old log (January to April, 2003)


April 28, 2003

News ! Phi(138) series have been completely factored. Last composite number was factored by Sean A. Irvine on April 27, 2003. Now phi(n)<=44 have been completely factored.

By Sean A. Irvine (April 27, 2003), by ECM (71 581 (739598118043 982015158224990910789722520751) (P 152)) (71 582 (853 4693507541 410151596968049 21978376124466277031 84734794330718881741137411239935583) (C 113)) by Franke MPQS (138 834 (28429 3381897139 1166481392809 6163108700193379889834401409201230206674333241673) (P 54)) (138 983 (50905027 4806515437 110875660333 67789485878413952502960800134846382315434273) (P 60)) by Leherbauer/CWI SNFS (138 756 (139 26497 7845760108982550004468437163543770387905270390879479) (P 69)) (138 774 (277 117579589 11989500699231159929262120698045712384663421) (P 74)) (138 797 (139 4003 734738985676527860136811593588479440295669449422227707) (P 69)) (138 826 (3742063338116852461413916545791182866326203467931) (P 80)) (138 835 (7979573432736002007330730311433096213) (P 92)) (138 873 (616418401 79866397892947 44055798661277891077856271999076703623080398383411) (P 58)) (138 877 (117577 25845044469578759421409705443050349675768229854004890240466099) (P 64)) (138 894 (277 829 967 5659 1122236796631534246521749310585063975658184299) (P 73)) (138 906 (139 277 967 112675008715773943 10371481210023422433455392374096856875065970476125177) (P 54)) (138 925 (9751909 310441447429 1637273237761881160493087200050950505893147101499311) (P 61)) (138 927 (139 4969 262440397 132540290701981099851685102766046595253297539) (P 73)) (138 930 (2347 5107 3365486731161076972373170292408738064666038968107931995099289) (P 64)) (138 942 (139 2111893847726862790183902457409664579803417835698113) (P 78)) (138 956 (9109 411241 473479 543859 52337990092128092579933783113326961907983) (P 70)) (138 979 (26497 637699 581488807 397146172543293778121144261267642571255139) (P 72)) (138 980 (108883 10907383 27053570647 355321868956741816437253504259724158557980245800025803) (P 56)) (138 982 (2855911 557212261 325027374419107508125440721987664263459323442219401056773) (P 60)) (138 987 (967 1933 37856313485533 190408977080268141747182125134043727879187353340049) (P 62)) (138 990 (139 1538839 2144645316803246943976388771838890806453 284651443372729821877723492340703960144691) (P 43)) (138 999 (139 3037 4831 11850694813506363730588390805989131671663450387736821866297909) (P 62))

April 26, 2003

By Tomoya Adachi (April 26, 2003),

(104 857 (313 1639426498227279529 8738005635445994338081086794973883440059473) (P 78))

(April 24, 2003),

(104 714 (6789017 267230489586355958322158132051872252553) (P 92))
(104 844 (313 2334426902583622770125984519458978567672441) (P 96))
(104 868 (152287969839617 4236687675247827281 1093304293569761808801913627776314173381273) (P 67))
(104 870 (26209 48049 113353969 1295620873 98442212857 2219233989404824577453864490332168622368684377) (P 59))


By Sinkiti Sibata (April 24, 2003),

by SNFS Ver 2.01
(81 233 (503772532459120822322023319930849042356027) (P 87))
by PPSIQS Ver1.1(Linux)
(154 290 (629981904553 549781561855055430671 5883977488490162395027 8393470267062200018243993634198975237952351907) (P 48))


By David A. Miller (April 20, 2003),

(192 469 (2689 6092353 318853813973171706004190209) (C 135))
(192 486 (1153 95233 66715313005441 148832596495847426682232768513) (C 121))
(192 521 (193 769 10177 7024513 122583789882986624833 200447841113565142470260929) (P 112))
(192 631 (193 448238149633 29059951909607337217 8863236959865136813711374721) (P 118))
(192 643 (1628781189452321187201541057) (P 153))
(192 648 (3471344641 6151848723841 6622267044939264137902536961) (C 130))
(192 667 (769 1153 36826371649 6716681876029957867496686082881) (C 134))
(192 723 (2113 695191873 19296430993792315833090433) (P 146))
(192 847 (4046295361 2175208790977 163132064531121519211009 2644965942787596929055862081) (C 115))
(192 880 (733759681 815294612191556607999626113) (P 153))
(192 928 (193 5002401409 4081510239346022856577 27857755858391424643224961) (C 131))
(192 943 (193 3457 118081 168193 46300993 8874540673 307698008303613698837521325953) (C 128))

(April 16, 2003),

(192 105 (9535226150337134522266549694936148673) (C 93))
This is 5th largest factor found by P+1 method with GMP-ECM 5.
with PPSIQS
(192 105 (9535226150337134522266549694936148673 1870501082366830344705802917274649013910273) (P 51))

By Tetsuya Kobayashi (April 26, 2003),

by mpqs4linux 0.61
(105 194 (211 631 15740971 4562925568165801394099442882869812707389041) (P 55))
(112 798 (3361 432433 10861176612453889 89951065378454897 371133857161238345500027988272561) (P 65))
(130 393 (2731 130505051 1169053308640751 4083372845071127204007498986076431933277868389211) (P 50))
(140 352 (421 4599999531303751361081 1159418097242698878613200094861) (P 68))
(144 466 (96769 938881 1292186737 19253066977 148552292700292861538119504496338959710761633) (P 54))

(April 15, 2003),

by mpqs4linux 0.61
(130 255 (131 8581 118691 60982741 588729635395764913655016491) (P 70))
(130 567 (145861 460721 739196933281 4567837946491 9453374030594447110597732453065584551) (P 60))

(140 206 (421 51941 15919838761 25219901868907187517527007004753826741408092961) (P 48))
(140 422 (319901 893346721 623369688074561 324493421863120193461935560559972481) (P 62))

(144 564 (433 43201 1229704561 3456057601 7799385313 3963755179347380371857448894321) (P 66))

(156 296 (157 1136980573 1440640505929 59929617173778034443671097214215553) (P 61))
(156 791 (13 157 1062673 1959361 777545103661 1826770722086701 879065002588236587724314100298017245395624369) (P 52))

(168 186 (1421449 10230697 636662322544533501659487779858593) (P 63))
(168 375 (358767193 6237236819236592401 106729198208873291317094360523861930481) (P 59))
(168 972 (241249 1533841 2278196929 6480265681 43864717419165217 1257398806272242953871229168149064259874833) (P 54))

(210 193 (28244221736431 3263614988870561857631324459199640652091451) (P 54))
(210 378 (211 17591245159699371974214241 155228089549313349617256484388516514773251) (P 55))
(210 385 (211 1608151021 27366707853563401 265962730692538109366802002298151939075788653011) (P 49))

by GMP-ECM 4c
(94 901 (1219854094681 63637415260506549567902622461106795782179) (P 84))
(94 941 (471383775944472083621 424458741564222465024220187225265037121) (P 78))

Errata

False:
(192 959 (9601 166657 195232416330107329 11682098500465423755247314049) (C 137))
True:
(192 959 (9601 166657 195232416330107329 11682098500465423755247314049) (P 137))

April 16, 2003

By Sinkiti Sibata (April 15, 2003),

by GMP-ECM4c
(81 399 (6481 891144143703149229178544941999021) (C 104))
(81 443 (11632801231 2185903746811 65721166909109931739562285563) (P 92))
(81 469 (3 163 811 1783 5677129 38088153679374209542809117961) (P 101))


By Philippe Strohl (April 14, 2003),

He reserved,
(180 261 (c99))
(180 812 (c98))

results,

(180 238 (181 21858821407081 27199020176668943419152881391173281) (P 65))
(180 246 (1492008020078941 149408461351801776242666882161) (P 71))
(180 284 (181 12629123229822481 4329966829671252845868383966701 369236793062240012542183612439221) (P 37))
(180 418 (1621 2351596360222281069176581 2139757763758529153433681241) (P 71))
(180 524 (7054381 36895041901 334456993284121 20472916271386512763622341) (P 74))
(180 534 (1801 16741 1423439821618642764937081 19563510435604266060710785550888128621) (P 62))
(180 536 (1995121 754383813121 122020910578261 4311268606300290049183626721) (P 72))
(180 768 (12241 270039241 1101688921 245637493206300361 67037874713644834722810021845368681) (P 65))
(180 954 (1986121 2457665911621 313319995676491655901181681 8112944270728187435402916689021401) (P 64))


By David A. Miller (April 13, 2003),

(192 194 (1416317953 8035712659951009157280043969) (C 110))
(192 258 (185089 3616547329 51836036869427189513177089) (C 114))
(192 274 (476280154285986108567361) (C 133))
(192 294 (769 108289 3364376574845302442865793 3897303728501267979725075222401) (P 95))
(192 394 (347329 642662670566977 5446603644474227321473 4128812445998244722251201) (P 100))
(192 405 (193 540524737 1000374292934432238959689537 622869585741055279315943281556923161601) (P 91))
(192 427 (193 1153 460309712608234631359873 1795671525470612515474489537) (P 113))
(192 471 (1096005313517159731014337 42276588242282405065819201) (C 122))
(192 508 (14593 2966002947256424756011224746113) (C 139))
(192 510 (7451746611883075193289638017) (C 146))
(192 530 (577 46273 1008001 20209820161 4313263728769 382090592458321930672040449) (P 112))
(192 581 (91009 12012289 67907713 580416715972190508065329729) (C 131))
(192 671 (769 84116596480227457 19346820259604016366003953427833089) (C 127))
(192 685 (23041 1791860874196993 13745083446533972874135119041) (C 134))
(192 725 (193 2229697 5165978497 36331326153601 63993339797092609 56852083102647935878273 20695714331561536292896968057409) (P 81))
(192 758 (1458433 3451231297 4114672742209537 362532181413709824961 6745573912012325819744965057) (C 105))
(192 814 (2162879547457 21340305173953 155981085393748196317536665281) (P 132))
(192 815 (708172033 28835829473721557301482497) (C 153))
(192 873 (577 597447553 244951564142100908353 14741580792650487947464129) (C 132))
(192 901 (5569 486801810241 76645567876417 28704880442479253617465153) (P 135))
(192 951 (715777 1088641 1396033 2860801 353235674881 41312310533807169410693569) (C 129))
(192 955 (193 577 15361 455889086844334841021761) (P 158))
(192 959 (9601 166657 195232416330107329 11682098500465423755247314049) (C 137))
(192 983 (43969 118273 4875399064163163848872203838657) (P 152))

April 12, 2003

By Steven Whitaker (April 09, 2003),

(104 503 (6449 57349503121 3224822163903763720987499531765345940457) (P 76))
(104 504 (937 1469521 87891708600490500921578269327594162642177203204553) (P 71))
(104 505 (1873 2192639481970329289 18571253040509803607943952962206676567024817) (P 65))
(104 516 (4223851217423606699436099461863408834513 59092626314209713213788628661708392959387609) (P 47))
(104 518 (6188338974596841170378676554515202179371310502830649478857) (P 73))
(104 523 (28397282565404574776802569883718705092391652870809) (P 82))
(104 524 (316681 15227473 68887708553 130466341043255341052386363453878178229978416288244569) (P 54))
(104 525 (554633 17291542310820857 50809652715016338847012378570457794406863529) (P 65))
(104 531 (313 37849033 1405121038355811817 3132195664669992137208774367442521) (P 70))
(104 644 (2118169 2654277170701838782383068482841 1759915321687758898506990876500682882569) (P 59))
(104 866 (313 42017 1295737 11015993 353939570041833747089873 2671949424242888012491968230916699535376153695217) (P 49))

No composites are left with less than 100 digits.

He reserved the following:

(104 539 (9049 21280793) (C 120))
(104 540 (42464798377) (C 121))
(104 545 (521 102233 151392584513) (C 113))
(104 549 (76129 3583633 267402617) (C 112))
(104 551 (1) (C 132))


By Tomoya Adachi (April 09, 2003),

by GMP-ECM 5
(104 879 (735697 1050713 317799137866215467289486807763858498789873) (P 88))
(104 903 (1249 34177417 61776937 26848771190697463676126414422399674139067761) (P 81))
(104 938 (9175760752521469289 3404996789350828481592735019564914096762885445969) (P 76))

GMP-ECM 5.0 [powered by GMP 4.1.2] [ECM]
Input number is
5047707267843693383247295673601455470936826285343961856442113677861425012058637138956151575533331689982645333593065184299849
(124 digits)
Using B1=43000000, B2=178426462988, polynomial Dickson(30), sigma=3138162930
Step 1 took 823954ms
Step 2 took 729529ms
********** Factor found in step 2: 3404996789350828481592735019564914096762885445969
Found probable prime factor of 49 digits: 3404996789350828481592735019564914096762885445969
Probable prime cofactor 1482441124065215914258199513617396275611319533577135760436883106169336550521 has 76 digits

April 09, 2003

By Sean A. Irvine (April 07, 2003),

by ECM
(71 568 (2131 17467 10109123 9556769218668429497 1395240041206419416930849234969) (P 130))
(71 570 (1279 7470667571 167735051921 381907874033734538610627961908833) (P 137))
(71 574 (569 83639 12668509460863612928038193145545563) (C 152))
(71 577 (853 36779 10726496610062307275836483367 41085030122340055287387115643) (C 130))

by Leherbauer/CWI SNFS
(138 462 (1657 89563 1088381694789297894175405246988212854767110531) (P 65))
(138 468 (691 36571 147799 1328334871644664024289165069251881782576702269) (P 60))
(138 488 (7626430661556753994469411262015375560048229186504029906911) (P 61))
(138 490 (139 470668837524823059590885382024469303349230573) (P 72))
(138 496 (17100961 24110533 3273713843009919687389570807267652134968540118833) (P 56))
(138 505 (139 277 1026031 5056317028934107954255034281369728845616247) (P 66))
(138 514 (6966241 34339469573253237325743103422073399749277441) (P 69))
(138 515 (139 12422086248939063319226011785421441505395069) (P 75))
(138 517 (4003 3987558920359970460537446845439030694393713139354590851) (P 62))
(138 524 (133309568665873 2121805287454058678070133807964598831475069) (P 64))
(138 527 (139 68309885184680919938545902690623614966700527274277517) (P 65))
(138 534 (156958579 218481663809221396926189306409727053801) (P 74))
(138 538 (12758354197 295696205791192439787778780190041910835388789) (P 66))
(138 554 (60912373 185334844508009760235989834525494252258117274945938293) (P 60))
(138 572 (5659 7173931 760060076054475764830788256047484058287238107665452893) (P 57))
(138 582 (139 251313905708452320847734045064895244658895261552719009) (P 67))
(138 585 (3423212055481 452933839756797031497490656592198573575856163017) (P 62))
(138 614 (139 41862834086966316365988701719751193545676339059678011) (P 68))
(138 620 (13999693301670407268641092743058269861449824731667) (P 74))
(138 628 (139 28843 186919862053 18539725803189183571495723587917883996577704939393187) (P 53))
(138 629 (139 277 548682619 582496871581405815817959160597317932070427826282364787) (P 57))
(138 642 (1657 6073 710977 270564871 115005358468763596441084346573646168861735476807377) (P 53))
(138 644 (139 16181881 7692491396949688158327366337633155817830732318313399) (P 63))
(138 649 (139 8971 280952821 776570104971958801579203354832825713406983475730442451) (P 56))
(138 667 (139 263099623 6406050667 3852188635238494964874772070234252476076144656929187) (P 53))
(138 669 (12842714785643595157 4516464772940394510502158858603484109363272859283847) (P 54))
(138 685 (6211 2834521 6671754211 15917691123284777757825985423493923312187959) (P 62))
(138 700 (1262640617165232414682772753595550792490698739503540261959529) (P 66))
(138 707 (139 538016136732379 574789784587991749258859487187494083841255370660603) (P 58))
(138 724 (11593 89977 9432981053881263959442045781103809800932800504749259142899) (P 59))
(138 728 (156636803693803 68901863455449134485724933830694496171790095619) (P 65))
(138 740 (277 6073 480517 3292302764794709322810738835386912344263441) (P 72))
(138 750 (277 75826908548171147206463078688254876018661509292271) (P 75))
(138 755 (2347 11756537962563494305193168043611844174049926948669737423611) (P 66))
(138 770 (259744981 7800833708611565109522114000482880756103633255316460493) (P 64))


By Sinkiti Sibata (April 05, 2003),

by GMP-ECM4c
(81 337 (3 3889 867402839925066838681 18408008647553825102528578581268571989) (P 75))
(81 714 (163 1621 3889 7702139378245677494605898121060474871) (C 109))
(81 735 (163 219187 5898107264147925556987 5109470715905776202500313623) (C 98))


By David A. Miller (April 04, 2003),

With GMP-ECM 5:

(192 114 (193 56691457 91386783702096536591213569) (P 96))
(192 370 (5569 23041 1510113270723583681 16372624743282971975476993) (P 113))
(192 393 (39937 21216961 55086362689 647618006242770336949893889) (P 117))
(192 405 (193 540524737 1000374292934432238959689537) (C 129))
(192 613 (193 2113 854192462593 5320174847153979322838593) (P 137))
(192 675 (95233 168155521 39364662584833 16316696923666001409584546689) (C 127))
(192 798 (193 577 355723331329 1194806965023065028673 158060881707628980660624769) (P 122))
(192 824 (193 97218406081 238148021005249 28667266392983119428329281) (P 134))


By Tomoya Adachi (April 04, 2003),

by GMP-ECM
(104 819 (115713209 1022815249 57517135239691069856260541351144721082776857) (P 80))
(104 886 (313 397073 511409612689 6543034400804728240756934695340412912202129) (P 79))

April 04, 2003

By David A. Miller (April 01, 2003),

Again with GMP-ECM 5:

(192 132 (193 7554128641 1049798729669003253769729) (C 100))
(192 188 (193 3346049656759512552001) (P 122))
(192 259 (193 1153 2689 1666665596048956082443387201) (C 119))
(192 291 (577 3018241 12753409 495207169 528120310440769 184712019277434759199814209 811335275396420725513606081) (P 65))
(192 329 (193 299959865372801999521518529) (C 133))
(192 377 (4993 35521 13108622209 151637375547841 4107003831915342154112990209) (P 105))
(192 404 (616321 137365145621859503386369) (C 138))
(192 478 (487681 22422379509039550786177 334277904621503777569033921) (C 117))
(192 524 (9198516673 46704274287361 9064987954308265084491457) (P 126))
(192 551 (577 445633 570657017857 9114141532033 232295365979350577576023873) (C 116))
(192 757 (193 577 1153 52609 3469633 5234719473409 1508402350209178561 15496768819546016468921514049) (C 106))
(192 773 (769 63161736769 79141459204055387933402689 543781140878372341986772417) (C 119))

April 02, 2003

By Tetsuya Kobayashi (March 30, 2003),

by mpqs4linux 0.61
(130 123 (2341 85355926983808450414967264064011) (P 66))
(130 496 (131 131041 41178555547312768491618401 20232176449184394248885792095181) (P 66))
(130 837 (678166061 3167065222751 66480173064660099049241 107590888756507856305993827488359945208749005911) (P 50))
(130 948 (131 329080705282318991 1323594716482338884677421381 7048383888446965079476236514332424438647521) (P 54))

(140 951 (701 27941012133301 69796155440201 35142106420244321 21308166915444746428833667801) (P 68))

(144 275 (1153 2017 27793 28657 305281 5580984902733687525305011515290845326816124417) (P 51))
(144 654 (12802609 89504359778881 214918463940790033 1975080812581757483805186128384526985204289321089) (P 49))
(144 963 (433 577 1153 75582726076369 826228962039294747027217 2444503168408919052277554084446198340246193) (P 55))

(156 376 (157 199822741 37588631166309757 2235243585074717866147134312994803946560030841) (P 52))
(156 734 (13 826388298478982773 11784097817820640493221 3438342186459958020986012352965221) (P 63))

(168 301 (2857 7284057800093082289 266024630471240850109817581393) (P 68))
(168 362 (70976461812176979528639121 2810965161801824993186396712830060377) (P 61))
(168 851 (817414921 363412046593 660068118168283358876161 40982174562629193671911186842196823017) (P 59))

by GMP-ECM 4c
(94 823 (941 1989243862633324766756199887911 136295250718862216325540450608815629930911) (P 60))


By David A. Miller (March 29, 2003),

(192 255 (769 574081 66162049 1627417856316481 90722952709447514391102482881) (C 94))
(192 275 (193 49921 2751916795087540033 3779936183047172498597953) (P 107))
(192 355 (10369 22648566799898965793304193) (C 134))
(192 395 (26891127973901492898241) (C 144))
(192 423 (193 577 504036044638657 210166410290395965609311810881) (P 120))
(192 445 (159937 7469100350613044532908353) (P 140))
(192 479 (357779318447562644898955200001) (C 142))
(192 481 (18723130177 169309214839661661185141849857) (C 133))
(192 599 (25153 159337153 4993712833 11591707908829057 3951789127262775709766933905537) (P 109))
(192 693 (193 769 470593 34876668683074278761089 7665919250976890616236561849281) (P 118))
(192 715 (193 10177 25067521 2363857045441 763441889065296091630889788993) (P 127))
(192 745 (2689 1112974120894742593 953008768718613943921391041) (P 136))
(192 753 (193 1153 6529 20353 687945628900993 14074478353201330711958593) (P 131))
(192 844 (769 6529 38593 50497 26692842872523185457026839048897) (P 140))
(192 868 (577 159553 1092415365043039736833 2025880245433010396491821121) (C 132))
(192 883 (193 2689 597697 1651675393 2506307462269837551790849 428731188851842072689099073) (C 117))
(192 896 (13249 37441 12823350232018561 558571097919091199760001) (P 141))
(192 906 (9601 21412033 420823571521 1273404987586177 800614967933916212357511077569) (P 122))
(192 956 (64081385104429249 19540770640830823085826421057) (C 146))
(192 966 (23617592277931424172955777) (C 166))
(192 997 (769 174234326977 103713113070411619236337153) (C 152))


By Sinkiti Sibata (March 26, 2003),

by GMP-ECM4c
(81 862 (3 163 3727 2844711355290660273349 254956660779265742543210869231) (P 102))
by NFSX V1.8
(118 155 (23011 90853336844660148659017003 5747467371301523851093751139383) (P 66))

March 26, 2003

By Sean A. Irvine (March 23, 2003),

by Leherbauer/CWI SNFS
(138 283 (829 441876738081860085248559132199888893023887) (P 64))
(138 310 (139 10894796253638570605873643768075009661403189) (P 65))
(138 322 (44070210678121342250459448193278787846228927) (P 67))
(138 326 (180027427250155571694542132048127866080116251587921) (P 61))
(138 348 (139 16809643 113760394292540710449557724809551569476907927202561) (P 53))
(138 349 (64820500125960413431791976530815050671601459714308218857) (P 57))
(138 350 (139 18774087988781687275199981225219216795406013) (P 67))
(138 362 (220524668833433630125593676399801855199802091027) (P 66))
(138 373 (7281943153 1013786825126332091896668370894828535504505428399281) (P 53))
(138 385 (4702780815244349860932324846746628643341136201) (P 69))
(138 399 (7039 330132830350107746634759973136141270620439994199) (P 64))
(138 402 (36571 246193 183641598623419994515662693368887205413) (P 67))
(138 408 (139 467636972643437129669694796335593083028288915852710819) (P 60))
(138 430 (14767 10003759 3598867845177104386890078235551941273837748250328743) (P 54))
(138 451 (124477 144763 16736081129052974782895097871192628881538459508723403) (P 55))
(138 452 (70381 2712936848362644571076571558542263289710810623829) (P 64))
(138 455 (6073 37639410386779881244876589803309341910777) (P 73))

He reserved all remaining phi138 numbers.

March 21, 2003

By Philippe Strohl (March 15, 2003),

(180 132 (41761 146869149629962730266255829825821) (P 65))
(180 226 (30166021 3983011561 446989111089210532039391370611377550711916173821) (P 49))
(180 230 (4861 8821 41941 2492821 142484657736528114691310582126082876541) (P 57))
(180 236 (541 6842701 7324452901 12479984804859920430142383598720361448771541) (P 52))
(180 296 (181 633961 235067972291461 5200719093365080000887717000610501) (P 63))
(180 320 (357198569573591539113841 891672108466328857437727591739914833601) (P 58))
(180 344 (181 2161 414881641 20121924241 93810204473764876552502723341) (P 69))
(180 467 (181 982290530236627884387221461) (P 99))
(180 473 (9001 1551601 24958589941 5187877080301 15377995212187132721777697132612278454721) (P 55))
(180 548 (44281 1551601 4146661 829906283203938361 243839873501156392168125585257287381) (P 61))
(180 596 (181 6301 154981 99480956285297059022420641 284952858019568151888592979042550008419668198421) (P 49))
(180 759 (201798901 20428037101 165920125453969131283681 357709129677469824914091709385916451697489490541) (P 49))
(180 959 (181 2161 9001 14221 570758482621 15226403355783416595781 15758910025436880979789452528064410059642581141) (P 50))

March 14, 2003

By Sinkiti Sibata (March 12, 2003),

by GMP-ECM4c
(81 660 (97218435624732053673315775993) (C 124))
(81 914 (262779513874578991 10073780666807346475527898008703) (P 112))
by PPSIQS Ver1.1(Linux)
(124 306 (373 29389 672949 24526364595110333 6656313170731004052557228989 26674441257318298003613475951233) (P 61))
(124 332 (4922336117 11308768753 109509661978069 1775221888122298188444917 1151309242344444147094386394989071196562837) (P 52))


By Tetsuya Kobayashi (March 10, 2003),

by mpqs4linux 0.61
(105 102 (105822706402769988941224628519932419428191) (P 56))
(105 488 (211 6716055620401 468554349488590891 1447515528076970892602443714386961343731) (P 58))

(112 458 (113 3618770562540113 46458764187718513 15164916658447729550276371466573489) (P 60))

(130 325 (41942823001 55163068165661 816286503765252589153221691061) (P 67))
(130 582 (37571 44045686231 340005582029883073201 1199763795326259723016649706025255408061021) (P 55))
(130 956 (7889005021 4810595919611 7974414163455954645608581 315053003659883200413358798357867469261) (P 58))

(140 106 (281 46511216756710048928547118707601) (P 64))
(140 657 (56701 52010389481 209275979641 699195676481 2064997950258495122643269896238641481) (P 61))
(140 886 (124181 228061 236055541 32743542721 326808545146335001 59057536103072520346320961) (P 69))

(144 356 (61773748669729 425813025940417 6531564033924563716109468278561) (P 64))
(144 604 (433 1297 18240295182791363452726996561921 41006386272183128752064022441937) (P 65))
(144 943 (3889 25057 221222737 4582156567873722810534428642353 726077821928265839311355441052614593) (P 60))

(156 245 (13 157 712906306213609 102134060607696065044966488533315153706165889) (P 53))
(156 866 (1350622750768884675109 4252165873754603444922829 180769075409036293781470118493049) (P 63))
(156 955 (13 2029 1809601 48186841 183245401 6903476182125799553161 14692280957207853854543108583077253613) (P 58))

(168 146 (9888817 4806135999380333901066900784938350685697009) (P 55))
(168 740 (1066953758573199001 1877365987631494220490001 2457313055686209874914597372817) (P 66))
(168 789 (337 48049 8317836409 7148251209961 11323789798609 1774239593760600358957926945133201) (P 63))
(168 935 (108529 12772701972109976737 576323331197512122425713 11468321495462733299175575622632502260161) (P 55))

(210 223 (14212214722135081 879131474299242939750199823118374821557361) (P 55))
(210 388 (594212431 203027169919633930711 4840047782515332485928309984421) (P 65))

by GMP-ECM 4c
(94 953 (11657 149629877426327510420254345827512696356027) (P 92))

March 10, 2003

By Sean A. Irvine (March 06, 2003),

by ECM
(71 557 (886231309656463 4333678946269434152626141877) (C 150))
(71 559 (362953 4195956079451 226739477524516031 17388816796312051256421907567) (P 129))

March 03, 2003

By Sinkiti Sibata (March 02, 2003),

by SNFS(by Mr.Tomabechi)
(81 278 (30133 807571 10359901 412005809720917 1994148019546522166934578034163) (P 70))
(162 156 (2907164657766550411 277950664522972068176888354359549) (P 68))
by PPSIQS Ver 1.1(Linux)
(186 403 (737210629 1480310576119099 195681355270757833 43573444015830447521479 11823858682257156000919808737756105663) (P 56))


By Sean A. Irvine (February 27, 2003),

by SNFS
(67 178 (66263021443032330027393567966957801520814700493) (P 102))

February 27, 2003

By Sinkiti Sibata (February 24, 2003),

by GMP-ECM4c
(81 688 (3 811 1783 1416144640609 195056401149373490767 100446190319959766190066843713795149) (P 80))
(81 710 (811 28513 272809 21944359 13422853474785626581 280977447455304247309453579) (P 89))
(81 807 (6777769123 149101771249 45474723452593410499830051861969547) (P 102))

by PPSIQS Ver 1.1(Linux)
(186 226 (16183 91533721106333323 1274920809358428451525328443 754917284468759001063734900438806819369) (P 55))

February 24, 2003

By Steven Whitaker (February 22, 2003),

(104 464 (1243987591081 143157460739485616762432709012084871401352686409) (P 69))
(104 466 (349753 7421473935822850404646509802867325902270821401) (P 77))
(104 467 (11481289 94438657 46376593304913183757988236297822095211268526281) (P 67))
(104 470 (7489 35257 18427215693727188156586820856050880334700054208846217) (P 68))
(104 471 (7177 1399529 20791080454355654699559932234767010940513511048897) (P 69))
(104 476 (50857 199314353942024391116885253124203680203876871460137) (P 74))
(104 478 (313 68957201 1326235396805479492115771847144087985291204333878457897) (P 65))
(104 487 (521 2282281 34654035382877240853226589157572318745516401) (P 77))
(104 490 (12689 11711477067621470245634131427507262564233) (P 85))
(104 496 (7764641 2720054588013779361008207676912740238721) (P 84))

This was found using Tomabechi's PPSIQS:
(104 816 (10089378179110777 1861402658196848211674753473 50652876930057217727983576468396362595121) (P 56))

He reserved,

(104 503 (6449 57349503121) (C 116))
(104 504 (937 1469521) (C 121))
(104 505 (1873 2192639481970329289) (C 109))
(104 516 (1) (C 131))
(104 518 (1) (C 131))
(104 523 (1) (C 131))
(104 524 (316681 15227473 68887708553) (C 108))
(104 525 (554633 17291542310820857) (C 109))

February 22, 2003

By Takahiro Nohara (February 19, 2003),

(160 102 (34616321 2786284975681 598575105028625107046090881404013020641) (P 70))
(160 228 (641 2485992421507760854561 1227587354768799991001661471516641) (P 94))
(160 274 (7681 3545770108348167361 1397647159263943223873982749761 35010663743140191980809146099041) (P 72))
(160 384 (354453489374749154086309814992321) (C 133))
(160 407 (283628789920255201 16550595576688802923928801) (P 125))
(160 415 (7841 251046975537828867796380412961) (C 135))
(160 699 (145601 11214872033921 75581191806153427841 8688997319161300078874346401 1239737621888486320404463068629761) (P 83))
(160 749 (148961 2292175088327521 571947415970622509627944665281) (C 134))
(160 804 (5540817583770060751239345281) (C 159))
(160 848 (14561 35201 582054241 142561202413300295207932001) (P 144))
(160 948 (3361 4481 309703164481 1286734981121 3852151754700481 13874226036088083521 104109498153267171316645474241) (P 96))
(160 978 (31212161 1072301412001 1426606571604546296207969441) (P 145))
(160 980 (103128291223937921 44453911951557904001 608196428449314322845557810561 3246327053371281167459850136168686401) (P 89))


By Tetsuya Kobayashi (February 18, 2003),

by mpqs4linux 0.61
(105 264 (211 631 35531791 42377791 48032641240445440317219498068728078122211) (P 56))
(105 353 (4035781 65434054154426439301 38434899095341072250927806832507541225455221) (P 53))
(105 694 (1051 9241 16830426584814902019774133247332441 221982580252186975441595337861973349269681) (P 54))
(105 737 (2584652780283750751 583102572314856174719041 9849449264371016233003613000212245834155204701) (P 50))
(105 876 (20920443913256393521 259095019857556497686150731 13935842565808634180887954749677074137063451) (P 53))

(112 155 (2005771153 53471607869796948617853753952399720171391633) (P 53))
(112 177 (1332913 2416849 48369479743621276154007672622171891349795189297) (P 49))
(112 247 (113 449 1318089446645441 28606262416779436980556337) (P 70))
(112 434 (337 2801 1981169 2610161 1705259283617 874267111069998418222144575377295457) (P 60))
(112 580 (86353 1894418598000433 31450076887053889 4641004297215239423287308620247206352825752689) (P 51))
(112 662 (21181034760895765057 151418555745985566977 32223994162220039026499983528626017) (P 62))
(112 792 (449 7393 1296307489 3457816458885704660101640753 134381602880587549342875575843229520817) (P 58))

(130 246 (131 88806769571168741 2548318609178923963311900165125393358333858941) (P 51))
(130 247 (131 13001 9523228827451 97984447749861844902507525178539648119395766251) (P 49))
(130 777 (131 220351 1679987401 10613510685961 29329535396981 1269612061069702929963141516590484901) (P 60))

(140 374 (421 53201 67061 5522046718867141 1494795060756049801685131441) (P 69))

(144 242 (1153 11401921 359115553 359292162731859721930341822731383298113) (P 58))
(144 488 (462529 10262795335198651117033068961 3866166994178222977830596754776929) (P 62))
(144 496 (21937969 2451943441 238803151058783569 279809850355388500040418791350966897) (P 60))

(156 371 (13 1574391157 262822779325937377 265527129273166231539001986937) (P 67))
(156 417 (426973 69894241 120557051113844593 90417495723030086761624850132797) (P 64))
(156 842 (10817509 1475665469149 56356898696790581799311221 5169215608867231769185958307094317960937962673) (P 50))

(168 310 (402529 1400320616280077521 181883789148876202459391973619513) (P 64))
(168 328 (1724646426721 15160857011497 945687987687616502429507415896391343449165697) (P 51))
(168 687 (673 8734993 443004245906041 7317068122186201 2186862103137896363787759809695951873) (P 60))
(168 928 (2017 757893529 276661825182289 642886424250382406977 211121818927467749509779066633369680033754380689) (P 48))

(210 167 (211 421 1051 3361 60049877486904088870554590627067673111) (P 58))
(210 271 (2521 3581971 414033143791 5096129660042527843523442575665563643561) (P 56))
(210 469 (631 192991 140772022021 43911970115161 53030181759988994374148712058068527883331) (P 55))

by GMP-ECM 4c
(94 685 (2069 242893915104717115464062540899100434662653) (P 86))
(94 709 (659 20082443 552343110190623379035858653124687182493317) (P 80))
(94 735 (187907 303151 14560526327372233321 2266457633508795415927719803194466089) (P 66))
(94 842 (27033243752030203 9827969443429630623103037896370484623) (P 82))
(94 858 (3341759514439646285402391335426190718667) (P 96))

(106 363 (25474992834206129621300495903923) (P 102))

February 17, 2003

By Sinkiti Sibata (February 15, 2003),

by PPSIQS Ver 1.1
(162 132 (4403086858093177 38786999354020071074515011098827339) (P 65))
by PPSIQS Ver 1.1(Linux)
(186 117 (373 2103103 28051793042724901378549 2977958469663499199358173803563621371566038157) (P 48))
(186 210 (2824411 32811267491487223 311916925021749907026007 3645373164960128486651997457) (P 66))
(186 322 (373 1303 1489 5257316359549 57316763230984429 12394482000746556243199 81535353301319728999952089) (P 65))

February 15, 2003

By Tomoya Adachi (February 13, 2003),

by GMP-ECM 4c
(104 822 (8124447241 104414724107201 340574059377164506108085134144700698009) (P 78))
(104 827 (2069497 662954004649 692602188507032971943508848864118241) (P 87))
(104 834 (4057 3270852209 324617989205071691106438833201674245403601) (P 86))
(104 849 (31280201244241 1066899061847378719556451796073809) (P 95))
(104 854 (511530665296740064540127993 948149194396048350508526447673855576841) (P 76))


By Takahiro Nohara (February 11, 2003),

(160 105 (16001 149441 683717327598241088248413597503681) (P 88))
(160 108 (572321 2538401 35209921 103332620636110944161 126960389655699654672895143775086679841) (P 53))
(160 129 (638747963655520227148433396148961) (P 103))
(160 146 (641 2347201 267075586592752371843841 3374342340157323464136716410721) (P 76))
(160 159 (1087571957761 140502464490637206189676216186666384481 6962005148187880958788721372569594773601) (P 51))
(160 316 (641 2927886094279391223341974789121) (C 127))
(160 584 (6005964861601 490820151227080677281 718000717024565118862141601 51317647100019800830966346561 34710963416187976276431400208543817281) (P 51))
(160 603 (3465204619476641 12264821830045116334555681 309281844291096043194713761) (P 111))
(160 616 (3041 1807606850081 19951922455571155974004212481) (C 135))
(160 621 (175418081 65907652531412512956281441) (C 145))
(160 627 (641 620161 300780881734259405760193441) (C 144))
(160 634 (5336801 44513761 2394070545281 18830970085750721 13223204465490781599841 2693765275855304484945281 662534291708400473148102760321) (P 60))
(160 652 (641 989197149877121 18025096837739806780321) (C 141))
(160 689 (5441 39041 256290401 969975521 68894680801 277802569709043039361 4638277432964448920983988691041) (C 94))
(160 699 (145601 11214872033921 75581191806153427841 8688997319161300078874346401) (C 117))
(160 702 (81281 917419448404621694825780321 4145240111327310438229605761) (P 123))
(160 726 (12641 5786947809787066561 612237570970894112214243841) (C 134))
(160 737 (53281 214027201 274877591204710738114589149121) (P 142))
(160 739 (92103580122529441 622908565052911409779284161) (C 140))
(160 744 (39772801 10289168274881 37520978337887452869761 46412947888549424361698429420161) (P 109))
(160 773 (21625264883515525595366440961) (C 157))
(160 775 (129778491266335840001 4147847711201633233370348161) (C 138))
(160 782 (17102169929868551349945233441 6481876948275185804302899576641) (C 127))
(160 790 (641 479201 363660501290159399681 330183197831891722802973121) (P 130))
(160 795 (24481 132001 121265281 729921121 467183093055489381121 3406107585098969225955041) (C 114))
(160 811 (32877805739564161 150746979165262811987041 139466070516662146170539549834401) (P 115))
(160 817 (641 342210028612458511694240641) (P 158))
(160 836 (20205281 15370371533468447335841 141741010749246180053748641) (C 132))
(160 840 (3278527805921 5806718026042721 183273169316584481 129881461048830315338561) (C 119))
(160 857 (2081 1627634981091250199613286144001) (P 155))
(160 858 (796001 12978401 121737425913951834080865761) (P 149))
(160 861 (7191841 55655199494561 2810374484349284827108439411521) (C 137))
(160 867 (2081 315585240161 583125103690136750401 46646059126353697598300071381296961) (P 118))
(160 885 (51521 770401 8570473965027952961 5442450626964632622141761) (P 135))
(160 886 (4481 318881 336376289630295019445813441 548958637312625412234820961) (P 127))
(160 902 (150283118498561 3340997513278642558612001 56184075692269486438682762561) (C 122))
(160 907 (1601 3675361 10554057701747745123663233973281) (P 149))
(160 917 (641 2338081 125512001 29667096613030827723186388801) (C 144))
(160 925 (372604436641 1326270748068001 11910313315096636903361 4164251815304345052532429921) (C 114))
(160 928 (101994721 292756134721 898592439944247802081 2525518908769133810967010721 29527971759143817135792981121) (P 94))
(160 935 (45542172161 96587671679086535006035495665761) (C 148))
(160 939 (1262081 124243841 22072320860129521601 1753253383676614403588517497943841) (P 124))
(160 940 (12640446241 2702705502898322165404183316641) (P 150))
(160 952 (263627681 7758242317326881 10249380960046668666580961) (C 142))
(160 955 (1094431848734265849298721) (P 167))
(160 963 (75521 113761 166706401 986365639912189604532716161) (P 146))
(160 983 (13121 4445281 112489921 233914858853024641 24881199527110811750435681) (C 130))

February 11, 2003

By Sinkiti Sibata (February 05, 2003),

by GMP-ECM4c
(81 585 (163 62047 92399941 1963781497 914858783091666080929 479257649005773105586205636477419) (P 72))
by SNFS Ver 1.6
(81 246 (163 313407994602330040879 3615102255637695903040816024209162163507) (P 67))
by PPSIQS Ver1.1(Linux)
(198 338 (28513 129097 12348853010209 33218922281491 17723441882179903176451 1217861362517711388447627690308161774774129) (P 52))
(186 203 (373 13126021 10531225597003 4894778536443006802143661 1887322341240309861841201371103580893) (P 55))

February 05, 2003

By Sean A. Irvine (February 03, 2003),

(71 509 (45499502261 1635358078432733 1092821746626933641 34177898007828528660094626617 52802322138323884105747063124568473) (P 83))
(71 534 (853 2131 6959 13835629908928838147424913613115841) (C 147))
(71 541 (853 45068671 2548305473407 27424733250935536781672009501 66896252375876724982245684909385763) (P 106))

February 03, 2003

Errata by Robert Backstrom (January 31, 2003),

(71 506 (199644059929 1545537418577 213296812141559 8536154593335809474890760293052341) (P 135))
Not a factor:
8536154593335809474890760293052341

It divides (71 507 (...))

True:

(71 506 (199644059929 1545537418577 213296812141559) (C 152))
(71 507 (853 2601677588985653459 8536154593335809474890760293052341) (P 135))

January 31, 2003

By Sean A. Irvine (January 28, 2003),

(71 506 (199644059929 1545537418577 213296812141559 8536154593335809474890760293052341) (P 135))
(71 509 (45499502261 1635358078432733 1092821746626933641 34177898007828528660094626617) (C 118))
(71 514 (4261 935639 121675081279021200043039 4032348878196284623068251429831) (C 127))
(71 515 (8025557 36616610544150077038691033 9139218576266333523958713049669979) (P 124))
(71 522 (6959 319927 292151369 5350501781 62509346165171 6830582482224854790088664783 11627305419264481783726914188237) (P 91))
(71 524 (122272793 627759128770078059052054967647) (P 153))
(71 527 (17041 57939666608413 5491027716327734467 23777499096616155702547 1951106804638937233947526211478287) (C 99))
(71 532 (2203589513 2381926174009492578059 1627785649575199405330733753 217622733391320986999922595589) (C 104))

by ECM+MPQS
(71 525 (1350847 18100258222342633 4418458189719629203 39709267619068718859738773 46652300516847660658941581441383637 7174497920203323196121747711734320787181) (P 50))

January 27, 2003

By Takahiro Nohara (January 25, 2003),

(160 126 (14401 60961 412942241 182784528223302421745900918279041 28778969365223646053095608707816277601) (P 48))
(160 134 (1159887669462184579916641 7647387505936460233288431495521) (P 82))
(160 139 (512641 3405697441 1383574695545647657544491645601 11835587540096369227640385804481) (P 61))
(160 166 (90450401 385147903841 1856459040017775952544943841 143958661185985965033985971683790721) (P 61))
(160 167 (39041 8640080658401 17454821426088526415305541665238561) (P 91))
(160 188 (1601 941866241 13778285618560961 8197457803996112192337554881) (P 90))
(160 198 (641 30864504712001 3044520874411198579999167682561 806345836081746998220893224127979361) (P 65))
(160 205 (1601 5593387640360075981441 1989698912353331108559319460161) (P 93))
(160 207 (292622141284170735100001) (C 125))
(160 238 (5418319681755214518711892481) (C 125))
(160 247 (6287292449329857677187361 75920254333738105810804001) (C 103))
(160 255 (863521 377078183201 6237924501479852489068445921) (P 109))
(160 257 (15361 4213850194983883745653121 13029324761523558521813421613441) (C 95))
(160 261 (175394763521 14284368329272626167496451907675521) (P 110))
(160 268 (4481 411357066509165281 374148932264481298503797761 586366391005744378739779116161) (P 78))
(160 322 (292801 2683635041 53398932799394508532457017601) (P 117))
(160 330 (1601 1451521 4133816322377247646704302561) (C 125))
(160 334 (9683893732288847979560641 14892588362725985995355327406074664001) (P 100))
(160 340 (209838306313044001 8279679907903890625459992276001) (P 114))
(160 345 (1306635093965733074554230130721) (C 133))
(160 347 (3642241 242864438161601 41435454089091976402637852161) (P 114))
(160 348 (641 800801 500561147154182325830561 3578361528729747773530514151841) (C 100))
(160 362 (848057159041 217099719737889698437311041 388258454489874109542269286086401) (P 93))
(160 390 (3041 1164001 28657104501557214721 81315857967550792961 23323377381763089201121) (C 95))
(160 398 (45281 1261121 420321711304223192614420001) (C 130))
(160 431 (69323451091215229489237565358304321) (P 134))
(160 466 (2295536709620160323375782081 264535017177800697234527477430401) (P 111))
(160 469 (25892732915681 416322190250582051346228961) (C 131))
(160 490 (1601 20146904641 37649572175473944001 121293105510691323841 10141866317516271746255041) (C 94))
(160 495 (641 4027690375361 125524057290137761 7865754192434194959763361) (C 116))
(160 528 (63841 11270932984475419201 69597564208456558543787521 35087940049571612877859449281) (P 97))
(160 531 (22213273018995041 90022430311616278341421601) (P 133))
(160 552 (3233716481 8715464743681 595311636346404507999160410721) (C 124))
(160 567 (20161 5042452357257266196144001 142182588892868820968782241) (C 122))
(160 568 (17489441 3104873584867676952226024161616801) (P 136))
(160 580 (1075425761 3713552607350344750454906081) (C 141))
(160 584 (6005964861601 490820151227080677281 718000717024565118862141601 51317647100019800830966346561) (C 89))
(160 591 (239201 104601121 440464481 959116001 434883073299208498408481) (C 123))
(160 592 (641 3767041 2485087361 55027932216854897950721) (C 136))
(160 598 (28207312801 31345080730721 1814793770826619676285441 8814110772814499515000824161 21768722415066925558379345921) (P 74))
(160 599 (4001 24481 640745839045572164200691295521) (C 140))
(160 934 (641 19841 12611626081 2397120532217922587521 20330561489636024560848297281) (P 124))

January 24, 2003

Tom Hill reported the performance of Tomabechi's PPSIQS.
Please see, here.

According to his report, we can factorize under 100 digits numbers within 80 hours,
and under 105 digits numbers within 10 days.


By Sinkiti Sibata (January 23, 2003),

by GMP-ECM4c
(81 685 (3 163 286991996490343 386861266908811333 131768648966049391392610879) (P 93))
by PPSIQS Ver 1.1(Linux)
(198 294 (199 2116423 4091511220039 7271299218840823 13307492084863681 844784769249752559859020513817) (P 65))


By Tetsuya Kobayashi (January 20, 2003),

by mpqs4linux 0.61
(105 262 (211 4466791306381397701 43181435865715752645369544680412294669771) (P 55))
(105 868 (211 421 8191 9961351 27164341 11529765031 894208945141 640704200353666930736123960205031) (P 63))

(112 260 (113 337 1984753 63844939313 2525087038719621471996689787601) (P 64))
(112 413 (113 337 3361 7841 2661233 618772296689 462768240519992620808211346433388720694512133729) (P 48))
(112 442 (113 449 5728582585601 467150324829217 22676843461321425439279046309156447194769) (P 55))
(112 865 (113 3193679081777378044817 6631452569491912858753 30181612630466487404730203170299576041857) (P 56))

(130 403 (131 14951 1146731 1327336198075079921 2648174572388836356788601358588481) (P 62))
(130 465 (131 5981 949261 4365271 564850295542651 66012494012444670763028817714399659314899315931) (P 48))

(140 302 (4564454517621942416773301 1702401863551060572197503801319341) (P 62))
(140 318 (10501 50821 951161 128702066501 8390409614793376590234599504754007447601) (P 55))
(140 765 (281 9533952490060601 22571053563850787590293581 2778905479663117567397123518921752281) (P 59))
(140 854 (35595541347863479361 693633203894446883038541221 461933396177506118356877780776419243263401) (P 53))

(144 363 (8929 4617793 548276705276627809 10527016184179468705819045356115991041) (P 58))
(144 960 (1873 66529 7690259763217 109581529213729 111799156216177 76150472012162725801968620661415516885701642673) (P 48))

(156 230 (157 61254404278741909 2806121996303837987539602670261) (P 64))

(168 154 (7393 1506457 13206541536307009829297017) (P 70))
(168 208 (319201 121811307073 52430619316509183306149671179999241) (P 60))
(168 708 (18274537 2059821961 112042348988577159957879649 906794321433871266307461982763145361) (P 59))

by GMP-ECM 4c
(94 548 (244589 662231 43559112460092518350655128290405836663021) (P 75))
(94 628 (72883277 15535977520357351211353761674421979516523) (P 81))
(94 910 (93106380162109346542243 8615213362929648579930804767842061133241) (P 74))

January 17, 2003

News ! The first big record of this year. Phi(69) series have been completely factored. Last composite number was factored by Alexander Kruppa on January 12, 2003.

By Alexander Kruppa (January 12, 2003), (69 903 (139 195026258819259257644548078519302406889) (P 90)) (69 906 (691 3983509 55880015758302961466765374420005649930724930089) (P 74)) (69 928 (9964563793 5597946039235688629 6802476471625328467025878993633608315392095011481) (P 53)) (69 936 (9544092361262842562521422263691203326501137686247540883) (P 76)) (69 942 (60859 11996679472778047 1743905491944115174604407373824366884600515222383) (P 62)) (69 946 (1933 3037 48163 66090350282294944589516221326900586756664630576809) (P 70)) (69 950 (1381 102673 729331 3904176079 1404143182523441382061323014585320846521287025391) (P 60)) (69 957 (691 276091191533128152688153 6301768444070203357611157463147683489471) (P 66)) (69 963 (4656067561 32572054472777265056117615016818407808425425214177450699783) (P 64)) (69 966 (7591 47020985234205586236438784309742172124559011) (P 84)) (69 972 (3037 13001163750703369 6917840062937722953332124208053040560985481903101) (P 64)) (69 974 (1245986821 6159823129069 1324850612774609412776486923621088231049645157261) (P 62)) # (69 980 (139 268019809999581542656303974464753616030019 2866156451778690746899284497463445187206369) (P 46)) (69 982 (139 967 309861633936146513230841658935559732497915632431326781771441829) (P 65)) By Steven Whitaker (January 14, 2003), (104 435 (8737 37189153 542892169 5531537293108360830680448780823794693870761) (P 64)) (104 440 (28081 41023034417 438329233560461777000461324110732628769) (P 74)) (104 442 (313 326561 15589476432050507240425413140864458208655390419828830947913) (P 61)) (104 443 (1249 74265964781299395675548281174908089162171650294577) (P 75)) (104 444 (51481 1913081 15039711926295563841857973498290069153) (P 79)) (104 448 (313 7194055575162783512953 3777693041924532383533118801797921808057) (P 64)) (104 449 (1249 243077723017484726064633002631726741655073) (P 83)) (104 726 (521 26729 43577 12095617 1160057081 15326871278057 6876587107223333002214625851139540001) (P 60)) (104 774 (313 521 11664923217891512552110205804857) (P 103)) (104 778 (203321 8780201 15129962938281580324196336175940529 2969472520594575448725373204495363817) (P 56)) #(104 802 (521 56369 22709201217547317527369444791694033) (P 98)) He reserved the following: (104 464 (1243987591081) (C 116)) (104 466 (349753) (C 123)) (104 467 (11481289 94438657) (C 114)) (104 470 (7489 35257) (C 120)) (104 471 (7177 1399529) (C 119)) (104 476 (50857) (C 124)) (104 478 (313 68957201) (C 119)) (104 487 (521 2282281) (C 120)) (104 490 (12689) (C 126)) (104 496 (7764641) (C 123)) By Tomoya Adachi (January 14, 2003), (104 802 (521 56369 22709201217547317527369444791694033) (P 98)) (104 856 (3329 379113022783840236389397407588320033 15213736556001223873629228033927084719270525977) (P 56)) (January 11, 2003), by GMP-ECM 4c (+ PPSIQS) (104 814 (4889 16433 581871889 118144803859120793 6738118548202717998052119933793003457) (P 70)) (104 856 (3329 379113022783840236389397407588320033) (C 102)) (104 859 (267791723473 69371666241533246928446275427279929) (P 95)) (104 860 (1858192108174874724097 8968928253336123926598515590769) (P 89)) (104 874 (1249 566035081 24912824999505036413579409282569 2537400283771291849560287927892368377) (P 62)) By Sinkiti Sibata (January 16, 2003), by GMP-ECM4c (81 591 (9397 113447406699188560153 502570900940953309415185303 1709395991131660533849462319) (P 72)) by PPSIQS Ver1.1(Linux) (198 235 (991 806257 7715752111 131364289947727 841550678587081 37333058808048939430907588429525911) (P 60)) (January 11, 2003), by GMP-ECM4c (81 493 (3 163 2917 87983232370074220741793176321) (C 111)) (81 575 (36409585213 29069948491736989728646021933 2016044085767779369443475172359) (P 80)) (81 602 (163 157627 164449088782893492472173895237) (P 114)) (81 878 (487 811 35803 2023543 351400872096164157959431 75153730860797411236404709) (P 94)) By Satoshi Tomabechi (January 11, 2003), by SNFS (61 359 (1709 2891126755392208738851573245222369825691004299386688544420255843) (P 87)) By Sean A. Irvine (January 10, 2003), by SNFS (67 175 (5227 13692816308221 22819103743675249005083482038444539) (P 97)) by ECM (71 474 (853 528078462147548304739439743908659) (C 152)) (71 475 (2324004513699717028769 19239671410829531927583797084231) (C 135)) (71 476 (569 76320883 9411260418415861 824056371505430372113019442481) (P 131)) (71 481 (5097904237422212479 32131293687271768147 72792438387248862015148433710762619) (P 115)) (71 492 (570841 457303730967319 28927288322149783684416164698241) (C 137)) (71 494 (139729 156112537774171093939381) (C 161)) (71 495 (16764968579 15068368950540670530116685911584703) (C 145)) (71 496 (1170479731 435810346042159541 651046483613598541634483201711) (C 133))

January 07, 2003

Errata by Robert Backstrom (January 06, 2003),

False
(71 447 (569 244502508005209 862858274074470763817395177) (C 147))
True
(71 447 (569 244502508005209 862858274074470763817395177) (C 142))


By Takahiro Nohara (January 06, 2003),

GMP-ECM 4c (B1=11000000) + PPMPQS
(69 980 (139 268019809999581542656303974464753616030019 2866156451778690746899284497463445187206369) (P 46))

GMP-ECM 4c (B1=250000)
(160 171 (1384779783561652208397281 2915577767374212718225091681) (P 92))
(160 232 (9281 381761 628170828641 10428497912098803947041) (P 109))
(160 344 (193441 10390598577650068801 10122177585730046453018556256001) (P 108))


By Sinkiti Sibata (January 06, 2003),

by SNFS Ver1.6
(81 227 (1983823477104274704939702438991743617299590388173885806073416941) (P 64))
by PPSIQS Ver 1.1(Linux)
(198 166 (199 51283 1084576483 16004650861 17648212358107 1573910931354088032748262689921) (P 64))


By Alexander Kruppa (January 05, 2003),

(69 802 (139 277 57790813 351663823615104312775185922729794184357813021) (P 71))
(69 821 (691 2347 37954428650742732092921203938938468995024108970670647431) (P 67))
(69 828 (3656586439189579393 71697349183205659015482966115007541733884363712237) (P 60))
(69 835 (80295708905953586359 10202672011499416659293383054502206600837) (P 69))
(69 846 (12361336741550761881621792768202718314750979218093) (P 80))
(69 849 (508331557 822558292238281 4621927074431850284042943168384341815516699) (P 63))
(69 851 (97406008233419302616460568645926185576551) (P 88))
(69 860 (3037 1490718255049 2800456752151685290915401154485086882999523873705397) (P 63))
(69 862 (139 5484349472887 11527034327497563568914312925491531682549868532841) (P 66))
(69 884 (119416093 15639535271974100191 223029722229880684985696398641139823391755239) (P 59))
(69 886 (277 2602003119568805559591151 523482671151299458628637804017916458137192426519) (P 56))
(69 893 (1657 628822393 1683909372869821 834593036725452387259150542720633648136692429427) (P 55))
(69 896 (2583499 1333361521 2424644676780575266654566236714444077846482745938697) (P 63))
(69 897 (91771 303463 1565287117693089828086844994043727899048682487007152531) (P 66))
(69 898 (277 749932781761 4583346999490413196119882009318620242288194229386979) (P 64))

He reserved remaining all phi(69).

January 05, 2003

By Tetsuya Kobayashi (January 04, 2003),

by mpqs4linux 0.61

(105 830 (20805751 71897911 3683766474702015453794466458791 117242097013708175862953719709072721140061620371) (P 48))
(105 970 (211 30595531 12765455736496832881 54949804971986643811 16472518535736061384586198424229798413104316601) (P 49))

(112 775 (8429233 95479217 501740849 1111720393074421865057 22233841830300984035669050977647984081) (P 57))
(112 833 (337 408241 9606611557356017 2680409561137708030289 249988067357733683414960864334737) (P 63))

(130 698 (501117751214720251 2866831956559988390601031 2423292730543598503365767040058106229313481) (P 52))

(140 133 (421 178501 180987334900807920746220399848224808473721) (P 53))
(140 418 (281 53725421 569453608570112635601 3172782936471902278362747848324969226862121) (P 53))
(140 481 (14027021 18367790123621 108485154610841 545903257974246491477707892169961) (P 62))
(140 494 (107324084931001 188765534279329268381 11665919183735229282434548994772377687247036701) (P 49))
(140 986 (281 242201 1685881 92311737471745541 1738358048288714441 6640232399385084148272947032084061) (P 61))

(144 282 (350699168314211387547169 1122612415269051924825300577) (P 68))
(144 532 (18289 1091521 3311318232433 15083985431953 86057637544801669682657026634549595159110982049) (P 48))
(144 663 (34129 2021487409 1622147055132297746906651089 2514421676277706293680853457 838312852218322513116363348673) (P 38))
(144 699 (5533587937 5135465135233 60608708933259062449 62612378619153570210901800529504513) (P 60))

(156 249 (13 4874377 13405190282173 4917518871910385230191938797466839997233739089) (P 49))

(168 130 (9738793 11599587794018028157769998177009339632583297) (P 52))
(168 416 (7393 1684075455199201344998499601 2954011297386124092752115097) (P 68))
(168 558 (683147457978049 14632797513656913841321 26827745567808159537793848419167438801) (P 58))
(168 648 (16322209 11820122133121 418477382868607603633 757142511403296728289884879195099020316881) (P 53))

(210 622 (421 128609641651 135129917067488363793813181 159450300672283964734023564127030591) (P 60))
(210 818 (631 11551 20161 26661181 520409954956451504061034891 4893015633990789694984154473629814797049714651) (P 49))

by GMP-ECM 4c
(94 533 (12582648558433521536162717448417587 55518894578312786404676868580660296457) (P 54))
(94 629 (34781 6094350144386747320147689547647528706635967) (P 82))
(94 635 (2916499565965305121 6102533590044515485495713931367323) (P 77))
(94 748 (241323333158931179690971 14416676799231534518389711836720609157) (P 72))
(94 805 (93801890571456983151768823 1902382587336271700886483440323101011) (P 72))
(94 890 (1787 88967480269735732703 884753822166549179442641319060294040931) (P 74))


By Takahiro Nohara (January 04, 2003),

(69 703 (269377 1467854958012333841315445106357442273) (P 84))


From Prof. Richard Brent's table (January 03, 2003),

(104 811 (536849 69844685778089 44859231223014833 26760743869589688389171813316525602835636920714281) (P 54))
(118 643 (11329 20533 307504343 54748146000173879791 40866447829956053519897 14571735157457069452660907451917 221102618559896410353956258665463809) (P 38))
(140 858 (701 40197884553253009530055992971012764224121 64947813831509959610531431862783089165836841) (P 54))
(162 953 (3 18793 1049878261 9054755024847229 1487714107320553254476503447 1498357612988011043489558405251) (P 74))

January 03, 2003

Happy new year !

By Alexander Kruppa (January 02, 2003),

(69 700 (139 321458065845295418563 102748087696586481113855435979969675500461573273) (P 56))
(69 705 (84181 1496749 987742252876327567283844023997792927546802333222375316887) (P 58))
(69 713 (63150015324120336013 2973331516084783638144215547445097955997644891697) (P 58))
(69 714 (24438764513716830133 2399324656382371371363533493088954189) (P 70))
(69 715 (139 641287 3488227 1956407424801816516087473204424999735701527) (P 69))
(69 718 (967 133641339007161131812542829492703071851612355471) (P 76))
(69 720 (139 21391 294646632606271504170994518418379270887564601626839755479) (P 63))
(69 723 (139 37951 4322962591801018044558108916049134534954172656921) (P 71))
(69 724 (139 669509333605004888473 16499232152712902767233428627901163944793587667) (P 57))
(69 733 (139 6485390346053743739086581001489142611103609902171) (P 76))
(69 738 (1381 7375411 103479624741199032150169646097975641023899480810000208177) (P 61))
(69 757 (967 71209 216199013797495888529778298737746598421432337399647) (P 69))
(69 759 (188611363 17746268591533 214701720361800482112738449103952856405848951253821) (P 55))
(69 761 (139 277 686481967 116829002053773388382880567395403485134011687948053611) (P 61))
(69 765 (829 7039 530708947 1585270171 996666837074697263351875505945463820268011144129) (P 55))
(69 781 (139 132396331852628017921227935070245889825266778072551592823) (P 70))
(69 783 (3313 7169398909 22647569851 947363641274723042594085590415767960855407) (P 62))
(69 787 (3547429 1514487038971857099938496619568809522034383) (P 79))
(69 795 (277 25117 4337479 280408704972357131958649036632121084217834423954136043) (P 61))

He reserved,

(69 802 (139 277 57790813) (C 116))
(69 821 (691 2347) (C 123))
(69 828 (3656586439189579393) (C 110))
(69 835 (80295708905953586359) (C 109))
(69 846 (1) (C 129))
(69 849 (508331557 822558292238281) (C 106))
(69 851 (1) (C 129))
(69 860 (3037 1490718255049) (C 114))
(69 862 (139 5484349472887) (C 115))
(69 884 (119416093 15639535271974100191) (C 103))
(69 886 (277 2602003119568805559591151) (C 103))
(69 893 (1657 628822393 1683909372869821) (C 103))
(69 896 (2583499 1333361521) (C 115))
(69 897 (91771 303463) (C 120))
(69 898 (277 749932781761) (C 116))


By Philippe Strohl (January 01, 2003),

(180 201 (541 2341 8101 722521 174638475313952667706087620881761) (P 63))
(180 213 (7609681 184017567421 2191466804657757249288323233732861) (P 61))
(180 273 (393706081 37506357026461 213637358281193422375510612291215548423161) (P 54))
(180 357 (71573581 15941942591477450814001 3119294652271009614004977181) (P 65))
(180 607 (4076225657641 8191050928546789700567594078056478281) (P 85))
(180 666 (181 180099001 47003156380441 17767318063134061 3796756065968466011177074681443781) (P 62))
(180 672 (8821 24481 31510125721 34977018815149922759058841 31260582385053875551729787268447108001) (P 54))
(180 757 (91621 1255419001 169690467241 95743477797462457741 517952346811596298513841303789238903481) (P 55))
(180 804 (67977367561 30570098228254801 1997107586025482881 32580975972437592475995859571252918631361) (P 54))
(180 819 (12601 25564611601 356330385286201 34079920120677241 11719961799165062558960269338197281) (P 61))
(180 974 (181 9001 238681 20464602481 22601062937161 122764057412676481 16169299234510883222196567721086149302921) (P 51))

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