old log ('99/05..08)


August 31, 1999

By Tetsuya IZU.
(August 30, 1999)

by ecm

(41 312 (83 4338397912404075046146757940981) (P 68))
(41 333 (2543 2770093392574757584962129667) (P 71))
(41 358 (83 972144713510396736576716929847) (P 71))
(41 476 (83 2297 9103 275829650677682241162146332319214361) (P 63))
(41 643 (1723 898331813 26916690407387006552749449563 737367570984607922283380522159) (P 42))

(132 258 (1220044946376634083206689 1245272390074261345705139220026118709) (P 37))
(132 595 (1453 15973 52009 6973957 206494196726023246620404089 3654481880501752114050863803837) (P 36))

By Masaki UKAI.
(August 28, 1999)

(100 405 (401 2801 396601 894654610103370797581972748801) (P 63))
(100 894 (101 701 1601 397559803590410161201) (P 90))
(100 965 (102001 1132494131687134201 163414360565106898901) (C 77))

(110 460 (2861 1832711 2153471 14524096621 66638162739463190245151) (P 58))
(110 572 (7591 5637451931981 18447107755859477731039301 29304278095823233167477653941) (P 40))

(114 462 (166783 5203873315437355590324517451923) (P 60))

(126 789 (29611 14331319579567367939724247) (P 75))

(132 297 (2465662274329 59207206960071665858089 3845551918962789868209109921) (P 37))
(132 524 (661 123632943497115740161 10534102911435022708565173) (P 61))
(132 754 (100333166180475889 39925067850150427700627598673) (P 70))

(150 921 (151 1201 83677014808410734475151) (C 91))
(150 965 (166376403723654720451 25959385110705593306456843551) (C 71))

(55 436 (331 108131 2761586416382582911 67580173096795727227036321) (P 54))
(55 536 (661 864860683145749808761 6445163053657735270711) (P 64))
(55 543 (11 3191 4474801 1263517201 15729766193051749296879019382411) (P 58))

(63 651 (1890631 67938167410500156170366724650923753) (P 61))
(63 731 (379 552259 10779644232827594820093628839609001) (P 61))

(75 760 (151 595201 4145329873762809041861274024751) (P 77))

(82 357 (5003 13274490888376158142166418931) (P 71))
(82 496 (215497 6041351 2461024302931094352451) (C 75))

(88 297 (89 136753 241900990732426334556064841) (P 66))
(88 570 (1478192205601 15845955032953 300181001837763635540158619897) (P 56))
(88 992 (89 91428597528984215256593) (C 95))

By Satoshi Tomabechi.
(August 28, 1999)

by ppmpqs
(49 312 (51973321 65517019 88622773 664909142446195982263461157171) (P 52))
by ecm + ppmpqs
(98 190 (643614589071285343807 6581362922922388391993627945666748029) (P 39))
by ecm 
(98 411 (491 15677086709186769836131) (P 85))

August 25, 1999

By Igor Schein.
(August 24, 1999)

(47 727 (283 37507 808307 13352742301 125588393427051299271659962331 71972137989909853108683300265931654081) (P 42))
(75 704 (151 19501 660534656070091230088939651 21911986550206339355935890901) (P 53))
(86 198 (173 32094926005291 3899905265565897023204596864428385403621) (P 42))
(86 259 (1721 149109655478770463 7371343353649016987482698143) (P 54))

August 24, 1999

By Tetsuya IZU.
(August 23, 1999)

(41 819 (307583 843790300889720413739 70054057205038353285571291871797) (P 59))

(132 160 (749285612361236697494221) (P 65))
(132 189 (3697 3594930406270617515707057) (P 63))
(132 395 (661 16369 539139948262229950976727088068313) (P 65))
(132 398 (27061 153618301 375858920473948202439253675021) (P 62))
(132 553 (709678488876143897990749) (P 86))
(132 561 (446313649 288237199930603118317 1514552223636682232183149) (P 57))
(132 585 (856813 67267778842216385514313) (P 82))
(132 786 (1321 1271953 26885820314239566369757 23603722162219809495792457) (P 59))
(132 829 (798496432717844556169 152185392426754131138309793) (P 70))

By Andy Steward.
(August 22, 1999)

by ECMfile2 (Ubasic - KIDA/steward)

(41 528 (83 10333 191105580063917 267610299613816021131403825721) (P 60))
(41 708 (83 1339121583330533 777668406796956285767208119 20631697622894012850096189285103) (P 39))

(43 494 (173 631487214494124226272182246257) (P 82))
(43 943 (431 9203 214657 352204792096060232123) (P 93))
(43 975 (760794456229697812600943141) (P 99))

(47 494 (78600827 96305633 3254929159912571892178939817) (P 81))
(47 723 (941 148944599693 4297208493581554998377715893) (P 90))
(47 943 (4654129 4425849847 118661493484981 151662915366592315832701) (P 84))
(47 975 (941 23689 59044310506021 14793342059424881431 415006657280347375289) (P 77))

(49 547 (7 39397 1071664760337802070421617128333) (C 80))
(49 775 (303703 114631189 688048201 1289683390728486468871119839) (P 72))
(49 938 (197 883 2334339127 328408231397 17990547612787 143454725242684646204632709) (P 60))
(49 943 (5881 4551826054521343026225679) (P 97))

by ECMfile2 and PPMPQS (Tomabechi)

(41 943 (83 821 2163404197 3802353367 2099397126586726921407093167 7969728445595676405001564567111) (P 38))

(43 938 (22963 1281229 4813936531673851629319 4932321202499400485892527 112134670585297450887144746292761) (P 36))

(47 549 (11898193633 52393321234531798957 83930453413286627846025280309 93777472695681813717597840071) (P 39))

(49 975 (197 18523 12274883585839261228969 3632530603656193416597869 3233588273622091534066710749541929) (P 39))

(55 775 (11 2158305228311 65902286957873741 344525738382196477988741311 10931487319715310705765327811) (P 31))

By Satoshi Tomabechi.
(August 22, 1999)

by ppmpqs
(49 559 (544097 16796007929 47273050750013306891 3102683071603523988766462471567) (P 50))
(49 862 (7 77323 148667 189337 23484700454881 138951051022057 1877979809172402265242463331132070517) (P 44))
(98 119 (883 1471 1924581681384748226071057) (P 57))
(98 136 (197 24697 123822876326324064373914767) (P 57))

August 17, 1999

By Igor Schein.
(August 16, 1999)

(49 287 (197 65141581 9059736578957 604676087071799486459776607) (P 54))
(55 593 (6541151 8041034005690369493041 784142407341236410310831811451) (P 53))
(126 639 (169517377 289824667241143687593949 384528412956021507825597509761) (P 40))

Correction:

false (88 913 (89 3826092477651022818713 292720663314597025035529) (C 72))
true  (88 913 (89 3826092477651022818713 292720663314597025035529) (P 72))

By Andy Steward.
(August 15, 1999)

by ECMfile2 (Ubasic - KIDA/steward)

(41 486 (121835897608630989482581540231367) (P 76))
(41 665 (73224737611 46238730134945720803752032861) (P 74))
(41 924 (83 1723 1144721 28967458056854559455177897059) (P 79))

(43 473 (556530253 208754129349543725918308919953) (P 75))
(43 516 (33129049861 1631842742338483 23789893513417690223784450901) (P 60))
(43 619 (173 51343 107388608257457117924227109) (C 85))
(43 796 (59233464626485133115670911727) (P 94))

(47 129 (12854817721 87850380350776135466771944661) (P 59))
(47 391 (26870740233039111291564680027) (P 91))
(47 665 (15887 1314779 1372646563 2516993304780241373 112427218867971099981451) (P 69))
(47 727 (283 37507 808307 13352742301 125588393427051299271659962331) (C 80))
(47 796 (283 941 2069 544340371 31636240715731 83920558980554347520479) (P 80))

(49 350 (883 271363 2318012023260053906564017) (P 75))
(49 514 (4999 7709078558770842629052881 44577639993087547047519248727619) (P 54))
(49 665 (6226956945906185551800182971 777784105639762810688863426027) (P 61))
(49 796 (727072054349076627527659 3685323657536874322546459) (P 74))
(49 903 (560046481504757394175941389 81625029429437469819249326747) (P 69))

by PM1file (Ubasic - Steward)

(55 665 (11 3191 64901 53223941 702186101 251312981671002957882953921) (P 61))

by PPMPQS (Tomabechi)

(49 348 (711725507641 626673118314853 4725411468041846358426958792798446876283) (P 41))
By Satoshi Tomabechi.
(August 16, 1999)
by ppmpqs
(49 114 (92317 189363967178271911926935661673799943) (P 47))
(49 411 (35281 97609 216679 427379 8533793941 31392172966940749429240279 326327036482137026590113259) (P 28))
by p-1
(43 789 (145513 526796404570699799033) (C 96))

August 15, 1999

Errata pointed out by Satoshi Tomabechi.
(August 13, 1999)

false (110 206 (11 331 250663051 151972250305829195571113401
448498915828800648272529421) (P 27))
true (110 206 (11 331 250663051 151972250305829195571113401
448498915828800648272529421) (P 28))
larget prime factor is 28 digit

August 13, 1999

By Masaki UKAI.
(August 12, 1999)

(100 276 (101 172169851832801 39825464212503418321764301) (P 56))

(110 206 (11 331 250663051 151972250305829195571113401 448498915828800648272529421) (P 27))
(110 526 (500709221 6110122199669454011 10028035648011414532999335902441) (P 51))

(114 648 (1483 13213138300054833961753845889) (P 70))
(114 795 (457 127317139 34069928472945306581908123903) (P 66))

(126 639 (169517377 289824667241143687593949) (C 70))

(132 718 (4018081 130133679117808385223958249) (P 82))

(150 323 (43404283542953418301 76839576370493946409133101) (P 55))

(55 593 (6541151 784142407341236410310831811451) (C 75))

(75 364 (151 2551 99517082283601 66450960092766812386041601) (P 58))

(82 851 (16891277417517756477026791 11354624752189367112818008969) (P 64))

(88 913 (89 3826092477651022818713 292720663314597025035529) (C 72))

August 11, 1999

By Igor Schein.
(August 09, 1999)

(41 674 (83 9031579050220042866031831231271 411557454741534185844043170845715641117) (P 42))
(41 966 (739 6397 2043523 64295327777352203740361191 385186168154024124959120824553833) (P 49))
(43 350 (1033 242845603712894779 10679491155060516393967 6129972379385979617170505464111) (P 34))
(43 903 (1984709 5378806619 16510396589083 283614018206861 5675001646144598310330048831338571003359) (P 41))
(47 215 (941 1129 22091 495851 19425808573 23071309380526704173 5330677626732499749793) (P 40))
(47 823 (3518891 101568051615883 1874241276976883791 1482189530302584341263 2818411050161146256719437156048827) (P 41))

August 10, 1999

By Aiichi Yamasaki.
(August 09, 1999)

by GMP-ECM4a

(57 640 (2053 60763 8062825431942116038237805290220587) (P 60))
(57 740 (6089650226271686825418755727307) (P 73))
(57 893 (629129749 1652699118534290146989197393581) (P 68))
(57 661 (4841025454046398938191894399029) (P 71))

by ppmpqs(ubasic)

(37 516 (1481 98939 26011112683442359451941173216988615859341) (P 50))
(37 974 (149 223 88350211179283 337140391567801524684935169612705779756384431) (P 45))
(57 459 (617311 64954187627853734099554809859360897) (P 56))
(57 526 (49163299 918415046508656116645005912392117142697303) (P 49))
(57 538 (457 206341 69734720314239075845037118946896126527583) (P 50))
(57 962 (58824977440107421 49358195179110185391798963831850252137487) (P 50))
(57 794 (6538823752717 1554677510584634892970275053993972272513) (P 53))

by snfs(ubasic)

(74 830 (7315645748239414679400427153780079056587761371) (P 60))
(74 923 (3109 1772779091448726493617588636367972192785563) (P 62))

Factorization tools (programs) are added (programmed by Satoshi Tomabechi).
PPMPQS and p-1 method.
The former is extremely powerful.

By Satoshi Tomabechi (August 09, 1999)

by  ppmpqs
(98 105 (168071 155932004537708033464604037299) (P 51))
(98 110 (3823 24298188732866962065445687241) (P 54))
(98 135 (2650230563 9999847980210094968036823988884331065127) (P 41))
(98 244 (7 197 16062593 12926647469 17139834785957338339543 221871539843047084830214159) (P 32))
(98 275 (4466939 9590775570867331 146612612925709895701968633316410497) (P 45))

by p-1 
(49 990 (336804931 781962640230873697 52292678711136284025179) (P 77))
(86 306 (169088196941312200465443451) (P 79))
By Andy Steward (August 08, 1999)
by ECMfile2 (Ubasic)

(41 350 (6370183861117 121632546477877008600955924097) (P 60))
(41 549 (83 5410706698702623979 7083906846415850037202457) (P 65))
(41 674 (83 411557454741534185844043170845715641117) (C 73))
(41 872 (739 373928693 833698369989866578998396007) (P 80))
(41 898 (83 175091827870009371615629809 161901548960189249730278330411237) (P 58))

(43 350 (1033 242845603712894779 10679491155060516393967) (C 65))
(43 362 (173 5010100411550784167 63768891256714958096402776643) (P 58))
(43 986 (202680977218256439718364189) (C 100))

(47 386 (343107239 19419334212281118994379491 263345185257511641511186525978439) (P 53))
(47 781 (16679497406643148517599097 21969384052450660053632429533) (P 80))

(49 531 (3930683 18739407383290622772241 1720493494324745306202429780577) (P 56))
(49 567 (9176917 1969511061949117 2448149488293677306044397) (P 70))
Update from Richard Brent's Table
(37 643 (223 27011 1463535373541341925268043842393045039113) (P 56))

(41 449 (287040702341 274491185968064922806999718008761311703) (P 57))
(41 641 (51907 50115148730177 3784001931986387951413760838315822798293) (P 55))

(43 433 (431 69317 823343533 2099986818763249033028236745618094853) (P 59))
(43 503 (431 148657709 294683387 18146104196299789906031600297941855913836417) (P 51))
(43 571 (173 1119387697 698229981334735323562639 55521271007539652267129050050361) (P 49))
(43 659 (173 1094437 1957925632184792122860778451) (P 83))
(43 719 (431 1291 885371 25956340597635873157913 900993369226645824340573293677873) (P 53))
(43 829 (1033 1291 22447 36551 24442308927733686280693 181106900093322625431447820619) (P 56))

(47 823 (3518891 101568051615883 1874241276976883791 1482189530302584341263) (C 75))

(55 307 (240131 4849348610047278523129476719444177371) (P 58))
(55 617 (268359781112606521879861 5744158460138394444833521) (P 64))
(55 983 (11 331 77551 143077560714541751 27426964229904858789423322033415016342359521511) (P 48))

(63 773 (127 29306593 1807241926459072835805649602752634572962372411) (P 50))

(69 277 (3037 613361963152584186845839) (C 81))

(75 823 (66751 473259240490957051 164746193245870100006350024733958448801) (P 56))

(82 257 (83 898164115540707132025619757954991283) (P 59))
(82 653 (83 19763 356701 681257 11592985115274150002781516807370939) (P 61))
(82 761 (83 219163943 9450169072151918254710889 258411205089680067331970244494056549163) (P 42))
(82 877 (83 16319 1080269 98161848476430494383 822417739195743811256707579787541071) (P 50))
(82 953 (260994777738952082779) (P 99))
(82 983 (41 739 51415265514920939634805687) (P 90))

(86 421 (247622173554991390023613 14126768291247437114310684479) (P 59))
(86 431 (39734034767667589 12858880540697997381737534553637) (P 63))
(86 449 (210333230425393335125587 1807169128519742754228550569679374540659917) (P 46))
(86 757 (2239000369 212595516194212577 1289632093270140216920241552203) (P 65))

(92 433 (2243135200517430609199757) (P 92))
(92 503 (277 1381 3221 1009609 1931553305772388324628093 123275752847255666786209297) (P 54))
(92 733 (17021 45541 17087437 197896417 6311542583383523355481) (P 80))
(92 967 (1013 15733 4102713382193 3727091568561392785973) (C 90))

(94 223 (283 659 941 60003258124660041922336979638687039) (P 65))
(94 631 (134228821687699 1263065527738214832521) (C 94))
(94 977 (283 379305439528097447 5852393751693657918650851) (P 93))

(98 421 (163536846658305241141483) (P 88))
(98 617 (197 481196991101936499327211) (P 92))

August 9, 1999

By Igor Schein.
(August 06, 1999)

(55 809 (2114696891675579531 16580040297989072788901051 43249931502283225383370741) (P 48))
(82 494 (83 3476719 8961843351755832263169645563 78006007955684451504589799861) (P 43))
(88 340 (6073 101377 294257591241226181543921 34564759366657626713973536633) (P 41))
(100 847 (5 8501 57301 7076501 306263475767588254644401 6941852116921746858280523160401) (P 47))
(100 955 (101 1901 3596070420620201 6706498969100628631090601 22015487841690285242029801) (P 49))
(110 807 (331 2137398880871 809111037442323746175541 18450548736517799871792632945884321) (P 44))
By Andy Steward.
He announced us the update of Richard Brent's results.
(August 05, 1999)
37,643,1463535373541341925268043842393045039113

41,449,274491185968064922806999718008761311703
41,641,3784001931986387951413760838315822798293

43,433,2099986818763249033028236745618094853
43,503,18146104196299789906031600297941855913836417
43,571,55521271007539652267129050050361
43,659,1957925632184792122860778451
43,719,900993369226645824340573293677873
43,829,181106900093322625431447820619

47,823,1482189530302584341263

55,307,4849348610047278523129476719444177371
55,617,5744158460138394444833521
55,809,43249931502283225383370741
55,809,16580040297989072788901051
55,983,27426964229904858789423322033415016342359521511

63,773,1807241926459072835805649602752634572962372411

69,277,613361963152584186845839

75,823,164746193245870100006350024733958448801

82,257,898164115540707132025619757954991283
82,653,11592985115274150002781516807370939
82,761,9450169072151918254710889
82,761,258411205089680067331970244494056549163
82,877,822417739195743811256707579787541071
82,953,260994777738952082779
82,983,51415265514920939634805687

86,421,247622173554991390023613
86,421,14126768291247437114310684479
86,431,12858880540697997381737534553637
86,449,1807169128519742754228550569679374540659917
86,449,210333230425393335125587
86,757,1289632093270140216920241552203

92,433,2243135200517430609199757
92,503,1931553305772388324628093
92,503,123275752847255666786209297
92,733,6311542583383523355481
92,967,3727091568561392785973

94,223,60003258124660041922336979638687039
94,631,1263065527738214832521
94,977,5852393751693657918650851

98,421,163536846658305241141483
98,617,481196991101936499327211

August 6, 1999

By Masaki UKAI.
(August 5, 1999)

(100 425 (3163801 24241753297501 78939559187099642524604378024501) (P 54))
(100 847 (5 8501 57301 7076501 306263475767588254644401) (C 78))
(100 906 (101 2801 825001 48526201 5827296893839620859201) (P 78))
(100 941 (701 124256897260595142201681991301) (P 88))
(100 955 (101 1901 3596070420620201 22015487841690285242029801) (C 74))
(100 967 (5 1601 12301 2479719901 2771311602611424564101) (C 81))

(108 984 (12853 30781 7330949867674877853572575786840933) (P 66))

(110 544 (331 9944754278471 326501376696672130691) (P 74))
(110 801 (6374941 392513529871 11685887545231244441251) (P 76))
(110 807 (331 2137398880871 809111037442323746175541) (C 78))

(126 960 (631 819873722543352285367665181909) (P 75))

(132 207 (405553676198650601455418773) (P 67))
(132 635 (84481 372901 119245064291160009387769) (P 79))

(150 634 (151 114901 862651 16757897069259303022621051) (P 74))
(150 683 (6151 766585801 4401175901906408498363284801) (P 74))

(55 809 (2114696891675579531 43249931502283225383370741) (C 73))

(75 656 (81909784542985016997187201) (P 87))

(82 478 (49037 6895881431 4002732074503913582072396723) (P 66))
(82 494 (83 3476719 8961843351755832263169645563) (C 72))
(82 970 (83 1559 7644041 52306235922817 7391953835565694465141873) (P 69))

(88 208 (89 881 340121 384902806358949906551498751736961) (P 50))
(88 340 (6073 101377 294257591241226181543921) (C 70))
(88 395 (127724609 369028812292264872546539657846691408593) (P 58))
(88 559 (11931633763137001 45233600438283618545537) (P 72))
(88 616 (89 135385009 28447672825001 229072448623990574588414353) (P 62))
(88 772 (89 10643031222683414140254800561) (C 86))
(88 879 (617 3169 25609 50513 289678906159897 82059411654047114452174823881) (P 59))
(88 913 (89 3826092477651022818713) (C 95))
(88 975 (353 147060062555087593297) (C 97))


August 5, 1999

By Igor Schein.
(August 4, 1999)

(43 786 (2753 49193 230042303565623 1706559175204399613 1563869562615252777130963) (P 57))
(43 380 (169469170141816451 27006388870360818371057681 46063311401842771755674372621) (P 38))
(43 816 (173 10837 492165257326681 304361820623586413369366551 3141325677787257660822251969983095629) (P 39))
(43 854 (338424863855294903787869207 483647682486129565700095341833 28266292665722227897915234402439) (P 36))
(150 815 (263119019220301 164183771583107663512201 22837552687340061061655341513046171551) (P 42))


August 3, 1999

On July 31, I could meet to Mr. Andy Steward and we were talking about
various topics during 5 hours my stay in London. It was very exciting and enjoyable experience.
I could hardly imagine that only I could get e-mails from foreign nation's people
but also I could really meet to foreign nation's people !

By Andy Steward (August 01, 1999)

by ECMfile2 (Ubasic)

(41 525 (83 686324888713 133947450245170129939805493113) (P 66))
(41 609 (83 1518313 2953069131747830061355762041107) (P 73))
(41 711 (1942595089 17994773803 453741072091693154753344070434863926009) (P 56))
(41 964 (83 37557055522701376034197272859) (C 89))

(43 380 (169469170141816451 27006388870360818371057681) (C 66))
(43 417 (1721 512819 1798003 217165459367871762252256769) (P 69))

(47 193 (34499 28993852670601648515955279503) (P 73))
(47 386 (343107239 19419334212281118994379491) (C 86))
(47 520 (1138999 3662697798164300444510141027) (P 92))
(47 740 (52453 60631 3953923 1711469563 1778651363 2565966881 14794945772117821030720927322609) (P 57))
(47 992 (128969 10645239396476158521411181) (C 108))

(49 612 (3823 1420113522232664500823 9427125137365676392351180384639) (P 62))

By Yasunobu Torii
(July 17)

m108_565 : c89 = p42 * p47
339454476633987827991648119815584190059817,
65751499309179922286704850060439793156666133317
m108_586 : c100 = p46 * p55
1500679141491156374052608422284045925857023977,
2937827761782452625165393343180307559347025255104344153
m108_597 : c89 = p39 * p50
688553193772421661184293413800599803749,
22421045226077929213708289768882085302298206179453
m108_606 : c97 = p42 * p55
649423414103075363359720562726599257269557,
3005434652113064128334065474992055259805458167896390133
m108_612 : c93 = p41 * p52
84081860724822645005221364045857305879913,
6609693776447656217780278706590701934383352747742941
m108_615 : c87 = p42 * p45
244661849117473414170511497496271082247153,
782860407086645448676651650708595682665823557
m108_629 : c98 = p36 * p63
392334297279438727791663743690143417,
189963901838446919049905293246262516905279690580833451727242269
m108_646 : c95 = p45 * p51
119527743208889066438237408989938606920609809,
293793601624980183326641826263942447162841695235113
m108_657 : c102 = p36 * p66
437609567633675139753823172260451881,
618395749130602623373058878442824979958566795206220371352500243513
m108_658 : c92 = p32 * p61
11888065859543688744983076610393,
5505964492059514740063912419671851629560449075919859165359753

m126_217 : c85 = p40 * p45
1615422378404195283374880250555286447041,
802166213949028868664187565416915795726634929


July 27, 1999

From July 28 to August 1, I will go to London for business.
If you find any factors, please send to me,
but I cannot maintain those until August 2, sorry.

By Igor Schein.
(July 26, 1999)

(49 255 (32831 390447877 7502524245927543231967 3669344677233901335667747) (P 42))
(49 700 (221873 664474514485153 93114831333756721088026673 1126202521507605379157052676859581) (P 41))
(49 950 (491 7253 30871 1038017 47647062569 12361202544967122663727 4564451739611019462255069666814715933) (P 39))
(55 644 (331 5046140221 246826450442626967454213761 528145536607657030587550631) (P 48))
(82 358 (821 303970159830787639518274483961 1976319537574790583323422105781) (P 40))
(88 767 (353 617 17002857873687401 113260939263915839969 65616920611775703378065177) (P 48))
(100 694 (135601 197739601 24327461818009430563854001 7038306848606284129435603198601) (P 44))
(132 901 (2748296243411533 7593145844321706896213713 828808621922687150694397879861) (P 48))

By Satoshi Tomabechi.
(July 26, 1999)

by snfs
(108 586 (1500679141491156374052608422284045925857023977) (P 55))

by ppmpqs
(49 254 (981961 65921857 108124087 6611013421062897868133506392587) (P 49))

By Andy Steward (July 25, 1999)

by ECMfile2 (Ubasic)

(41 351 (1723 37064329 116184161 35270886212071273709923098713) (P 55))
(41 608 (83 2546839 2965871449 443017106511125121998416633) (P 67))
(41 816 (83 5087527 7376664118268093140302427) (P 83))
(41 854 (421891 810653 75656809 456275071452643600431934845629 3438315857221888406505164824904233) (P 35))

(43 246 (4903 16943 236610521869 46187550897704670982294798955467) (P 50))
(43 418 (5419 7399871922515657966879 21550168014087350173646915169527) (P 54))
(43 766 (4809384193 6113323687903793 87676336946829865939280265285677) (P 64))
(43 816 (173 10837 492165257326681 304361820623586413369366551) (C 75))
(43 854 (338424863855294903787869207 483647682486129565700095341833) (C 67))

(47 526 (3306074446813961 1787434881418068450155899815282007) (P 77))
(47 570 (283 617300921333 34676365921575679499494759 6364260033559086327673764007) (P 60))
(47 636 (247375040770839484707550919) (P 103))
(47 747 (283 1693 811514373568159620088805536987) (C 97))
(47 867 (1304627 250812379859 99388854076364385062809127) (P 92))
(47 905 (341254258979141473514209841) (P 110))
(47 913 (283 1129 4889 5747727119873216683 944700488865945250873829) (P 85))
(47 925 (28859 28606848919958989750592235490939) (P 101))

(49 150 (197 1006559 105953590047689175464270652922393) (P 52))

by PM1file (Ubasic)

(43 917 (173 431 1549 5419 8222057557067636644603420882415653) (P 79))

(49 766 (197 224911 71260864143686948683 17703920753233461347255327) (P 69))
(49 782 (491 883 209917 451990098872812878233073602931247) (P 78))

By Masaki UKAI.
(July 25, 1999)

(108 956 (16417 34580056573 153428712697794712814985232549) (P 64))

(110 616 (3304510165451221 6922339571646166986671) (P 75))
(110 626 (22323684504818022509371) (P 90))

(126 858 (127 883 476106247 40071435369402632235448610990341) (P 61))

(132 602 (285517 2581756320133 67266650931684722577313) (P 71))

(150 455 (751 1327382913065915407534801) (P 80))
(150 480 (184351 6517201 18952201 2248823678101699084201) (P 67))
(150 514 (151 486601 11859751 48074034451 6699710036467711578451) (P 61))
(150 728 (1531168501 213024103818137223887101) (P 82))
(150 815 (263119019220301 164183771583107663512201) (C 79))
(150 944 (7951 147888226415253521763151) (P 92))

(55 417 (131231 518522973643677425346221) (P 76))
(55 820 (20977441 592348054541 2730150346618855684143718451) (P 71))

(75 385 (1786382199157588388524501) (P 80))
(75 491 (96001 928140323901127773093751) (P 79))


July 23, 1999

By Aiichi Yamasaki.
(July 22, 1999)

by GMP-ECM4a

(57 776 (114799 470295091153455323399604955837) (P 70))
(57 700 (621298671980440489810781153189479) (P 70))
(57 616 (229 243076156030619145197779356668693246127397) (P 57))

by snfs(ubasic)

(74 795 (506683700121224144604219689822072960794211585059637) (P 54))
(74 988 (3109 18131 278611 2397130359535706787621767233203208532160360439) (P 50))

By Kunihiko Miyazaki.
(July 22, 1999)

(49 255 (32831 390447877 7502524245927543231967) (C 67))
(49 267 (7 197 32378170949298925507) (P 80))
(49 516 (2549 21169 42304772373826550701 7625115939516081120143) (P 65))
(49 643 (491 5881 1242968738162593914394511) (C 88))
(49 700 (221873 664474514485153 93114831333756721088026673) (C 74))

Errata pointed out by Satoshi Tomabechi.
(July 22, 1999)

false (55 677 (30971211152173427357311 93821152040360458891) (P 71))
true (55 677 (93821152040360458891 30971211152173427357311) (P 71))
not in ascending order

By Masaki UKAI.
(July 22, 1999)

(100 415 (101 15273391169045223255001 45519604143737739419803901) (P 55))
(100 579 (101 4001 65794249009201 72489700461666210662974501) (P 66))
(100 687 (5 204601 3269701 1440122691581057774539778862001) (P 71))
(100 694 (135601 197739601 24327461818009430563854001) (C 75))
(100 960 (101 1801 219460641869746892543338901) (P 88))

(110 570 (58411 11743768510992766957721 1717727049062567046012521 93023195055078225890959713851) (P 31))
(110 789 (11 7151 3260219830100703152909381) (C 87))

(132 901 (2748296243411533 7593145844321706896213713) (C 78))

(150 822 (238019284294962105301) (C 97))
(150 837 (151 4538851 2253728068947151 99411439511525370184951) (P 70))

(55 539 (506706600402205858359015301) (C 83))
(55 644 (331 5046140221 528145536607657030587550631) (C 74))
(55 677 (93821152040360458891 30971211152173427357311) (P 71))
(55 754 (661 3407604735627890050441) (C 91))
(55 941 (331 270821 165709569079091135400611 273427671054654223511721571) (P 62))

(75 212 (1806151 202313565106289619251513551) (P 61))
(75 558 (2038280569505949305044201) (C 86))
(75 592 (151 24151 39451 4822351 336408749268687840186751) (P 70))
(75 814 (209550217790049151 3767449812176932516430701) (P 75))
(75 824 (151 17695201 92001182977466148570417451) (P 82))
(75 830 (4801 4951 242253691836290434210021201) (P 84))
(75 990 (6596176051 231328318411834755312167534401) (P 81))
(75 997 (135034538303709811461001) (C 97))

(82 358 (821 303970159830787639518274483961) (C 70))

(88 464 (89 353 1038140401 39548870928296852312609) (P 71))
(88 546 (3092321 375392255284298204569) (P 83))
(88 767 (353 617 17002857873687401 113260939263915839969) (C 74))

By me (Hisanori Mishima)

(132 837 (2113 124397959908595010086549 133620808894049834669989603081 377173645417551527995849677697) (P 32))


July 20, 1999

By Andy Steward. (July 18, 1999)

by ECMfile2 (Ubasic)

(41 255 (56909 2809900728154496612941167093449) (P 62))
(41 423 (13859 3937939276512174529 2457249173807297109807847580738539) (P 49))
(41 513 (1291836715997391923 273540372714120475494464347) (P 64))
(41 572 (5003 319898300030576257968085051) (P 81))
(41 581 (112093690369 10059758435697844719121121) (P 75))
(41 706 (57738526223319676692229 2339055918866072961291433 2334392037705544295936833783051) (P 37))
(41 718 (2417033 1019875568633859942791 1603983862009053207435435226877) (P 57))

(43 298 (431 11353 216141981266694404826825852473) (P 68))
(43 454 (1549 718785600601 21362105482435027630701551) (P 72))
(43 539 (431 2237 128399 1632797 853704024341245273496156849) (P 71))
(43 679 (173 391817 14665753 2327036178321015815567994084299 3649027975272881632346496118849) (P 44))
(43 706 (173 303371142277434353 2602293846673022992577 1074898870154486161598775959) (P 52))
(43 845 (2513179 7849278739 437393374491513490254034255651) (P 77))
(43 868 (431 22756031 63204256319 20803892426207919257 1565918405261703287295068389) (P 57))
(43 888 (173 5591 2248910459278035001761529244207) (C 88))

(47 500 (294096713671757582840135328140129) (P 92))
(47 535 (479541950005209036594296953) (P 99))
(47 782 (283 2866656253074595471396849 12286490873512983943407001 21351798622949043180389609) (P 56))
(47 868 (941 4231 28859 51607 1459727 8875142210826187064963) (C 92))
(47 950 (2459173763 993670612436461 495154009241286847269027229529) (P 83))

(49 299 (287141 254086561 60382663747635891105770284337) (P 62))
(49 448 (197 870374978699282664015174397 17574476543878558753032036293) (P 54))
(49 950 (491 7253 30871 1038017 47647062569 12361202544967122663727) (C 76))


July 17, 1999

By Igor Schein. (July 16, 1999)

(100 616 (5063233745070601 15573444861045738233101 5458221367340773548159624901) (P 46))
(100 987 (5 2190647101 37475672031601 3071539939640201 2938641567320106366232696288365901) (P 48))
(110 385 (2882771 6180251719681224728731 80301911827893396298620978711971221) (P 41))
(132 874 (1160759465449 38878065886741634713513 59342105041288665600954973) (P 58))


July 16, 1999

Errata pointed out by Satoshi Tomabechi.
(July 15, 1999)

false (55 868 (4701841 7045391 7268173787639710176331 1181938984223318033508401 623920573534920772829951) (P 35))
true (55 868 (4701841 7045391 7268173787639710176331 623920573534920772829951 1181938984223318033508401) (P 35))
false (88 929 (4126421641 456046406452921739300473 359199002086434779716129 35963954908389848983244318201) (P 34))
true (88 929 (4126421641 359199002086434779716129 456046406452921739300473 35963954908389848983244318201) (P 34))

not in ascending order


July 14, 1999

By Aiichi Yamasaki. (July 13, 1999)

by GMP-ECM4a

(57 892 (3079 166154596963950312070330075453) (P 74))
(57 717 (964897 147774545882281035733719169) (P 71))
(57 671 (74271207461164239111314003904909862663) (P 64))
(57 547 (7639 255975691248032197464965712565093) (P 63))
(57 629 (229 402558257026839979833908405017) (P 69))

by GMP-ECM4a+ppmpqs(ubasic)

(57 823 (314483162817469097169282379051 13694898844450311020384032877810480101) (P 39))

by ppmpqs(ubasic)

(57 602 (229 188555317 30283391055790815882685837990177369) (P 55))
(37 510 (149 223 2221 6518841810044187177561736184979120660628469) (P 47))


July 13, 1999

By Igor Schein. (July 12, 1999)

(88 805 (881 1224169 102320417 4927958737559737793 3329536775732260527328355332934289569) (P 44))
(100 375 (101 1780301 108141737241001 27219332455944186631859982844201) (P 50))
(100 622 (5 1901 7901 185401 3047531092786467401 35623380193464542933933568023007913201) (P 43))

By Andy Steward. (July 11, 1999)

by ECMfile2 (Ubasic)

(41 543 (821 5003 132289692561020343447071 12390505368728560429861868063) (P 52))
(41 640 (83 1595091881 1032058172873555781384549319) (P 75))
(41 891 (83 1723 82493 3575018617 2244322969424992910537604923) (P 72))
(41 936 (83 76275680638748296063703259413) (C 89))
(41 942 (83 134569487749 18861023288452873167533108052653577199) (P 69))
(41 962 (83 123589555152899521360518800809) (P 89))
(41 991 (83 1123628325992323 45566041673211299793005251) (P 78))

(43 288 (431 1033 5591 334461071688169094544479) (P 71))
(43 366 (58309 77573 59692444487482949 396156163443966672366235523177) (P 52))
(43 570 (173 2237 4270043707 331662487301 576557832274607715912403) (P 66))
(43 696 (394682635845907261 76289963287585815918001139) (P 76))
(43 700 (75031784461 16380554850500532440786258201) (P 81))
(43 740 (139837 2986351 23716067953 39773933137305811 427287113670718233575643981583) (P 53))
(43 880 (431 1745111587576565405545695199 71578895752801724560290337807) (P 65))
(43 962 (11783 41453 136397 881055415348918050349) (C 91))
(43 979 (9203 499403 543349 11082911419 4000844951541369901 57514460099114971452788096630606989) (P 47))

(47 176 (5196979 42040373 520981343369387096743106647) (P 63))
(47 182 (14427994988416391580399239) (P 79))
(47 184 (1129 498372491 149747569031 21628200130156880776541110139) (P 53))
(47 275 (283 2069 63257853733133 111039236672834291665346089) (P 67))
(47 344 (283 249834348587 885033178570039564608400849) (P 76))
(47 366 (51371836841004473713421) (P 96))
(47 457 (4281629710460065433423 20930055709731303333915887808439) (P 70))
(47 570 (283 617300921333 6364260033559086327673764007) (C 85))
(47 612 (47 659 2003611 13161505587122209907483 76963326981279236346198431561013179) (P 61))
(47 746 (8491195128111535389421 395482741489897950996314099831) (C 81))
(47 782 (283 2866656253074595471396849 21351798622949043180389609) (C 81))
(47 860 (10659977 10544680452215893 4656921450952890761724527) (C 88))
(47 885 (99829 7469802382423668094008137791) (C 103))

(49 612 (3823 1420113522232664500823) (C 93))

By Masaki UKAI.
(July 12, 1999)

(100 616 (5063233745070601 15573444861045738233101) (C 74))

(110 385 (2882771 6180251719681224728731) (C 76))
(110 705 (13041802037495659925604493541) (C 86))

(114 796 (618679 11047741 273087384520805062953600652097239) (P 60))

(126 495 (127 809843131943478327674211877) (P 68))
(126 524 (631 714340156743517588736877433) (P 69))

(132 295 (11680006089545459390698513) (P 74))
(132 604 (5821855385412388575793) (C 90))
(132 888 (2113 3037 3697 62418799363240263088993) (C 85))
(132 958 (5281 17170009211195248981 162496642331372899639981) (P 74))
(132 959 (116293 19189871621333377437893650297) (P 86))

(150 620 (751 365851 4976401 15214351 349816063669353094351) (P 69))
(150 649 (64147341505160506740001) (C 90))
(150 656 (151 199501 49104001 95106926991653104616198401) (P 72))
(150 797 (723901 16481701 1842030519162875523673836451) (P 76))

(55 596 (4792481 1038595338977699428033360561) (P 78))
(55 828 (11 5724841 70073170321266515371 9492916763583264580031) (P 68))
(55 843 (3631 1884527779417923995086601) (P 90))
(55 868 (4701841 7045391 7268173787639710176331 1181938984223318033508401 623920573534920772829951) (P 35))

(57 699 (401053 15422660971649717698747766677) (P 69))

(75 645 (347883301 37575643688069724751 1968970468931603273540166151) (P 57))
(75 680 (1951 4495801 152509051 83811025351 5349863252868898593451 837967588820426678311631563951) (P 33))
(75 725 (151 6314996666439301 11932080491407670981747551) (P 72))
(75 783 (751 331113354934051 50283028387456165911948001) (P 73))
(75 917 (151 144856801 37440232291645951275601) (C 86))

(82 737 (41 83 17713 79996564380730447897 2585503889511778953157591 218943815346500068984347841) (P 37))
(82 778 (41 89627 6826888955494059547 62678491344566376210741349) (P 65))

(88 150 (89 617 36823517299123442146601) (P 60))
(88 781 (2729 820073 1379178408732639710052881) (C 83))
(88 929 (4126421641 456046406452921739300473 359199002086434779716129 35963954908389848983244318201) (P 34))

By me (Hisanori Mishima).

(132 440 (114584596507237593381349 24300914578021790206882561 3275973863651922266379079249) (P 30))
(132 453 (38281 648324337 99189234430248214126513 7898110058600302632403128461173) (P 39))


July 12, 1999

News !

Sophia Kokyuroku in Mathematics 42, "Factorization of Cyclotomic Numbers IV" was published.
Authers are Mitsuo Morimoto (International Christian University), Yuji Kida (Rikkyo University), Aiichi Yamasaki (Kyoto University).
Contents are,

  1. Factors of phi(n)=30
  2. Factors of phi(n)=32
  3. Applying Number Field Sieve on the Factorization of Cyclotomic Numbers (by Yuji Kida)
  4. Aurifeullian Factor (by Aiichi Yamasaki)
  5. Number Field Sieve Method using 4 degree polynomial (by Yasunobu Torii)
  6. Some Techniques on Integer Factorization (by Satoshi Tomabechi)

(Sorry, all treatises are written in Japanese and published only in paper (cannot download from Web's sites).)


July 09, 1999

By Satoshi Tomabechi.
(July 08, 1999)

by snfs
(37 665 (145271774757735242415525257372036105741139602159423) (P 52))

By me (Hisanori Mishima).
(July 08, 1999)

(132 304 (17774461 363338449 61572266982347393491763017) (P 58))


July 07, 1999

By Andy Steward.
(July 04, 1999)

41,605,3279253715253828283931669819
41,605,6690761948976598120925036873599
41,638,6354883607019640556503053497
41,778,3093469020263931816971753671
41,898,175091827870009371615629809
41,913,253109950842261504912803
43,187,15585693866368941370364759
43,370,14134114104930663208770017
43,518,6008439245045996667935983793
43,778,655607083185424005519265891
43,885,1824640499870393218274269
43,885,627319685988896195934633332081
43,908,7761328666612732366641067129
43,913,31084798657356549839403521
43,993,66889119024753112215749057
47,518,4254696766166467539220283
47,546,23001295815624562652239
47,546,11979817714445860499579102669
47,631,297877973293053264179446377841
47,655,100924965537081516991969007
47,664,1279926167206018083071
47,664,2825659494363327674658328259
47,793,15894183092224015760173193
47,993,309517597569908814615276061
49,168,3291885292724234918350619
49,187,403768403361364250047343
49,187,9822592608209148549186511
49,546,545039488611149737922963
49,546,27159272595882879138999313891
49,579,1202809371659380425475543
49,655,46831781948841477136016749
49,908,120595502694967640657932933580641


July 06, 1999

By Igor Schein.
(July 04, 1999)

(43 401 (3527 10430130640350668987294145919 68201642949875251996507736183) (P 49))
(49 662 (29390400558334369 145613422336555256777443 459377495097688185485992014449) (P 50))
(86 352 (1240660540738938335764901 13807270432426573237794248881) (P 55))
(86 871 (34057 1274547855353165347 47269577570624799996461 3388500458605078172244291062763811) (P 45))


July 05, 1999

By Aiichi Yamasaki.
(July 04, 1999)

by snfs(ubasic)

(74 770 (6641907319048206131278526397492728985339995329) (P 59))
(74 952 (607837 298840610216629275291011950664168068882866614167) (P 54))

by GMP-ECM4a

(57 644 (6271 9463 8741650815627459070211759971) (P 66))
(57 427 (2281 145984019979346376441777163241) (P 63))
(57 764 (5701 6693397 924022852644540522102441991) (P 67))
(57 744 (19716496205629 4052188260447648182317751599) (P 63))
(57 858 (229 27452797 132457972151060059882779592575751) (P 64))

by ppmpqs(ubasic)

(57 592 (388899239077 326007363369486609529474976886384609937) (P 50))
(57 314 (50681885428729964884545561470493478160881) (P 50))


July 03, 1999

By Igor Schein.
(July 01, 1999)

(43 358 (1029702941 6190230454171508264324047 855707282356586140069540569572389003) (P 38))
(43 664 (155317 25847331649 943002167335110089573588351 378985952283085751728199674255141) (P 44))
(49 447 (197 3529 76441 13092250940721028672513 2793171694484887188053884958407859) (P 46))
(49 958 (11299793 4531741570302889391 49960449511371810312763471 398044739794149667586210803) (P 48))


July 01, 1999

Errata pointed out by Satoshi Tomabechi.
(Jun. 30, 1999)

false (43 501 (1291 20297 3557245091 12474384227848139 142981928449264339737073) (P 59))
true (43 501 (1291 20297 3557245091 12474384227848139 142981928449264339737073) (P 58))
largest prime factor P58=1490321813671577325995069706866354131898404808969721245117


Jun. 30, 1999

Errata pointed out by Satoshi Tomabechi.
(Jun. 29, 1999)

false (86 404 (431 935254998465383898271 209339268503584961549 166636010663314581501173) (P 43))
true (86 404 (431 209339268503584961549 935254998465383898271 166636010663314581501173) (P 43))
not in ascending order

false (49 622 (1 15600645242401396810697) (C 96))
true (49 622 (15600645242401396810697) (C 96))
trivial divisor

By me (Hisanori Mishima).
(Jun. 29, 1999)

(43 356 (173 4903 812737927 289517631396669141191018507) (P 66))
(43 358 (1029702941 6190230454171508264324047) (C 74))
(43 365 (44549 2600194951 400725780063765009089) (C 73))
(43 423 (34083441397 573680170778084835167) (P 80))
(43 510 (173 759037 305864982463981363427773 4064092418295370067353891) (P 58))

By Igor Schein.
(Jun. 28, 1999)

(41 873 (77396521 356119441 3919633142095972809240977 116986752477574533161237705302081) (P 45))
(43 688 (173 1721 10837 124305875046373 525944679536645455381 21799288442872512376666577473) (P 47))
(47 322 (2351 294127 7648944689 644885196598062683021767 992324988402864933788496098206573) (P 40))
(63 922 (791029 17810411572404147119698915039 55338363500996457404652480761638369) (P 38))
(100 524 (5387674093498001 1270327820772337153601 15207797191246790757046201) (P 47))
(110 672 (331 53681 162251 1053581 73026629822294932104751 116096992537585663742783371181401) (P 40))

By Andy Steward.
(Jun. 28, 1999)

(41 637 (59074523 9641754896948272283 10584844740541066504164631153) (P 58))
(41 834 (83 793843 26275141350242954199883) (C 87))
(41 867 (83 6971 21157 68389 7717513 2417902103 1980074428935289067733143303) (P 60))

(43 183 (173 1761214269883982958937993613) (P 66))
(43 226 (68113 561085157 543480249745769175795457781) (P 59))
(43 254 (173 5591 93456055850671 3909302540952535511189 46725518312219594562012227) (P 34))
(43 308 (173 8429 910139 165412759935076855400993) (P 70))
(43 401 (3527 10430130640350668987294145919) (C 78))
(43 445 (63716161516711278231031087) (C 86))
(43 501 (1291 20297 3557245091 12474384227848139 142981928449264339737073) (P 59))
(43 584 (5721835221854991146471) (P 95))
(43 589 (4654955956134730927 12077004043194831905845469) (P 73))
(43 648 (431 4817 541367204657 81130746474360134711 165783212656257374996972831) (P 54))
(43 664 (155317 25847331649 943002167335110089573588351) (C 76))
(43 667 (173 1033 2091665107810066316000129) (C 90))
(43 668 (173 2753 14908961 112359259 667362051152183283781468819) (P 71))
(43 797 (343313 10409358141041573315843) (P 95))
(43 923 (122538821 439229846059036498260031) (P 93))
(43 933 (1291 2148486989750333 346123419268961409675726409 5067919929162456426658147889) (P 53))

(47 214 (6863 30269 92779 14183849 3228114280893095463031 17353113375828832943939683) (P 41))
(47 299 (283 659 530409134488975292933) (P 88))
(47 395 (2129648053004048920593769) (C 96))
(47 466 (1212623820448633 349909878996102372519105263) (P 82))
(47 536 (283 3038363 1178147325748470828792091) (P 93))
(47 603 (17092662397 24561601288057538311) (C 99))
(47 611 (1787 217647868061668371808153669) (P 99))
(47 781 (16679497406643148517599097) (C 108))
(47 797 (941 3392162867 208866924837396380515377047928179) (C 89))
(47 812 (14947 16451 74212434617687170670665781) (P 100))

(49 136 (50791049 698226230075599021963922050247) (P 53))
(49 374 (18523 836921 278147685817 4448997498640344823716509) (P 62))
(49 466 (304211280494481576158923) (P 89))
(49 514 (4999 7709078558770842629052881) (C 86))
(49 648 (417089 4130897 1308999623504180383136089) (C 82))
(49 812 (197 176597 7988788956508416799 39827772802762057157633) (P 74))
(49 840 (87219467585993 417995841167461353672023) (P 86))
(49 958 (11299793 4531741570302889391 49960449511371810312763471) (C 74))


Jun. 29, 1999

By Kunihiko Miyazaki.
(Jun. 28, 1999)

(49 214 (12251 22194593023 35093566689617804364109 177867099063712836071805957713) (P 32))
(49 264 (116576881 42880221605777751788307233) (P 69))
(49 375 (3137 88200413331463828788709) (P 82))
(49 447 (197 3529 76441 13092250940721028672513) (C 79))
(49 458 (373969 5230457 1397782463562360541) (P 82))
(49 469 (307809132585347 6496370044368583 198983816513321975032139383) (P 56))
(49 473 (21876737 1619881410473327 2023001814929522896984019) (P 66))
(49 622 (1 15600645242401396810697) (C 96))
(49 662 (29390400558334369 145613422336555256777443) (C 79))
(49 766 (197 224911 71260864143686948683) (C 94))
(49 880 (16073 1572202180183816986743) (C 99))
(49 957 (1373 3137 50177 10116916615531153 1410094888127986139647) (P 77))
(49 983 (1373 36457 68209 5141963 18320089261781171243) (P 88))

By me (Hisanori Mishima).
(Jun. 28, 1999)

(41 975 (6151 55115891 2590129901 78807172016880833125141439 675181225786177441547116625598449593) (P 37))

(86 183 (4817 9461 11825861 114542961482809532269 666776593361168970653538301657) (P 31))
(86 292 (9649543795873411 828682241021074547125713313) (P 61))
(86 297 (250519412616502763230613) (P 81))
(86 312 (1979 127947211078789 24694744059281555620396116791 25417585812936560745148555873) (P 31))
(86 352 (13807270432426573237794248881) (C 79))
(86 404 (431 935254998465383898271 209339268503584961549 166636010663314581501173) (P 43))
(86 412 (1291 179999 21898267 19081087896384907187983) (P 72))
(86 482 (74821 20458111 13589886024876809940806093 18796045599492331766976851) (P 51))
(86 491 (1033 6219754327520815009) (C 92))
(86 495 (1549 7609197527 13301203417 80749411643 2426707979162734643) (P 61))
(86 497 (173 21157 129303373057512772367) (C 87))
(86 523 (173 1229553696623245289587) (P 91))
(86 525 (431 2623259 45606059 111265597 1698618826792332373899216041 13380549294915198573054916530463) (P 32))
(86 572 (431 1291 936274618691461897457) (C 90))
(86 588 (3358952589944191 145988494894599840937) (P 81))
(86 712 (10143520286093863 87305742001049246959 7194359960951384565306244363) (P 56))
(86 731 (47562817 31076247472221737 1408274481884867044573861 3488605643491104946891021) (P 48))
(86 768 (680314009 264144200857 473121408071739744697) (C 81))
(86 778 (124342322643209879139739) (C 99))
(86 785 (107190548325908340121 867190097864779958958797 582476503805525064544088087) (P 51))
(86 830 (431 39336793781810554258693 5273387144197256873311231 147596327565826398515920951515451) (P 41)
(86 868 (166841 52529283407 924588106810632862441) (P 87))
(86 871 (34057 1274547855353165347 47269577570624799996461) (C 79))
(86 890 (173 173807 10840650147113222947787) (C 95))
(86 897 (280557973738549114661737213) (C 98))
(86 926 (1191068796973938337849) (C 104))
(86 987 (173 49193 5969863 238572391537 87739853190601603) (C 84))
(86 989 (20899 5597562363419180849) (P 103))
(86 996 (11353 33333257 3964282028008408292779787) (P 90))


Jun. 28, 1999

By Masaki UKAI.
(Jun. 26, 1999)

(100 524 (5387674093498001 1270327820772337153601) (C 72))
(100 864 (94238008164335998088398055563357801) (P 83))

(108 815 (109 2053 1485494249248140305369801152321) (P 70))

(110 448 (11 331 58894923957682121 106370146122517101820381) (P 63))
(110 566 (331 392314826077351 3459657743625774848416271 4059610485490377721417697041) (P 41))
(110 672 (331 53681 162251 1053581 73026629822294932104751) (C 72))
(110 740 (331 991 3536822323741899339841) (C 88))

(114 606 (229 34392852623949711613184209897) (P 70))

(126 482 (127 14570450124963892291564867) (P 70))

(132 704 (1966009 3157500669694085112289 3837954777992018811073 892382515366878904778760819481) (P 35))
(132 803 (7358341 653162641348193646989539573) (C 83))
(132 872 (1453 270003761698463752762798117) (P 89))

(150 497 (168475615459888473846973033801) (P 79))
(150 518 (353401 1508401 548504081401 23426183276366789479501) (P 63))
(150 993 (492785101 38287446751 664240853583954495001) (C 80))

(55 915 (331 84701 723530560097731 554284388618803959505511) (P 73))
(55 951 (11 1906071400549031 13049422812508066711) (C 84))

(57 822 (3307 22729744269725693959473744480989947) (P 68))

(63 846 (127 42737689 691406898821824353355772421103) (P 66))
(63 922 (791029 17810411572404147119698915039) (C 73))

(82 588 (739 30013 45962363737590541459889821) (P 78))
(82 621 (5003 310781 8931701171 47508679166180746963151) (P 70))

(88 917 (89 12497 2905057 749841886290134366333333609) (P 80))
(88 928 (89 176353 4436267089 2652852587995147429937) (C 81))

By me (Hisanori Mishima).

(41 559 (83 15531457 266414939186100759010170859273 58414812853524806660308420591849159) (P 37))
(41 715 (83 1627391762974121812519 11479052933054431762997 246939243654215606664778549) (P 43))

(43 502 (16926263 33207560994449 10068817638048381728291 3415943028828246915939039348006859) (P 38))
(43 546 (26317 6741083477773 92227763139796929651003659 233436824728816936801838068660769579) (P 37))
(43 630 (7912517 69887471 12522053051957 137572218790017572153 43931391748286545269629913984793) (P 38))
(43 824 (173 29327 123778511 20097204991216723 72584412530773997580557 198359223140577568622131860689) (P 40))


Jun. 26, 1999

By Aiichi Yamasaki.
(Jun. 25, 1999)

by snfs(ubasic)

(74 683 (2591 4374047412752322126333405457418638600367) (P 59))
(74 705 (24591607 58731840866334796947047016965051411127865939) (P 52))
(74 924 (37 93441939391226799952264607397532091576324029) (P 62))

by ppmpqs(ubasic)

(57 686 (220260504763513 10535829035190010429944323702941) (P 57))
(57 896 (4561 13273021 96308341 817587882937832102735387275856143) (P 55))
(57 437 (1171123 58237481942466691864834982709360072830331037) (P 46))
(57 532 (20749 549481 93810475049997994159113422809472892605377) (P 48))

By Satoshi Tomabechi.
(Jun. 25, 1999)

by snfs
(86 108 (677758025043485464444254649256929) (P 53))
(86 110 (3654829 504181104438429253926134775506468153) (P 44))
(86 115 (12329005515674199840736926288732726581) (P 50))
(86 122 (173 12915662630816356567310353375920391) (P 52))
(86 132 (3982747 5544724154702547791902800734875633069) (P 46))
(86 146 (131548095197395714334092367) (P 65))
(86 147 (7187881 42859554623846084633728294969875031) (P 50))
(86 174 (176345581 71259203851607801929029392025309430690903) (P 46))

By Andy Steward.
(Jun. 22, 1999)

(41 314 (83 25661252225172393731153543) (P 73))
(41 380 (83 83 4357891 8767740814450447816239923701 106572989640272966555028135829) (P 36))
(41 394 (118262533 892334282438046371111) (P 75))
(41 398 (5003 35999 2090035840713415644258977) (P 72))
(41 507 (83 6720229 38610193 4943711312358594461968489) (P 68))
(41 543 (821 5003 132289692561020343447071) (C 80))
(41 559 (83 15531457 266414939186100759010170859273) (C 72))
(41 621 (83 51157501592469631923855149) (P 85))
(41 646 (83 25450376323049 383440707200343444219761) (P 74))
(41 681 (83 6033893371500119 785378857509365484876955459) (P 69))
(41 715 (83 1627391762974121812519 11479052933054431762997) (C 69))
(41 730 (409536885878257 147150914848133768735356584239) (P 71))
(41 737 (19995127 391355097345529631739353) (P 84))
(41 747 (4019 249961627166539969550731151) (P 85))
(41 770 (83 84871 418447 9875526222103 1773456634169317771215121) (P 66))
(41 774 (83 39419637571229 4563603020178045290201983159) (P 73))
(41 790 (9103 19865700905954389587679) (P 90))
(41 793 (13378527524176637001263437) (P 91))
(41 849 (821 641300990624340282567887) (C 91))
(41 873 (77396521 356119441 3919633142095972809240977) (C 77))
(41 880 (4659141696679 586612121718113 562645782876297733044599) (P 67))
(41 975 (6151 55115891 2590129901 78807172016880833125141439) (C 73))
(43 147 (3296817311 25814727652176328282687537 641095261482330581927675123) (P 30))
(43 171 (775807 5131363 185562464593710607331321 10771673915462874443152517) (P 33))
(43 176 (14879 10345359767 592104592295708631244909) (P 57))
(43 192 (431 6338029 573336398799736435083347 10353560855052385496336789163061) (P 32))
(43 232 (804417905173329108967831) (P 76))
(43 242 (265453990231 448296866202213689303) (P 69))
(43 264 (13159 386809752656960637023081) (P 75))
(43 284 (611699382920215913 221580915677610437163975013 230812040791146913227894041) (P 33))
(43 291 (173 5419 10837 914540718425224282297117) (P 70))
(43 340 (190759257066549362283600563507) (P 78))
(43 352 (173 20641 31477 33512309 5483790771653953385201) (P 67))
(43 362 (173 5010100411550784167) (C 87))
(43 363 (3907583 467014165393 348056577486908544548341) (P 66))
(43 385 (1979 3908768143371370435417) (C 84))
(43 391 (4817 6451 1128662436693346889194435079) (P 75))
(43 415 (4468022013282470776385183) (C 86))
(43 430 (173 197016400591096871602903) (C 86))
(43 450 (554847226760279 1971660548210264143 46046453320660066756921 1518129429828661522436025769) (P 29))
(43 462 (13159 209954833307 4626886355834546350193) (P 75))
(43 465 (173 12793110792555793677561811 5275502786881448935573572773 9564499441837542861459314807) (P 29))
(43 490 (70951 2886136085514973306403159 34746093697390543164323329) (P 59))
(43 495 (173 431 669840493003182867287 1268908341486511756707361) (P 64))
(43 502 (16926263 33207560994449 10068817638048381728291) (C 71))
(43 530 (33713 1046191 674090398099 15313241073455438451744863) (P 67))
(43 546 (26317 6741083477773 92227763139796929651003659) (C 72))
(43 558 (1291 3011 18233 515227 485511596296567476137) (P 79))
(43 571 (173 1119387697 698229981334735323562639) (C 81))
(43 582 (540125258574110411414309) (P 93))
(43 587 (3527 16993019646436815194584403) (P 88))
(43 592 (330241 127684525511 51676015578854488880017507) (P 75))
(43 630 (7912517 69887471 12522053051957 137572218790017572153) (C 70))
(43 636 (173 947 36293 1374533821738979544088207 446157072392246468061493283) (P 58))
(43 680 (4903 39848617 1243259075910997 1326142870296463461019537943) (P 66))
(43 688 (173 1721 10837 124305875046373 525944679536645455381) (C 75))
(43 698 (173 2285279 15608141 5052823015816336597699) (C 82))
(43 719 (431 1291 885371 25956340597635873157913) (C 86))
(43 726 (42571 721453657 18193752501710543) (P 91))
(43 738 (98729 1722034671832572795384563) (P 92))
(43 745 (56827769 1301213656273 3262958174022369430637) (P 80))
(43 748 (335465987074659700249) (C 101))
(43 750 (2468534094603648219233) (C 100))
(43 770 (180773 25083765686563036934387 4841051165105223828438361 829058596175649241602876439) (P 42))
(43 773 (173 5308793219747684564456843) (P 95))
(43 794 (25801 443761 7414031972953289026521457) (P 87))
(43 824 (173 29327 123778511 20097204991216723 72584412530773997580557) (C 69))
(43 829 (1033 1291 22447 36551 24442308927733686280693) (C 86))
(43 839 (396719 17478116140299281722694839) (C 92))
(43 885 (524322188349679 110925455298001273945098263) (C 84))
(43 890 (10415891 1258991850548563367957970611) (C 90))
(43 901 (173 173429861782479110184451) (P 99))
(43 906 (18749 6525649286477 27020210124629713498796171) (C 82))
(43 933 (1291 2148486989750333 5067919929162456426658147889) (C 79))
(43 954 (514711 2760773 1530648276619471 56050452808822117547359) (P 76))
(43 978 (14258721289847058123731 10319374474968042122103019 31661246280395685339218039) (P 53))
(43 993 (350881 505859996859701147 111604532111927916878087) (C 80))
(49 134 (7 2843 66347 55061000244872680000533389) (P 55))
(49 141 (7 2549 130613664159447500268648601) (P 60))
(49 162 (7 160231 4367567 22903037543801525579753047) (P 55))
(49 212 (3137 1630721 17410061666137365491323) (P 66))
(49 279 (91465587713937022085222331654669163) (P 68))
(49 285 (197 55469 17753785939 764445781316932640255471) (P 62))
(49 321 (5989603691 763434695689 182505758534251449809) (P 64))
(49 323 (7 6959 8429 2146691 9134360012147622534431534183) (P 63))
(49 336 (5881 263812669 1576662127072427146249) (P 73))
(49 382 (491 8233 1919429 1028034079129052384131) (P 75))
(49 448 (197 870374978699282664015174397) (C 83))
(49 455 (197 93435161 6789320957435707516847687) (P 77))
(49 504 (4019 32612147 2196673534319041 10901779942808762236602521) (P 63))
(49 522 (275196643 85453179873215818637 122294103765645178306717 739190359762345165925027) (P 39))
(49 531 (3930683 18739407383290622772241) (C 86))
(49 790 (675319 67702512444769456733655443) (P 91))
(49 838 (140171389276619177 2645014944571229386801 101375008671115086539485351) (P 59))
(49 947 (491 131356751 4060518537273762257) (P 96))
(47 123 (2821230760874348399371901) (P 72))
(47 126 (4231 11093 8115492635655598882909568653769) (P 59))
(47 150 (44890198756184775822911) (P 78))
(47 212 (319847211009639330023) (P 87))
(47 233 (6299 287190388949690627346072293941) (P 76))
(47 274 (659 5469822589419434641561783) (C 85))
(47 318 (911707 1946354380038779 3677507773829553818315281) (P 70))
(47 322 (2351 294127 7648944689 644885196598062683021767) (C 73))
(47 339 (941 6377807 147428191 1004440667 10502510697921308300177) (P 68))
(47 345 (1223 319074541 1020582076129667 19238435885102829151033 3322915072939212934183073) (P 44))
(47 348 (1223 71929912621507 48260848830141803547607481) (P 75))
(47 372 (622187 54999589 48746733050677902834259) (C 83))
(47 405 (2539 641245867725544347251) (P 96))
(47 455 (1693 20399 246416448892943506606021) (P 92))
(47 534 (283 151717 1441679 95491841779865912837 9067016919500912214851) (P 70))
(47 553 (19553 34620776066229880257893) (C 100))
(47 558 (283 10550467 28202257 31862792588205359371 1060058320611498410707 1939958123999722350414347) (P 45))
(47 562 (5263646127139317429179 35171664321238924685387) (P 83))
(47 582 (283 447057853056727599714031) (P 102))
(47 599 (11492013088849 30096285329310273149) (P 96))
(47 612 (47 659 2003611 13161505587122209907483) (C 96))
(47 627 (283 2351 741521734690765454671831) (P 99))
(47 652 (283 1129 21836884542380592736829) (C 102))
(47 680 (276173 1236850392464033293555553353) (P 98))
(47 690 (139591 2945773 4463899637 16505656836377 10720398967836703801) (P 78))
(47 692 (20399 28817470021 57398661023281785967927) (C 94))
(47 805 (1129 93719 442271 9255130398550277876804034211) (C 93))
(47 848 (74449 15574446052163350296761) (C 108))
(47 879 (10328627 699907633707893283317) (P 108))
(47 883 (3823265197 144788522447604995041) (P 106))
(47 921 (659 10529 1715248739 1005011562778058149 9871899046760496079199 561621850483190962748711) (P 57))
(47 926 (1600667470942583 135148454346719524509433) (C 99))
(47 982 (659 10074901307247275616486637343) (P 107))
(47 985 (1129 1924651 2422965527 15330582167031192001 1560900749940643719169) (P 79))
(47 989 (15511 1141117322309 7210497236320587300901) (P 100))

(43 171),(43 192),(43 465) was completed by me (Hisanori Mishima).


Jun. 21, 1999

By Tetsuya Izu.
(Jun. 18, 1999)

(41 280 (83 2362244767 1205141176737978398509971455447) (P 57))
(41 301 (1042631 1689858953 66508679882624917155217150002959) (P 53))
(41 308 (83 25913 113501569033 755717672432922027998109086790586091047) (P 44))
(41 374 (2297 2144629 18937819 136911851589177371464939777305382587787) (P 48))


Jun. 18, 1999

By Igor Schein.
(Jun. 16, 1999)

(88 895 (3169 6894104369829027209 4559896498857442576241 1829626768415521455692776937120033) (P 41))
(132 966 (1329241 294990675722557 450342322843882112749381 2296832356577301988888081) (P 51))


Jun. 15, 1999

Errata pointed out by Satoshi Tomabechi.
(Jun. 14, 1999)

false (110 420 (11 41025447607981 41588953051048894916345678561 19273588977304129423977011) (P 37))
true (110 420 (11 41025447607981 19273588977304129423977011 41588953051048894916345678561) (P 37))
not in ascending order


Jun. 14, 1999

By Masaki UKAI.
(Jun. 13, 1999)

(100 553 (5 101 505316153853974101 1157323349194925366401) (P 69))
(100 582 (5 5701 169003305331100325047401) (P 83))
(100 775 (24069733301 345446227001 3638767607454689584571101 9605365154931090568984339901) (P 42))

(110 420 (11 41025447607981 41588953051048894916345678561 19273588977304129423977011) (P 37))

(114 771 (1317692599 29673908262409012242801377227 16082233915112855972237803611691) (P 36))
(114 952 (229 21739710639733 164811364344353680683767210689) (P 63))

(132 440 (114584596507237593381349) (C 83))
(132 670 (352309 13097629117 2859098031109 5905848334820898580777) (P 64))

(150 141 (151 10305253073638940061146745301) (P 56))
(150 969 (151 1051 299875695519948601 34086331877692399212050551) (P 72))

(41 511 (114373873619590023066017077) (P 83))
(41 562 (83 83 795647 369953208999509 423981000422880720989699) (P 63))
(41 966 (739 6397 2043523 64295327777352203740361191) (C 81))

(82 364 (83 2294369677 278949331075547128397042689) (P 65))

(88 895 (3169 6894104369829027209 4559896498857442576241) (C 75))


Jun. 12, 1999

By Satoshi Tomabechi.
(Jun. 11, 1999)

by snfs(+ppmpqs) (110 159 (331 3851 55117005241278008350839432115751) (P 51))
(110 162 (11 507358209149794077737531) (P 64))
(43 129 (1033 56503 1310015264871275073519830827) (P 54))
(43 133 (173 115327 463682327384363122095154648517) (P 53))
(43 146 (29814173239 971327245177909062503300123010142129) (P 45))
(43 155 (75095287 1039753904865225697020689) (P 61))

By Aiichi Yamasaki.
(Jun. 11, 1999)

by GMP-ECM3b

(74 834 (139602719076555948330974057472574327) (P 71))

by ppmpqs(ubasic)

(57 420 (4592149 666842651719928765561850269241421) (P 55))

By Mark Belangee.
(Jun. 09, 1999)

2070157802654406597388773250622056351814939103128952047013785168505682757834533509435973
// C88 (57,391)
1690026642806346634982479010864224150954621
1224926134428768094408561618399507295231127913

1392761889108958206502051249754613645043315881098993136214546453210113871579223151631357 
// C88 (57,679)
11845566128919113761874016627114135408739
117576642091317688744659499085329230435015647263

348758005718797569400106868404824283214782164706667509886001699484539076196337550989063
// C87 (63,290)
37617134652358487136423313779875653
9271253883153788705120685238280645964652566858410971

8130641519230203514677845963997986299448025471118353963700028363898855166504162370767
// C85 (63,310)
9109671763831795974246176696071338039133
892528482915416972931909866257634080559990299

1095785749389736627952122739655754099863547799758643582498700734371308122723681602625887
// C88 (63,371)
19899658528355977216208266163952614203
55065555412837812933716422832696815042891565738029

812609086939219577444553467921118068575354642267144434447866280791764039970440960693939 
// C87 (63,478)
4628522876930269787807150470026647887
175565533226479027151233117921602253625397291944797

2135153010341669987259048165890549833404724000243402167232064265755919193837151673613
// C85 (63,556)
1577370003550078476891173388108416893
1353615832389501229713985808250220563335485817041

272497226193503838529492584762849948028881260508272676309604160585409837148290243542677 
// C87 (63,681)
188121093643647753791990450732829147600073
1448520316970340961124814423430986062919056749

515447473242801271994034468014217241644248787757695288966451505722402476283387338577897 
// C87 (63,717)
4883828227197256463841693355424866817599819
105541687640109233494190615085796574148564763

181243611894796736335268695425242997503961622141759448584305909495979144512095878867549
// C87 (63,735)
7530491201737118957612731925665199169949
24067966755340981609987524273941016404469182401

714253762982789226270297463278335715050821209928529019750015831211826153528786800663963
// C87 (63,766)
9353018163640681964448146793687195428533
76366125937765146911026640406547515116193469711

651763811534665982636933462634280364827421763631295487775404880773382271616527863470199
// C87 (63,843)
1252354934524259433169015372641187725283
520430585265554867851700214470851363605892399453

32804570999575389965242894373294769207520180222220196085075894396280780629800287947939 
// C86 (63,939)
881400218617437750118398091414914594446563
37218700774810971395191699831248309503122753

191536074798676663520048930997759537047340739219458633392521455006613278811384963583221
// C87 (108,615)
244661849117473414170511497496271082247153
782860407086645448676651650708595682665823557

52086868618283123992034936049702894672256888761857154777955214139326602524855763905457 
// C86 (108,725)
90474943505810235591443035591749884322241
575704903479029449426213807560138800524436977

291535715285012687544871287973155387263454024864624174615043634939649704321836581161629
// C87 (108,833)
1234466140367505600644778801882632022300433
236163395456291184339326286686955240107832013

1575183405622062882988337767429886752795686958938653558420458752558861255185666199937 
// C85 (108,856)
13410682714865885823071823695651929
117457361352375830951889538997182877991640744661353

184042078295530566566137285098585743008682190970662953254204209759367430228275704558001
// C87 (114,249)
2420100413002696534554654221831054387407
76047290148256134536044433480107550409566428543

4615057313030181903382550355346927375995972975802448583287827919074238470729991583073 
// C85 (114,427)
8094037587903058157883180962702740379503
570179871653624965903553969165439043727366191

247974801544091873990532753560414324701348235883372041315452537192878564952480914103831 
// C87 (114,974)
2194204719998430622987337497746444622533307
113013521155979117031867014927159694998082133

1295837253213028785969034102780913257549388822907199838452960676931566690615299295089 
// C85 (126,217)
1615422378404195283374880250555286447041
802166213949028868664187565416915795726634929

79454456612999992536982504235194928087976464885307576102488838541253916651579489867391
// C86 (126,291)
2493706609547349982414604482291078062889
31861990624238800551340682540650596786345052519

2172858184149067508842674014521468951313670423123725759297667980114369853352365445127473 
// C88 (126,737)
1975940463812046676142416564006806360545233
1099657719421930838253067831342112380703549281

3817137082584574962006299174150948896188455889872948513854120419765891299916141717719719 
// C88 (126,755)
117393129080727790353724515189570452922097
32515847498703628914749132842572113341544002327

3132794475223511232419129722739710878502177149830938726837810924156512057472240739887
// C85 (126,816)
683269853758617477112794570037681864531
4585003213576946240567313825653447836709441077

-- ECM --

2969467056198460870967500798441008626548016566177529254713937535913094954057542316242121
// C88 (57,720)
3449499820489646991092711789241979549
860839892949161889671405043431873619981888353004829

78638333456555334042312502678953017255699159666285920628863684322803301522204336537469589 
// C89 (63,407)
3566733939321399558812499398841367
22047715022869612524002310821143666447421295261999894067

224763293363021538039301563087637347326694678054037894893684404645263695853888064314489
// C87 (63,544)
4878650171920531070055860490633566437
46070795290194202275073228719677942206158930747397

30046714157051453181816611497178431010878856791631234546375725507969348891620221556194317 
// C89 (63,693)
1168128059327404097196621819151
25722106336827519163814634813302617414771989377975416831267

884419681589783364967505880012585002373684206926830182061564702410563015235895888450462697 
// C90 (63,697)
2426334711546983518330262893
364508522826965900291340771793953824962785370001495078622971629

244687894115759805923194082089567300064816814833650730186153946011469782746880752602656717 
// C90 (74,685)
41885633906180250485929391
5841809501172571723090607504334201081075576755236482290554686787

57272834850963164747001300319386611239421193591164518257099710859880629908056954305680723 
// C89 (74,690)
14351906443399654245460711424409017
3990608152082997887826407276363706480628534726023418219

79404743212530137880823738015730326043202185184981174367638287213957111363603508705739921 
// C89 (108,785)
10355475352189273715211104659935313
7667899397369818207261622769016014916993819538938929217

423136050346657310119396500339067378815129214761620219924928506106994288185778057735190911 
// C90 (114,583)
3256014637442281478564984839
129955205201118550689067366068883804814308692826524869316994249

246351045611340575026214843761904409497960347559263778461600802931705536413651258793537629 
// C90 (114,644)
1112711862081665584257167251
221396979762996416516226109173847504878941847890283297104524879

90720911348248246036285559723293898700955052921845300160410784620759286411906294253109 
// C86 (114,806)
69311721350104746595942331132648994059351449 P44 found by ECM
1308882676423547588483636836420899654041341

337291707444353640884219853195423072146324079431719054627743464055282390256136105947150969 
// C90 (126,807)
18759637744640174352841363052120611
17979649289375080085026160418531190213148285318590745779

224667926841649673849749902401569093069027724900845293576499674622556489736421554526028281 
// C90 (126,866)
364323671612262107152003681057
616671230412819503284973916737130064617930267244563326006233

620650361524548470236569684058837104205339530242840144053704627811744756766801364486417307 
// C90 (126,984)
12915982638667628690786323471
48052895307125681400608669530676144915685396128083409036987317

Jun. 11, 1999

By Aiichi Yamasaki.
(Jun. 09, 1999)

by snfs(ubasic)

(74 643 (149 3331 4240873138086232161412270064574579010526307187) (P 50))
(74 679 (2887 6217 2175056403200064282597984935437977021852140129) (P 50))
(74 908 (14752429672838364074833342941069112826623864181151167) (P 55))

by GMP-ECM4a

(74 870 (119881 50554283520503462542196637873178101982151) (P 61))
(74 717 (149 3798431192983181618623254333152687) (P 68))

by ppmpqs(ubasic)

(57 674 (20363144017164913 2016355512484184922821553963422754307) (P 50))
(57 831 (229 228884523076078183 61291020085055703749734231414503157) (P 51))
(57 605 (78938615987461 29858867159552268887383506199702966495801) (P 46))
(57 814 (22003 292183 194816767 175182150337134126965230560336096441035251) (P 46))
(57 840 (229 14198767094090671 11176509580170964998310796856144391691557) (P 47))
(57 927 (15277 451897 18513430027 30755906826656886554091937914046065259) (P 50))
(57 934 (544292634562849338769 1775430443388887838603639592466401) (P 53))


Jun. 08, 1999

By Masaki UKAI.
(Jun. 06, 1999)

(100 716 (24743619602101 655472448843701 9535920571802011601 909553844676642742355981833294901) (P 35))
(100 777 (5 344304345242801 61706582286254072501) (P 81))
(100 976 (101 1601 7736389855886570125801 1471117629805413157091401) (P 69))

(110 671 (85691 52497982209021625032791) (C 86))
(110 991 (881 4199761282629472505221) (C 96))

(132 966 (1329241 294990675722557 450342322843882112749381) (C 76))

(150 737 (151 32326066051 129204734472901 503591184009632557768393501 56890377355582115692031202451) (P 33))
(150 816 (151 700509961211249790901) (C 94))
(150 824 (2851 34351 170164003164979061758150751892301) (P 77))
(150 997 (6121123051 23180755491509430569937520651) (C 82))

(55 323 (11 3012131 1645105661 51408676489180392872491) (P 61))
(55 859 (35743425618569176895641 38806807264249686504297181) (P 70))

(88 921 (89 881 3648833 32526467956966838774657) (P 85))


Jun. 05, 1999

By Satoshi Tomabechi.
(Jun. 04, 1999)

by snfs
(37 607 (105958138724981026190260026127597964528496763) (P 57))
(37 802 (3928516135357893486470614472568309267761659) (P 62))
(82 114 (3971759316429990712618064027) (P 55))
(82 117 (83 79489401609349894591488231195193) (P 49))
(82 132 (157523 1092275746754045835207528009169108372051) (P 41))
(82 172 (83 821 44933880532505337584740894706521230691) (P 47))
(82 184 (83 1056254562122946096529349) (P 65))
(110 136 (991 1575055825235908904581134479690150535731) (P 44))
(110 143 (991 1005597193212742043886040164772831) (P 51))

by snfs+ppmpqs
(110 147 (817081 76906393715500563462534001 245803542007242435809850841) (P 29))


Jun. 04, 1999

By Igor Schein.
(Jun. 02, 1999)

(100 992 (5 101 231901497148105603201 734080971691766601000001 1470350427838817717463699643227489601) (P 37))
(110 584 (390721 8991401 143875999468973867167601 383897311603283219372401) (P 52))
(88 968 (353 291457 885840907576241 387396862905152333729 66410076474112126535895108587969) (P 45))


Jun. 02, 1999

Errata pointed out by Satoshi Tomabechi.
(Jun. 01, 1999)

false (55 301 (11 24091 928621 135761209881473286261783941 40799458875548118997661191) (P 37))
true (55 301 (11 24091 928621 40799458875548118997661191 135761209881473286261783941) (P 37))
not in ascending order


Jun. 01, 1999

By Tetsuya Izu.
(May 31, 1999)

by snfs.exe ( programed by S.Tomabechi )

(41 214 (83 3760677391037285039166965081561) (P 61))

by factor.exe ( programed by S.Tomabechi )

(41 895 (83 170601366824869 140279836049787613768847 1143032016081926984495359692571064771) (P 43))
(41 250 (5413 6151 1926919 615315638948316964831252192733443) (P 50))
(41 258 (83 2384020708961 5363952337114627133229824509363301424719) (P 43))


May 31, 1999

By Masaki UKAI.
(May 30, 1999)

(126 470 (317097916639214156694043868899) (P 67))

(150 862 (4655851 5393227866178384762416451) (C 87))
(150 918 (151 4022974693657088802301) (C 95))

(41 360 (83 6088563797 6218052455355593501062027 13020526575622903723767638921) (P 38))
(41 917 (83 220697051693145517339 8878752188347095387419) (P 75))

(55 301 (11 24091 928621 135761209881473286261783941 40799458875548118997661191) (P 37))
(55 748 (3149401090470031 394890959947727648021) (P 79))

(63 867 (87104777452663829004396037571869) (P 74))

(75 391 (7008264109464930187609051) (P 79))

(82 566 (72389406071 17728986933533 7717993855431341775325601) (P 62))
(82 626 (83 4025680418707904785711) (P 89))

(88 143 (89 2210331312312734888201 19227044942313060161850113) (P 38))


May 29, 1999

By Satoshi Tomabechi.
(May 28, 1999)

by snfs
(37 514 (149 223 50812044584620561371995820907134911) (P 59))
(37 591 (5651055802913434079479012001411028323435627) (P 58))
(37 708 (1116861734167948701704790913455419) (P 70))

by ecm+ppmpqs
(82 532 (41 83 2297 550139 11464093 45494617611645102566621 15029801365277324546829530174207) (P 36))


May 27, 1999

By Tetsuya Izu.
(May 26, 1999)

by Mr. Tomabechi's "factor.exe"

(41 183 (83 821 27799 541612044339134680665046179874397) (P49))
(41 200 (54899627137 437315434858452571589896875904595097223) (P 43))
(41 226 (13464351968009 8044106459824735662316890142203759526207) (P 42))
(41 249 (821 1155893731 86627533302778020148261886771042383747) (P46))
(41 253 (83 161869 50023691 43770576979929136698886473928409) (P 50))
(41 254 (4019 3764063008523 4242815758452553264270431129754753769339) (P 41))
(41 501 (83 1231 4967233 13486457335389673 19107275915165559635141107598992009) (P 46))
(41 629 (83 256516993 5383478843 35217684311 27336626248261895384875885463953116107699) (P 41))
(41 678 (163181 35771710259 9211746195599723 15781069055843544619564008109) (P54))

By Aiichi Yamasaki.
(May 26, 1999)

by snfs(ubasic)

(74 530 (11027 45288384778888692847927432311166012891) (P 57))
(74 574 (2887 75067078733959621027559095026345129162022469) (P 52))
(74 819 (593 3690408930253967281772636504830504208685581) (P 60))
(74 632 (58130561604321145878419127321573838992509) (P 61))
(74 668 (9103 33464133999522814426907187244549124149) (P 61))

by GMP-ECM3b

(74 831 (149 92797726629857329972630259561254377462493) (P 62))

by ppmpqs(ubasic)

(37 988 (1032340627 4231768667107 654540660081109090353815458089270877) (P 51))
(37 721 (149 22349 451751723 1195827691913992453769126094924714279793) (P 49))
(37 891 (917971 3409583688871 110932783229043815687452798310391423133) (P 50))
(37 464 (149 77479 256867361169298556755622377282878616883) (P 51))
(57 390 (2053 390109 230690229116927818763536237706446849) (P 50))


May 25, 1999

By Tetsuya Izu.
(May 24, 1999)

(41 286 (83 2000029693) 13291677341668853402792071741) (P 59))
(41 402 (83 5413 111767 40127849 1503171320878485467493505163) (P 59))
(41 518 (19927 4880969 437998901 21444264013429008078949759) (P 64))
(41 530 (4414395500951 240291545536056843230263) (P 73))
(41 584 (83 1108313 11260970328123966679 248953609289280465609211) (P 61))
(41 721 (1487099521 98528182729985471003 7103149796181830669250443) (P 61))
(41 741 (83 2707 46005081059563579304453 64632229530311307167072061511) (P 58))
(41 856 (83 821 3367603471 167367614685516964333 851021064636931528140944233 1488602030013948983024665889) (P 29))
(41 963 (1366367 4137595590421 92897902442844689 1003115700814913048933876853601) (P 54))

Errata pointed out by Satoshi Tomabechi.
(May 24, 1999)

false (75 804 (151 601 8994639151 61273009121851 173271364484249654764290277501 1539316899159725808186993301) (P 32))
true (75 804 (151 601 8994639151 61273009121851 1539316899159725808186993301 173271364484249654764290277501) (P 32))

not in ascending order


May 24, 1999

By Masaki UKAI.
(May 23, 1999)

(100 611 (10501 947826042740247425801 1166178869440859860601 45082932732364953185586301) (P 40))
(100 700 (101 21209637208825826511901) (P 90))
(100 992 (5 101 231901497148105603201 734080971691766601000001) (C 73))

(108 839 (108541 1479211279089531270982823197) (P 74))

(110 567 (11 67211 351121 145920611 876915298981921168531) (P 70))
(110 584 (390721 8991401 143875999468973867167601) (C 75))

(114 646 (571 8734413137851173232624657) (P 74))
(114 944 (94586927548237 466164222205496206440588013) (P 67))

(126 793 (8191 4510056601 14983751635326740151770616271) (P 63))

(132 165 (9244357 190037459533739090685228169) (P 56))
(132 620 (111947206017731822497) (P 92))

(37 572 (149 3923 545818528492372729591680085575584723827) (P 55))

(41 861 (83 3715093 3476880266611137515267) (C 88))
(41 895 (83 170601366824869 140279836049787613768847) (C 79))
(41 970 (9267149 45861725042553011493197 231895196438465672175562841) (P 64))
(41 986 (821 18114224057104244420091236549) (P 89))

(55 394 (11 7090182842560511333409331) (P 78))
(55 688 (4703711 15039648380674322164651) (C 85))
(55 976 (1560131 654134967069782163241 2044863361997937053101 364933728096049346531549834341) (P 42))

(57 336 (56786658766561288530937549) (P 66))
(57 860 (229 626702605985256729122808433) (P 77))

(63 328 (127 58207286113160991555565102626271) (P 57))

(75 513 (2009860935372062663251) (C 88))
(75 799 (53086351 112768947936298351 104676284602318153955059051) (P 66))
(75 804 (151 601 8994639151 61273009121851 173271364484249654764290277501 1539316899159725808186993301) (P 32))
(75 873 (6301 70501 8394858752618025039771451) (P 85))
(75 908 (1498351 71501629140301 1593283018305009267601) (P 78))

(82 725 (903641 1286630351821693 575555256753996283630519 880875322571946322029403) (P 46))
(82 979 (83 3214073 33230322735909803292825818372807) (P 80))

(88 183 (46867421080781966465039801 74215388556717662167192177273) (P 36))
(88 968 (353 291457 885840907576241 387396862905152333729) (C 76))

May 22, 1999

By Satoshi Tomabechi.
(May 21, 1999)

by snfs
(37 596 (6101152852375413032923198037127707) (P 67))

by ecm
(82 425 (2543 169115436928080022965973) (P 79))
(82 472 (83 339541745065855071827482229) (P 79))


May 18, 1999

By Tetsuya Izu.
(May 17, 1999)

(41 939 (83 286952633834876557 382314721196648267) (C 82))
(41 939 (83 286952633834876557 382314721196648267
 1255283476205530283511549287957) (P 52))

phi(41,939)
  = (C 119)
  = 80739572305561240050006484607355798554413901731391\\
  = 53722986299570662094373710912197074427117358624291\\
  = 6478670081203101201
  = (P 2) *  (P 18) * (P 18) * (P 31) * (P 52)
  = 83 * 286952633834876557 * 382314721196648267
   * 1255283476205530283511549287957
   * 7063749730043245732054993909734614136110537029173809

/*
    From: 1999/ 5/14/ 18:34:20
    To  : 1999/ 5/14/ 22:23:01 (03:48:41)
    ECMX.UB (UBASIC on WinNT WS, PentiumII 300MHz, 512MB)
        B1 = 130000; B2 = 5200000
*/

----------
(41 265 (83 35753 74835251) (C 83))
(41 265 (83 35753 74835251 985706889646964704976879
 9049206560792846067720845021) (P 31))

phi(41,265)
  = (C 97)
  = 85403742912937877675299536427961430890696171287677\\
    82023021199438203448187667880009746912753943241
  = (P 2) *  (P 5) * (P 8) * (P 24) * (P 28) * (P 31)
  = 83 * 35753 * 74835251
   * 985706889646964704976879
   * 9049206560792846067720845021
   * 4311434670934375091814397644451

/*
    From: 1999/ 5/15/  8:39:35
    To  : 1999/ 5/15/ 11:01:47 (02:22:12)
    ECMX.UB (UBASIC on WinNT WS, PentiumII 300MHz, 512MB)
        B1 = 130000; B2 = 5200000
*/

----------
(41 802 (1559 179581 51058390956900676714590647) (C 83))
(41 802 (1559 179581 51058390956900676714590647
 2044358566584872062863277 (P 58))

phi(41,802)
  = (C 117)
  = 14706745721481772479494280652893948166365242127576\\
    48022329353029562260983199757341083296336414046562\\
    66136223182667551
  = (P 4) * (P 6) * (P 26) * (P 25) * (P 58)
  = 1559 * 179581 * 51058390956900676714590647
   * 2044358566584872062863277
   * 5032524384728667898258625796343579004532693520712037242951

/*
    From: 1999/ 5/16/ 12:26:29
    To  : 1999/ 5/16/ 14:34:05 (02:07:36)
    ECMX.UB (UBASIC on WinNT WS, PentiumII 300MHz, 512MB)
        B1 = 130000; B2 = 5200000
*/

----------
(41 292 (3652778766426473) (C 84))
(41 292 (3652778766426473 27142929418884928354118219) (P 58))

phi(41,292)
  = (C 99)
  = 41381280030988545418553968520845627641732324602500 \\
    2887263688491008754909402145564919911515375126901
  = (P 16) * (P 26) * (P 58)
  = 3652778766426473
   * 27142929418884928354118219
   * 4173725026036510345017163315346907142204140162890197189223

/*
    From: 1999/ 5/16/ 22:49:04
    To  : 1999/ 5/17/  0:42:56 (01:53:52)
    ECMX.UB (UBASIC on WinNT WS, PentiumII 300MHz, 512MB)
        B1 = 130000; B2 = 5200000
*/

----------
(41 377 (14325853463004997339 (C 84))
(41 377 (14325853463004997339 2743222993320100101003654991 (P 57))

phi(41,377)
  = (C 104)
  = 11345078715900138888385894003722346871085885066755\\
    42554471741294054353287885529552670991127981574440\\
    1801
  = (P 20) * (P 28) * (P 57)
  = 14325853463004997339
   * 2743222993320100101003654991
   * 288686115434067241425832796321141447440290677729872691749

/*  From: 1999/ 5/17/ 10:12:22
    To  : 1999/ 5/17/ 10:33:26 (00:21:04)
    ECMX.UB (UBASIC on WinNT WS, PentiumII 300MHz, 512MB)
        B1 = 130000; B2 = 5200000
*/

----------
(41 393 (83 1537726807806703763 (C 84))
(41 393 (83 1537726807806703763 2123216689433816268619603 (P 60))

phi(41,393)
  = (C 104)
  = 59814778435704367294483356737432960938821394529238\\
    16743261404934809603854712654930822550228889837626\\
    9001
  = (P 2) * (P 19) * (P 25) * (P 60)
  = 83 * 1537726807806703763
   * 2123216689433816268619603
   * 220727732082194067853205949193890043105952550412702820747323

/*
    From: 1999/ 5/17/ 10:33:26
    To  : 1999/ 5/17/ 11:29:25 (00:55:59)
    ECMX.UB (UBASIC on WinNT WS, PentiumII 300MHz, 512MB)
        B1 = 130000; B2 = 5200000
*/

May 15, 1999

By Satoshi Tomabechi.
(May 14, 1999)

by snfs

(37 552 (1760154273625112138159885548358195969501021) (P 57))

by ecm

(82 356 (83 739 4168567318546117 17417131050563998130483) (P 60))


May 13, 1999

By Aiichi Yamasaki.
(May 12, 1999)

by GMP-ECM3b

(74 796 (1259 9769 13483972357883508934039716904132112201) (P 61))

by ppmpqs(ubasic)

(37 524 (8363 1192739549 88216165840506863201283268575052870661) (P 47))
(37 545 (6017990744279 142964981270941404772232433788398003) (P 51))
(37 655 (593 25377222017803 4765530397298930128792633032195406367) (P 49))
(37 864 (6217 21333446988060743 34271866685443688587009206052473941) (P 52))
(37 876 (2887 3257 3787321 7296697 38924635497240849215912267587608158464489) (P 45))
(37 954 (258378031 11613221446819 152555852479298582942223657481462873697) (P 48))
(37 648 (906510731225441 2454235080594965917785782959488567265049) (P 47))
(37 893 (26641 4254041379559799 191996812229786192847639798558133991303) (P 48))

By Igor Schein.
(May 11, 1999)

(55 598 (11 3571151 61627617515552176136050861 15099447829406374372433707089696665881) (P 41))
(75 365 (19051 22387714416268419427501 165060843063818355701987720034601) (P 44))
(82 376 (538331 2327968564545240748961 113742762365738016709107139259) (P 47))
(82 598 (140641536425104543 829007026965407926450453 1094734523231615314314444319924213) (P 37))
(88 766 (89 197895017 58345289165730955641878857 22839378811339838735699279569) (P 51))
(110 645 (11 991 299510311 935894930278548865535336581 165015844266360426021729913398014891) (P 38))
(132 622 (7393 10429 167113 20438672740935671592613 5121870571599177575406349) (P 52))


May 12, 1999

By Tetsuya Izu.
(May 10, 1999)

by ECMX(UBASIC)

(41 155 (1952703645502483938800838198911) (P 58))
(41 194 (83 2360278500136403636167929487) (P 63))


May 11, 1999

By Aiichi Yamasaki.
(May 10, 1999)

by snfs(ubasic)

(74 499 (575774254639941083688921767652374771433167354081) (P 50))
(74 510 (24483598756211315430580423674702281) (P 64))
(74 980 (149 3701 11956990384204699985661989356446779997657046609) (P 56))
(74 847 (12433 159485493966000642430268368814830695221179) (P 61))
(74 684 (108254620636072333368382874353599902753) (P 65))
(74 848 (149 21761850374969328912668518354364653) (P 69))

by GMP-ECM3b

(74 884 (223 1541791 1090688010335321038934798875502219) (P 65))

By Masaki UKAI.
(May 10, 1999)

(110 645 (11 991 299510311 935894930278548865535336581) (C 73))
(110 752 (661 1097573111486953693489483741) (P 86))
(110 776 (11 796291 924661 58214592569101 41033153974344839460451) (P 67))
(110 813 (661 1504607093771 119026918288081 53056369799058990617441) (P 65))
(110 855 (11 47923465281035366066103833401) (C 88))

(132 658 (4261357 4473308797 20152200859461001 66798915441552933937 597475023094740497636004769) (P 34))

(150 600 (14401 234629389801 14258935965151 104619081328182362244151) (P 60))

(41 456 (83 231120915699337657199) (C 85))

(55 334 (11 176117393904756941092831) (P 77))
(55 532 (11 105601 52126175641 8756765116719505867411) (P 71))
(55 731 (11 661 123381344605188748346731) (C 88))

(75 365 (19051 22387714416268419427501) (C 76))
(75 724 (6151 15061679250901 534961028582441381193936900451) (P 68))
(75 796 (36155884792202088715972877251) (P 88))

(82 376 (538331 2327968564545240748961) (C 76))
(82 453 (54449 3263385079 16992190653664745371239983) (P 67))
(82 598 (140641536425104543 829007026965407926450453) (C 71))
(82 687 (3527 22935478709313600363388019) (P 85))
(82 726 (83 2278460693 6785933486113 3728533082090179388693) (P 69))
(82 766 (83 370723 66486929404019984731350013) (P 83))

(88 335 (617 108955250797801 11635331483590651268865766488497) (P 54))
(88 362 (89 1409 140778580483135662433169) (P 75))
(88 766 (89 197895017 22839378811339838735699279569) (C 77))


May 05, 1999

By Igor Schein.
(May 04, 1999)

(41 536 (83 1559 15734899 2289468587389060551711066569 3880412922896337258271757623665227) (P 36))
(88 265 (45988917970785593 525904228936259527151480705772934848577) (P 42))
(88 284 (1409 8537 88783928201 21372062615971055796281) (P 58))
(88 299 (1192361814874986097 594604141558485833567057) (P 58))
(150 632 (751 124351 38522654701 977901386198920583373901 3053435044053096822899263703251) (P 39))
(150 694 (657451 10509272332881901 15265619781177105771601 2788053868956588752791032001) (P 43))


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