number

p(7918), p(7974), 

Mar. 05, 2000

j(tau) 537 : 117595425511365264582457071572582161531642717235252527049262401932220581435068224746729 (c87)=
85347480491366142394682008774327 (p32) *
1377842964248503674789414552290380690737967610584293727 (p55)

partition number

p(6699), p(6894), p(6947), p(6989),
p(7077), p(7124), p(7161), p(7364), p(7438), p(7498), p(7510), p(7525), p(7562), p(7618),
p(7747), p(7783), p(7804), p(7847), p(7879), p(7900), p(7906),

Feb. 28, 2000

Wol4(93) : 1398728326987876000585166847803276155660527898845921096567461338512987055966141182803621357984723956247 (c103)=
4030605259546089252506534781931 (p31) *
347026869891346101825378269799882924813176486706025887430770827847080837 (p72)

j(tau) 955 : 1372167645796803504511198379120039926624699917318381211592499095370859318543390724299758207248249498511208752393423032385035887669585463751471093227175317 (c154)=
6682868115691115512359744399915137 (p34) *
205326159673121038461171344526449519872400388063423956987786596519639248921944657813231108653797516742203239352392293141 (p120)

partition number

p(6334), p(6684), p(6859), p(6879), 
p(7247), p(7331), p(7359), p(7436), p(7447), p(7487), p(7539), p(7656), p(7665), p(7802)

Feb. 21, 2000

partition number

p(5466), p(5590), p(5645), p(5731), p(5834), p(5839), p(5884), p(5897), p(5910)
p(6335), p(6538)

Feb. 14, 2000

Wol2(170) : 13512475206617811656547051853517883769378751257517150107010915072566825464472182325453082545339654533494226411686540884569902908756313 (c134)
755315132885705521237919351641 (p30) *
17889851028130430500640441946590024128246109043145663854246617809881576072224457444417038176715716705793 (p104)

j(tau) 831 : 28280930366041833173768456921902611212070900062487108794786236677154156850740100591700077823625042756796305014531401706171848715232712904559100873940713 (c152)
602114763419795175570091231 (p27) *
46969335555594627909492200149619049495415178896769425273615888183134696882897131272781480212912633933190935137817023109850423 (p125)

j(tau) 896 : 42571521827327920755135024144586341869522241327692401441077372818737736705252166900161437442307238462156468660601035391298952425281170541290221839 (c146)
1287310678562777525717032447 (p28) *
33070122493551474326429028586770268145455668268605539571596936841913129050422975320567776805010275117094193790869277937 (c119)

partition number

p(5478), p(5527), p(5696)
p(6071), p(6419), p(6566), p(6601), p(6603), p(6635), p(6651)

Feb. 07, 2000

partition number

p(5533), p(5618), p(5720), p(5858)
p(6241), p(6341), p(6760), p(6839), p(6932)

Jan. 31, 2000

Wol4(62) : 23963403643068484048757051695401886282854107263957656359255410505349851306377290714103366447 (c92)
258468374092734108249956370173 (p30) *
92713097790721651702128474941600208310519488311405047832438939 (p62)

partition number

p(6119), p(6293), p(6361), p(6625), p(6642)

Jan. 24, 2000

Wol1(256) : 42937389227690104114600077662903045031408601580199266276912000007694932544871887963880519942639 (c95)=
173478361465666347211070280827 (p30) *
247508616434493929743107334452074647902047452880528465264491286557 (p66)

Wol1(317) : 245600878725326985146281725040961929198182710177834192143979002967613830481427598535966643513949028981500483074896124315285931723 (c129)=
1075057622600065015738171 (p25) *
228453688027747334314019042520196931565126236553556990975144660396429492621522681497808581017812904750513 (c105)

partition number

p(5627), p(5941), p(5952),
p(6077), p(6185), p(6668), p(6686), p(6818)

Jan. 17, 2000

Wol1(297) : 60802349367425550063740373304843251891965212272616186804032711612026574159343081075930622326034557 (c98)=
56392524021772514772370646356121 (p32) *
1078198758118194030028879509333658573326609017633739249336537520517 (p67)

Wol4(79) : 931527156592108631209410331934668750473940790646279870940175802723819160338514433638086602321361869 (c99)=
11352571942690042069466490660707 (p32) *
82054283495813650543203839822325241640274480088082582574175324663567 (p68)

partition number

p(5131), p(5326), p(5423), p(5434), p(5611), p(5774)
p(6641), p(6767)

Jan. 10, 2000

Wol1(324) : 1301879057228900715250502702612040021516471726260025940198871463676494183629050339757282963198431367089393706754159595201 (c121)=
1524708592812605872540410601 (p28)
853854345260391672271602914149254134667317442348573837800671971406269175755889130356478424601 (c93)

Wol2(162) : 23205400799999854142664195201078291321523135526556301609148000631304285825326238056481746251 (c92)=
460567906323549410738923768243 (p30)
50384320056591257745763890699107200282018342725366454654734857 (p62)

Wol2(193) : 162971944213062683112965451097717869793227125225896790086596855124243491708125454078064258034790631266932014853036937529691755616186507827 (c138)=
58696468410756153296430694389791839 (p35)
2776520438548190467371766696805836769424719312441403594593984937191761303803681468501643564320063941293 (c103)

partition number

p(5942), p(6003), p(6202), p(6368), p(6646),
p(6685), p(6874), p(6877), p(6878), p(6886)
p(7000)

Jan. 06, 2000

partition number
c74 of p(5416)
c74 of p(5896)


Jan. 03, 2000

I factored,

(by GMP-ECM B1=1000000)

Wol1(245) 201971042190895676858592072669931535314741848000686347167292682645508302197146403619415767364139789105439089 (c108)
into
3996553190909505452964614248543 (p31)*
50536307799004328863367253927483383204837628939098003539188806838545515698223 (p77)

Wol2(142) : 106921010700393464367434644220383867698266973231923120970913630153086467179700022186286381111753287930166021000220333920517 (c123)
into
218250580293934076559444583937 (p30)*
489900235575067388216896602818582274693194494203911447432865127463845851676186108616828654341 (c93)


index
E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima