old log ('00/09..12)

Dec. 31, 2000.

By Aiichi Yamasaki (Dec. 30, 2000)

by ppmpqs(ubasic)

(114 719 (3496609 983406540335868356684518806270269140070407) (P 55))


By Tetsuya Kobayashi ("Hamayan") (Dec. 30, 2000)

(82 590 (1723 68389 3913391680398947 73481209711343085825578126333) (P 59))

(100 329 (101 3001 4723444601 4119856733783359800554749406560901) (P 52))
(100 335 (68568601 68856901 706499555525301098168727066504536660201) (P 47))
(100 354 (101 26501 356552816401 138615002618892218818038231209964514702301) (P 43))
(100 398 (5 127597501 1882403401 12386445233086175982678846567168395342701) (P 46))
(100 476 (101 133627287622712956901 3521908379296598317169791001) (P 58))
(100 588 (5 101 2321530655297215102185101 21789363021953841226545294425786342173901) (P 44))
(100 642 (5 13238826251201 64843465430701 189365301830276121674481653705094001) (P 50))
(100 688 (5 12401 2169873545917597591392901 382911470952276202365205201501) (P 55))
(100 713 (5 674572988501 684640603750364801 18359927707366677248680523382301) (P 53))
(100 889 (84401 2126801 67166101 340341555060701 409184302520994112690149275099320845901) (P 46))
(100 930 (93901 1171801 83888284573675098253901 8996465112083500837546619249565901) (P 51))
(100 931 (121001 2657801 19520217401 18028243050001 15588357059458135313779096936247533601) (P 47))

(110 327 (11 137205892531521314017712328345330105204361) (P 59))


By Masaki UKAI (Dec. 30, 2000)

(55 993 (11 3631 7151 10503514781 26004706095009951170440412461 522147177432015322169838406541) (P 44))

(82 762 (83 8584909 82142169378581286728506903 94074317936942891625453742007) (P 52))

(86 446 (195479 6491688893936908373570236463 12959634011121070419898922146297465381) (P 42))
(86 702 (1794976349 123114531159400842483198882311) (P 82))
(86 859 (43 173 431 224723353695847812239320638731453017679) (P 79))

(126 609 (127 4723249349808311271077120225091955073499510451) (P 53))


By David A. Miller (Dec. 29, 2000)

(75 648 (601 1324951 194698738045351 155627526036983289774067775682001) (P 58))
(75 660 (7351 159897440949720721318097106129120151) (P 74))
(75 667 (1801 11701 859317574051 667622525239139202007141774814251) (P 61))
(75 672 (1801 29401 5481547096951 119461321768975088014259929332299411101) (P 55))
(75 982 (81834301 269022646829457901 221045468476224043556769630464255808301) (P 56))

Dec. 29, 2000.

By Tetsuya IZU (Dec. 28, 2000)

by ecm (Izu, VerB.30)
(150 215 (426546610578229269782068217802301) (P 61))
(150 525 (868951 5722679717444577603515637601) (P 76))

by ecm (L1=1000000)
(132 937 (1557469 11805817 700090249 428044470637584808035107010545044729) (P 62))

Dec. 28, 2000.

By Satoshi Tomabechi (Dec. 26, 2000)

by snfs 1.5
(92 276 (32792390764127380258120747822594675763497) (P 67))

Dec. 26, 2000.

By Aiichi Yamasaki (Dec. 25, 2000)

by ppmpqs(ubasic)

(114 649 (98953 3829208153423520848938277467843271588180017) (P 54))
(114 674 (300163 8802932067101241022598648556922012289492802481) (P 51))
(126 564 (127 413127720369066101059690899157597469203) (P 59))

by GMP-ECM4c

(63 982 (1546273 266903551650094609021219449403291) (P 70))


By David A. Miller (Dec. 24, 2000)

(75 424 (303735451 42931496907152818354953182689651) (P 65))
(75 718 (19323683101 36786469051 102611467923133433774897837381445601) (P 59))
(75 833 (1143453455699648101 40483137873136757207602559443504542901) (P 62))
(75 880 (34214405837205867410682560551 366265120183175306186340719813401) (P 57))
(75 964 (151 5701 291280990041568916101 56976839246362690445632520403758251) (P 59))
(75 967 (9360167686338150726985161084158718901) (P 83))


By Takahiro Nohara (Dec. 24, 2000)

(69 546 (829 5107 28429 981825564796946036703887410312597) (P 77))


By Tetsuya Kobayashi ("Hamayan") (Dec. 24, 2000)

(82 248 (639563429 27501573571909189882466356260261400083504613) (P 44))
(82 278 (821 14843 15991 53205144598880818595875153875087724617883) (P 46))
(82 445 (2088872128008049807 26045484968668233985138685598491) (P 57))
(82 468 (83 1409090707 6337392223 43280682570304400580006660736981) (P 55))
(82 533 (83 4507455816926722838413 5022552989114964773823711480154300487) (P 49))
(82 540 (83 55351 280433512279229149 2393438019568930083239513655301) (P 55))
(82 596 (83 30980876981777756731343 65413372067780184023991629453272695593221) (P 46))
(82 684 (83 268454361269 239126215646117 85112215957732431636123064973) (P 57))
(82 788 (5003 4990603 3107546130928801873 657185019471373080558558765893) (P 58))
(82 791 (739 2707 2604642179 68752465984907 16402554824439205727336962496078419919) (P 50))
(82 849 (83 245377112749 1085485214388165307 2563132876801432290423786013917681161999) (P 47))
(82 858 (821 543497 369381696837335601079909 3440422853075622889361598917145822019) (P 49))
(82 862 (83 92269111567119466585693770517 122874560651625701663896369032216684013373) (P 46))
(82 963 (83 180794888467 1177840674429927726359 6314604160665124156310542664247788177) (P 49))

(110 278 (56596910932304421618933221445565938041) (P 61))
(110 284 (893898858003663317147658897645528645472913711) (P 54))

(138 267 (139 277 15733 21911433931336953948456834225598404223) (P 61))
(138 321 (16561 4928416062703966824392743141) (P 79))
(138 418 (277 394819 141903196204491085045175083063) (P 79))
(138 634 (20563 381422348833 1990281835085743830497845071271) (P 78))
(138 719 (10627 294839850108981931672330633734061) (C 90))
(138 832 (7702405214521 3559010331031723718518648017967) (P 86))
(138 957 (139 546067 79867509280316835650869438729) (P 95))
(138 997 (4003 13418795998540860220200274723) (P 101))


By Katsuyuki Okeya (Dec. 24, 2000)

by snfs (specialized in 88-series, by Prof. Kida)
(88 519 (89 8537 719161451977 2391559442932553126190148090363543817) (P 55))
(88 540 (89 580529584097 579403862297888326119891278210959729577329) (P 54))
(88 550 (3169 184273 1403953 113985866452386730122585123631055681) (P 60))
(88 551 (159721 210639881 6531028185326472283459551329) (P 69))
(88 572 (89 14067715993 102273364875233753314849757014085611227540316409) (P 52))
(88 620 (89 878681 28881161 329911926791010184139650266546577) (P 64))
(88 647 (89 39953 1029162377 8992512703033457280530219863861486777) (P 60))
(88 657 (183242401 36543728727545958862775273425085521) (P 70))
(88 669 (89 3169 16193 29987341576519338241965885833 5360343664480554183762605284247691881) (P 39))
(88 690 (617 13553 2260633 8459931193292130256636847575969) (P 70))
(88 796 (55001 42808390837537470751269400954669975714753) (P 71))
(88 800 (239587217 7510597817053046083922614721) (P 80))
(88 863 (89 9769 70844437538550083052100409781361310348010112433) (P 65))
(88 878 (427417 752489102495275808906964003964752835138832532230206393) (P 59))
(88 891 (665887093169 31257915215273859757747970655058129) (P 72))
(88 897 (89 36008001967353891423915067061841436899355897731744558233) (P 61))


By Masaki UKAI (Dec. 23, 2000)

(100 608 (5 101 21401 12397446087490020520795445501) (P 77))
(100 745 (101 401 4210135801 10891013924865738818527601 1454966608246085918174437901201) (P 46))

(82 372 (739 8750061848471077 28772230281275391994791293) (P 59))
(82 469 (83 739 1231 2297 60271 169249 350996669688862480546631507) (P 60))
(82 802 (83 102841565345117 158372477534871625493237057 138380001212168052974310498789084467) (P 39))

(88 615 (353 2113 7443136404424582570446233 263875739245909837471518680537369) (P 49))
(88 800 (239587217 7510597817053046083922614721) (P 80))
(88 820 (89 13809841 1886345639107301208097707077017) (P 78))

(126 560 (379 2213015232782955407599708815933973395661412341) (P 52))
(126 564 (127 413127720369066101059690899157597469203) (P 59))
(126 934 (127 96467635425926821359034304492122023787) (P 67))
(126 980 (127 3509667558181 449859082993244962435437922470680607175543) (P 52))
(126 994 (90283708957624392230052267437563654383615566813773) (P 58))

(86 436 (173 4903 40825191557352878940968549 3133746230983011479365518041720833651) (P 43))
(86 519 (6709 21157 362438518714057 54906201477925885488691877) (P 66))
(86 566 (14879 96493 634681 5092147 2145298235738319468701015923) (P 67))
(86 637 (18649421060482620521 3870990224574512693335337837747) (P 68))
(86 679 (3613 606559 3379027 1531790951861736803 10329067161806261883095711128879) (P 54))

(98 486 (197 413267 211554659 282712312389353016292448218327) (P 68))
(98 524 (7 42043 99079 527371313695610418372333773 184476809114321169541640968710591823) (P 42))
(98 842 (82167317 241251415217247686196746711) (P 89))
(98 866 (883 1281430191019973 2345419843449887840145119) (P 81))


By Jun Eto (Dec. 23, 2000)

(92 329 (244268801056300795963697 14309438720198153378228626635217) (P 57))
(92 429 (277 461 4181400217181402577364062778861586016997) (P 72))
(92 447 (169097 5278477393801968776660692301) (C 84))
(92 458 (578957 1227649 9642559719105899926833042187529) (P 75))
(92 498 (461 127301436198771584778935828417) (P 87))
(92 517 (277 3313 104043997381 116428167892902682173440582439258781) (P 68))
(92 536 (19597 514649 226915693561 1099984475519917434295396005193) (P 69))
(92 554 (13249 112299862282728524214020087149) (P 88))
(92 610 (829 1657 189538608808128185574900773) (C 91))
(92 650 (100385893 3631118377 27451998660528000704286154061) (P 78))
(92 739 (25185567781510813 8022862465552065453973946665109) (P 79))
(92 870 (15017768946704733102634439861) (P 102))
(92 928 (11317 149794916419747453828792877 5926810499543089796827756097) (P 73))
(92 990 (277 669403668106210364259901 12303731252400330744210658109) (C 78))

By Yasunobu Torii (Dec. 21, 2000)

by SNFS

(63 747 (47583699758501577402552542645615910037) (P 66))
(63 825 (379 3757921616686108078510153107119913448359613) (P 60))
(63 941 (25539221035066764721145839446826730399887) (P 67))


By David A. Miller (Dec. 16, 2000)

(75 445 (900868125688906720201649211281766301) (P 70))
(75 583 (2251 262964084596803180865495022258428236451) (P 69))
(75 612 (3001 668823107867984401 186258512066420680504451588667301) (P 58))
(75 698 (851251 62854219910395882720386311301957151) (P 74))
(75 813 (151 19801 53301059342324357385139312073157901) (P 76))

Dec. 17, 2000.

Announcement.
I will go to Frankfurt for business trip from 17 to 24 December, 
so this is last update before my departure,
next update will be 25 December.


By Tetsuya Kobayashi ("Hamayan") (Dec. 16, 2000)

(55 381 (92294831813483896167378368920871232771601) (P 63))

(82 259 (8693 77735017 55588396493264694694283445089) (P 56))
(82 372 (739 8750061848471077 28772230281275391994791293) (P 59))
(82 428 (83 235276123 5823640247 23728183385483183648592978197767) (P 54))
(82 502 (6380749 43769498957717399 69037208652226497022160340040187003) (P 50))
(82 728 (23725280046345580940389847485283 51872688846492349370406175430526607) (P 49))
(82 810 (2708351864179853 957458361272450077 85911765948575234746938737029306797122041) (P 42))
(82 822 (33211 52432955192840156207964162097 155126161619449415650096595071061) (P 52))
(82 838 (83 397127 2058857 2937754742382269599 61334557175067301176520663933153) (P 53))
(82 844 (83 7123751 9634776747935882787072809 14918635646053286481155524876889) (P 53))
(82 938 (2517521213959 6427860303795533851631 15294326722414361006837044422329239) (P 51))
(82 952 (83 2789 24387703 18996962112615339692639 794516701814974799811434503304924916091979) (P 43))

(110 254 (25308840912704184569502413217964161040869221261) (P 50))
(110 261 (11 331 2450572338127093764656468948437760974398751) (P 51))
(110 482 (5501 180071 1916998381 47700415082307329608905051188136976494331) (P 49))
(110 706 (11 1321 709349829861846054421 85793343241226229688720769364751749243571) (P 49))
(110 849 (11 331 94324121 62274510159564671 23790554988745296796494978715361403949501) (P 49))
(150 369 (11551 13157136301 62251885889162791341988942372017842097937651) (P 45))

(92 265 (18493 38917 19368550792216265470864404253 49763857469729356640011428974107777) (P 35))
(92 452 (5317180435356125449 305782287711436160992037648693 1533781682082840142817392908365017) (P 36))

(138 549 (139 515620579 1599614633544388824473957320321) (P 80))
(138 579 (277 20953310086997763677143082043577 136474111515034529061437422202617) (P 56))
(138 837 (139 6211 2155423 8955282577 106015618594496551 627609388033567577382854844158089) (P 57))
(138 872 (9214006909 742847934157889751102411319) (C 93))
(138 946 (829 4831 81008623 69920488865047 303913856303659938032786679829 12422126086201662141793075148048023) (P 40))


By Katsuyuki Okeya (Dec. 16, 2000)

by ppmpqs ver.2.71 (by Mr. Tomabechi)
(88 488 (89 1321 7893633995017 54876179544514098103097666884178658750135937) (P 46))
(88 925 (89 575613320129 61829477894449 10450412887764192316299230479454712213217) (P 52))

by snfs (specialized in 88-series, by Prof. Kida)
(88 684 (89 147751963624920450343614256146499489) (P 77))
(88 748 (22433892889 360991998955259533555914649117605440796079193) (P 61))
(88 874 (1498278892572643341077338609) (P 91))
(88 927 (617 39754313169200023205991654205638902910517626299478193) (P 64))
(88 932 (489524073741320059625370795685239527302129420801) (P 72))
(88 945 (433049 160999507821131068818161455969 9778019396773461147021798025000595729) (P 48))
(88 949 (89 2729 58126982439523226575244311073) (P 85))
(88 963 (999834793 3404313606009895604156100257349995272530076108081) (P 62))
(88 972 (89 617 8774071603042990966845917268110980388441) (P 75))
(88 988 (11353 1607233 119134847520768179340928714146473) (P 78))


By Takahiro Nohara (Dec. 16, 2000)

(69 831 (139 586844427657130565775223959391) (C 97))

by PPMPQS Ver2.71

(69 206 (139 336997 51071998349641658565993597016785696675037) (P 54))
(69 319 (139 111576662705197 11410837893037661837055064063 838586868841311964533913297200889) (P 33))

by SNFS Ver1.5

(114 511 (2198309652165544904973151994059860870961) (P 59))

Dec. 12, 2000.

By Andy Steward (December 11, 2000)

by ECM (Ubasic - KIDA/steward)

(47 506 (4889 195427 661949 20357009535009816768178921) (P 85))
(47 508 (283 8031222300363210319989054208313657) (P 89))
(47 750 (941 331607059313251574279373277) (C 103))

#(49 553 (19772579 31650140528787429587 26165452024548246648781087031551) (P 57))
(49 771 (7 335443123 702216265090339366669 395850109166870619016229693839481) (P 59))
(49 952 (15970954475858262391009676432263 4372242413401074837864004741116079) (P 61))

(53 296 (9011 3312480760905189265640603) (P 101))
(53 398 (100913 139709 302399978899297 54251624059569806291) (P 91))
(53 508 (58937 22672035887 592167393253 211488298851315080999) (C 94))
(53 609 (3499 7785924024217 15618968719792348903007 1629553686163672057022041) (C 82))
(53 846 (21505985379121 154125944206772535043589 1786964319518804034366463687417) (C 86))

(55 693 (991 32315581 333297581 20479689678397061653860584778151) (P 64))

(59 604 (709 15308839414268789 49647783008389630082270276069) (C 114))
(59 693 (123361690765451578678190957) (P 139))
(59 771 (1370989747995820607331707) (P 144))

(61 988 (1709 10859 5921759 3066454806423424289182105037) (C 139))

(65 156 (131 355031 4682456221 227182697527111534983194000101) (P 59))

(77 156 (13138511 27564691161615630819543749304919) (C 94))

by P-1 (Ubasic - Steward)

(53 456 (743 277398490449798079729022087 842371966532335854757711819) (P 83))

by ECM and PPMPQS (Tomabechi)

(47 498 (156424091224277 14171119289641482249709 3853486850493606930272621 723319070017500547674904699) (P 37))


By Henrik Olsen
(49 376 (491 883 26929235319003304455487971589509829445789371) (P 60))
(49 604 (1104131407 255417327470284382224848280863231706493516680646213) (P 58))
(49 847 (197 1373 187181 446881 3871617315973660403552962831198861836778289) (P 65))
(49 876 (7 197 883 7351 284855273354673043386858462349903856153) (P 76))
(49 891 (17053 396229583 271018850421674815573012883847135892129003678020383) (P 61))
(49 899 (4999 423067 706679 3937701267280285710726797799174252397083955801977341) (P 58))
(49 949 (2549 74384609153 495847946126843542253018178923522663) (P 76))
(49 959 (197 41651 16142875267 160159087380593150411012202460161158345382890195133373) (P 55))

By Jo Yeong Uk
(43 952 (13331 78062725011459885230738026314601 87447617709771294752683223626085311488763) (P 49))

By Robert Backstrom
(43 459 (1223093 381739723358382022149998707137633205855917787301) (P 59))
(43 472 (947 13159 83241342248930123891195981944358977) (P 71))
(43 498 (173 47893589459 349080484145919223784641692616321330811) (P 62))
(43 508 (7216691 235591407076137280054583591070091564788816247) (P 63))
(43 517 (43 21157 17551531458899330191120834041939985510310576397929) (P 59))
(47 301 (476061296466011963720025546816861833 1136117288786615724753378866604564039737) (P 40))
(53 134 (107 3181 2168549 727791021817 89043466880849021653395115930921) (P 55))
(53 150 (58615987 8876039232854969232140049196702853) (P 72))
(53 156 (107 490993 12937871549993048370195087699481 1734532486070138418080199628885674043) (P 39))
(53 158 (5407 386573867536606489241600570179404138122901631258044413) (P 58))
(59 130 (2802973 38046569963 474637073892550047723163 90286574228547932315971566326089) (P 50))

By Sean Irvine
(43 506 (173 338927 2408689 85638802580060870651462497895721885170653) (P 59))
(43 610 (4903 973177 1217663509 16335060991965563552793684727833936349458323) (P 56))
(43 621 (19867 36293 1093862381 1427678621580027716203581388564057993859497711) (P 55))
(43 646 (43 69207780302108477 1325244455448665894418746677648469510117297) (P 58))
(43 708 (173 296264922392509583 10244229822670647592969030546059986645907158327791) (P 51))
(43 748 (335465987074659700249 2051835012149262635445777356776080398908022719) (P 55))
(43 750 (2468534094603648219233 481825704734987371822109797113318027588062047) (P 55))
(43 771 (34555403 37966572333091 11802802552795171942335850552453583776594799813761) (P 52))
(43 842 (5849 31219 1543099 1720310203 26929125490485845528876516243451606250776665055029) (P 50))
(47 296 (124363 21117964613 2169245472959814433773116320829317379543) (P 59))
(47 319 (5612109610355579 77359227632879999571980412304415773) (P 65))
(47 377 (47 1129 3761 4862302469 12774464048306926251043039614208507) (P 67))
(47 398 (8273 2409216604174049 328934651535851274753088754001524609548727) (P 59))
(47 545 (283 155383 1342900733 86874547423 1647412744832884541151755856557447) (P 65))
(47 553 (19553 34620776066229880257893 11371371858211573463730042948751401258702092789) (P 54))
(47 584 (15511 3906641 190888007765350703 18763154401248584100937523887099847151171313) (P 56))
(47 638 (62981 1400754195157 69508255418809 3409371685578964893356410823507837530391527) (P 56))
(47 824 (8273 4227131231569948301300707587277 911573936570933868464419548758605319149) (P 61))
(47 839 (21988104759090494373659929570415047 4195121386578593902610942873053560046499431) (P 58))
(47 926 (1600667470942583 135148454346719524509433 2299806221759246328815402364674340920906179) (P 56))
(49 609 (491 14407 16661 187181 494444545032446735485311536747028589307263099) (P 56))
(49 741 (197 24103787 348116903989 14326148080276057216278262599929) (P 69))
(49 753 (1130307109 288616814333 164843891913636036185042057369662644169) (P 63))
(49 846 (36457 226283 1591001642983817 4702749371769266614379659343683930118641) (P 59))

Dec. 11, 2000.

By Takahiro Nohara (Dec. 10, 2000)

by SNFS1.5
(69 280 (277 967 1791135424407488547175995484059107113) (P 66))
by PPMPQS
(69 494 (967 6073 37842913 26203664251 1012479464446995231595436226686374744970778811) (P 49))


By Yasunobu Torii (Dec. 10, 2000)

by SNFS

(63 730 (53275537861758192367309384391810992909939) (P 63))
(63 901 (965604326838887500981302515858046785539) (P 68))

Dec. 10, 2000.

By Jun Eto (Dec. 09, 2000)

(92 426 (277 1381 7631677 96756677 2097219967069946986347218847773) (P 65))
(92 452 (5317180435356125449 305782287711436160992037648693) (C 69))
(92 548 (273149 13372661 3764394471781 7296302137695986663122075397773) (P 65))
(92 717 (5981 6257 4644161 137465702944500714040706653) (P 86))
(92 265 (18493 38917 19368550792216265470864404253) (C 70))


By Masaki UKAI (Dec. 09, 2000)

SNFS 1.5
(126 989 (2269 8604200252307401306087647513742877087523) (P 65))

Dec. 09, 2000.

By David A. Miller (Dec. 08, 2000)

(75 363 (884939701 1982844678481180282072385868587632950901) (P 55))
(75 411 (17851 6774451 172525608597254597589854164453201) (P 62))
(75 496 (151 14251 24920551 658006259613115446517994736177563701) (P 59))
(75 501 (601 58974558795955464255900172725321301 163292740874408705472012414196324801) (P 36))
(75 779 (78456504151 1541893404508677326833070630401 189273481745316451965424913806051) (P 43))
(75 842 (2851 150151 19972951 214775610421571859817915266638725587601) (P 63))
#(75 872 (751 4356444198912761313874190251) (P 88))
(75 915 (18451 188255904448847485215126749592751) (C 82))
(75 932 (51151 14464666429199954304498634986301 900278121623572934498915759078433392551) (P 44))
(75 986 (151 1051 45537327912893014599901 13589911892812256007565157545201) (P 61))


By Tetsuya Kobayashi ("Hamayan") (Dec. 08, 2000)

(55 371 (48723545826401085957224379222840724644883183521311) (P 54))

(110 394 (881 170651141305481 548941108090782927741349233546766255377701) (P 45))
(110 671 (85691 52497982209021625032791 8939692972165658455502564148084690061) (P 49))
(110 686 (5501 53593719185130446318921 128325071218614822876568689609224171) (P 52))
(110 698 (91915142771 44345478769678571 32121186700576516245893528983261) (P 55))
(110 731 (1985417501 681366529909724944231 390600298885613190599497730627715403771) (P 46))
(110 734 (11 7591 434947811 505451687633531 55882945155393241063908289281899774741) (P 49))
(110 794 (11 169181 94575049031 13746804087391 1386185267287133179937342921173032374512801) (P 44))
(110 819 (661 8271366369421 11067971628011 2317183163981800154764336965371926750342621) (P 46))

(92 405 (277 123854505133 28993934347566763507212516557 499195632650797111877930800792369) (P 41))
(92 518 (461 1013 1933 41685937 25906168577865743681 319785684671741253585247283716094117) (P 48))
(92 585 (461 136897 6095737 177547975217460830329889 144993627292525902794003247764517600761) (P 46))

(138 357 (6954600529 16256600339569 72998894982865852532002696963489) (P 58))
(138 579 (277 20953310086997763677143082043577) (C 88))


By Katsuyuki Okeya (Dec. 08, 2000)

by ppmpqs ver.2.71 (by Mr. Tomabechi)
(88 446 (154898999015340315209 6155496224784925813866253761416797953401) (P 46))

by snfs (specialized in 88-series, by Prof. Kida)
(88 365 (217092217 1536774710717248966333132179366137) (P 61))
(88 480 (89 8273 1975257453343985733594041351971177) (P 69))
(88 489 (881 3995556745303330591530986758445177907257) (P 66))
(88 492 (233452561 31190341983578158103440630731281) (P 68))
(88 494 (1409 112714482380330441771810801203468277425120129) (P 61))
(88 502 (70753 65371695203320621555103094749805009704809) (P 63))
(88 508 (89 242658481013553212267534889449862236921) (P 68))
(88 509 (2377 103294769676207533414004954563459313276286157562817) (P 55))
(88 511 (89 3183988014428274758651287910680430902296121) (P 64))
(88 521 (89 10688018417843838737369988477161 77347740296097352956513708744757721) (P 41))
(88 526 (7872217 30098666107977815170866814638916000836005761) (P 59))
(88 535 (10096769 44809910341657311270647848778110250756149586313617) (P 53))
(88 558 (89 6967313 3863949077987264786361424269446761) (P 68))
(88 615 (353 2113 7443136404424582570446233 263875739245909837471518680537369) (P 49))
(88 677 (89 353 16251424202863493478070726007565679323434826337) (P 63))
(88 704 (353 17517589409 3202366477764741174708333224582804760850060820113) (P 53))
(88 712 (20681 1169081 4166216775297683735445077238011414953) (P 68))
(88 743 (89 1409 7645606500969737750754929543366699245156192889) (P 64))


By Aiichi Yamasaki (Dec. 05, 2000)

by ppmpqs(ubasic)

(63 955 (631 1009 111637 30410119582984772300616348019261856541445117) (P 53))
(126 658 (127 883 18646051065208328023172396609149797516523) (P 57))


By Yasunobu Torii (Dec. 04, 2000)

by SNFS

(63 851 (100297119270920329318746738453079575689331574663) (P 59))
(126 856 (7229633353043733149232953834227021850496535551109597) (P 54))


By Takahiro Nohara (Dec. 04, 2000)

SNFS Ver1.5(by Tomabechi)

(69 177 (139 776533671347048603048268146687011171254847) (P 55))

PPMPQS Ver2.71(by Tomabechi)

(69 161 (161095666746796214631066265657733618591786251) (P 53))


By Masaki UKAI (Dec. 03, 2000)

SNFS 1.5
(126 979 (144627068216839159716345478096071257085335209) (P 64))

GMP-ECM 4c (+PPMPQS 2.7)
#(110 854 (11 991 2266668366718891371965411) (C 89))

#(75 504 (1616551 3639693164718614047848451 237866706576952023350255184704490151) (P 42))
(75 872 (751 4356444198912761313874190251) (P 88))

(82 763 (91941517 97484950931 4102335360682767350871077963611 224716567962383223822722582530811) (P 34))
(82 992 (83 7449606450269760263369 421002157841071989924450827 14505025392848220540199449676637) (P 39))

(86 275 (894229979 1268751955938631580626030740659348783) (P 58))
(86 591 (1319017169493475762770096697) (C 90))
(86 765 (173 160649 96812953 342953123 1755652128611 227624700464116433762329 26129705875838187845615665711) (P 34))
(86 898 (173 947 14449 109384777 6527037511822427 419963503598394430942964322709) (P 62))
(86 986 (173 1549 6451 291779336310451180047194993) (P 91))

(94 260 (6581 138965860937925469151916749) (P 82))
(94 450 (283 239112971 268824209 1010224393 97076791029536771303527060463113) (P 62))
(94 964 (283 11200970132022723280917504756827014417) (P 98))

(98 623 (2549 4623006137 17565941172422305172485627) (P 80))
(98 792 (197 543901 896113 78815045276720201300322921271571) (P 76))

Dec. 03, 2000.

By Tetsuya Kobayashi ("Hamayan") (Dec. 02, 2000)

(55 966 (11 331 1429316610481 124043378674931 117793202090544814577536142229146081) (P 55))

(75 504 (1616551 3639693164718614047848451 237866706576952023350255184704490151) (P 42))
(75 684 (151 459468864448560654139970625001 89945220983487122464185497374625401) (P 47))
(75 948 (151 751 1863397307027623335613818430801 5967789320970977789616304251464401) (P 50))

(150 278 (2551 318601 66271491061481529109624582829553070129048501) (P 46))
(150 291 (151 40986901 32812487295532486906821634935132315751) (P 52))
(150 418 (163351 3309059165551 200438534803412102150689183668151) (P 55))
(150 559 (151 151 39901 12214389679201 184607932201505230167721706606783019001) (P 50))
(150 630 (751 1908208801 7767836679751 1831979408704626012169582789027520878201) (P 48))
(150 662 (28051 499099068566348749201 3909768482708480591796272421441983101) (P 52))

(49 834 (7 3529 468049 10894568919068211591730451027 641111592218362533489111364324712611) (P 49))
(49 926 (2843 49756561 341652473053192730270194980313 88985534156272550410214003237478548210503) (P 43))

(92 321 (7818917989 202701644057306729 13373391136378104923106727878953) (P 52))
(92 495 (1013 86297 17555620781 304595299966210189 76626022218559683453493053061721) (P 52))
(92 565 (831699559484051381 3317910700561105641444421 41967138593468462752290777983693353) (P 45))

Dec. 02, 2000.

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


By Jun Eto (Dec. 01, 2000)

(92 201 (461 1723473470936067399692234769373) (P 69))
(92 286 (461 86143568546750689000670635631929) (P 74))
#(92 334 (62412386223148829093 1059102931036760259712104673 2330545576178938720172839921229) (P 54))
(92 344 (5944896018522754870406760949 2330545576178938720172839921229) (P 54))
(92 362 (8671786141 10380751401802705495108199610289) (P 72))
(92 368 (115475041289899451834562137 6089646809029198996248033257) (P 60))
(92 405 (277 123854505133 28993934347566763507212516557) (C 73))
(92 411 (2546561 2653588337058013 157793964939373571553196049041201) (P 61))
(92 858 (829 81421 301264895653 183656824728129790954102245233) (P 81))
(92 890 (461 162146723449497212472345923597) (P 98))
(92 939 (17021 83813 2766349 30777084876966917450312249) (P 90))


By David A. Miller (Nov. 30, 2000)

(75 308 (738247801 41231771229770133448633128843664201) (P 57))
(75 468 (2230222268145301 1303804419810216971187424148275201) (P 59))
(75 972 (601 6446101 173829001 4465995301 3690321302549531938120284796987373701) (P 56))
(75 981 (47365221601 778044901446610836821637177184165098901) (P 71))

With PPMPQS:
(110 972 (1015081 1971091 1394118571186111 732280593198789162504272263016987555545223011) (P 48))


Nov. 30, 2000.

By David A. Miller (Nov. 28, 2000)

(75 315 (151735300424974194536781468732751) (P 68))
(75 387 (1051 15601 19801 718485079363831931060588242742851) (P 60))
(75 410 (16145432559355518593716703795251) (P 74))
(75 524 (4201 37951 2113155272888726558315078476801) (P 71))
(75 526 (180950794834054117479751725733501) (P 77))
(75 559 (140288248320236157921947494772551) (P 78))
(75 565 (47738342792199220951 11614281743237640708610115401) (P 63))
(75 575 (3334801 115957068151 32403795939375499764920161651) (P 65))
(75 600 (2298036234214696527202043008201) (P 81))
(75 618 (1951 3343651 1009770391801 27753180187235400556076134179901) (P 59))
(75 684 (151 459468864448560654139970625001) (C 82))
(75 767 (526051 289590433732268243401 6059343924948681599029908151) (P 62))
(75 770 (2851 324283460667257933204214301 2211778313002626421546189726926301) (P 53))
(75 868 (4201 2437191901 19978899748234367684335327076101) (P 74))
(75 901 (7155404512065751 386261395237998444976244211451) (P 73))
(75 914 (751 23080842901 253422149976466675153451310451 34556371389913844883750636344701) (P 45))
(75 946 (151 400972081352679589169463653401) (C 88))
(75 976 (1051 1058702342038632590766151 4086840453476693590715261401) (P 65))


Nov. 28, 2000.

By Kunihiko Miyazaki (Nov. 27, 2000)

by GMP-ECM 4c

(49 487 (2917967076696916496637922315370237374793) (P 74))
(49 501 (65563 1740609614899 94083271509424170960943989733) (P 68))
(49 553 (19772579 31650140528787429587 26165452024548246648781087031551) (P 57))
(49 573 (200117 302723 192123000243265249800139321727) (P 76))
(49 598 (30871 23641030974013573 190766912047644403059239928448753) (P 64))
(49 650 (197 1646303 11190738745347329603 206025261467776346940583492597) (P 62))
(49 652 (7 197 883 29401 218149 1068103 2859641 1463010514725324800814265616623) (P 60))
(49 707 (2549 78360465331 2347746804607 13466905212186088675355798449) (P 65))
(49 708 (7 243747953 22254741420061198026637 878840423652998940450542236243) (P 59))
(49 801 (1709589001421359250028191966983) (C 92))
(49 834 (7 3529 468049 641111592218362533489111364324712611) (C 77))
(49 898 (2843 11542728865142779195573328123 43678484781488439307932984408653) (P 61))
(49 926 (2843 49756561 341652473053192730270194980313) (C 84))
(49 971 (44662410598949266501032614825237) (P 94))


By Satoshi Tomabechi (Nov. 26, 2000)

by SNFS V1.5
(75 240 (727501 6974363536330118090546323858801) (P 59))
(75 280 (1201 6451 31376892490618747470656289238079616253975351) (P 48))


Nov. 27, 2000.

By Takahiro Nohara (Nov. 26, 2000)

(69 402 (139 34767483193 1379196728786576652994955595961 3290180109344847985800700282663) (P 42))
(69 406 (14776435978354785142524964487491 748966487727992946138435379064729192149) (P 45))
(69 452 (139 2347 277603065388517472924365586916129 330912128994517195276113032473009) (P 47))
(69 598 (3037 9976130962843217104869229 1658967958545856439413658133780819949) (P 58))


Nov. 26, 2000.

By Aiichi Yamasaki (Nov. 25, 2000)

by ppmpqs(ubasic)

(63 748 (127 81019 41244139575839550751427504721969487495189) (P 56))
(126 725 (379 3907 105625020674691034188442938035900969625073) (P 56))


By Tetsuya Kobayashi ("Hamayan") (Nov. 25, 2000)

(75 253 (3807547667728475999886274010918980201) (P 60))
(75 261 (499832662555122154582954156172154123136201) (P 55))
(75 262 (337201 8807276216724556443942659304369901) (P 58))

(150 143 (27799941712472890805476750478685843927901) (P 46))
(150 301 (567188664813301 62084742951492409933941123333955051) (P 50))
(150 305 (10336962517201 84035891181968685619395542327677501) (P 52))
(150 333 (601 137326771501 19721042930066528302090939845638251) (P 53))
(150 381 (55861951 337201801 10186440321593163156847948754094814903444201) (P 44))
(150 408 (151 44793748828582801 208028197631471757301923434412294437701) (P 48))
(150 462 (15436470601 19734401101 10239731099689478190837606270902384634001) (P 47))
(150 496 (1051 2251 2029801 276713067451 2471924815200642916137784529294963427901) (P 45))
(150 611 (151 1951 11513464951 3798233077351 57723887114501864303343684161773834853401) (P 43))
(150 636 (1051 511721187563171636553751 299308282851935554784822795956183845451) (P 47))
(150 703 (197551 15089306315821836987049201 540292356875247110475693776189344951) (P 48))
(150 763 (2934840483028104021430951546801 4690469467845246972476730346530319536601) (P 46))
(150 840 (283049101 42207483164364933917401 1004970626321917615654278928457579359051) (P 47))
(150 873 (70051 1060555192920179451531331651 7746236682744426925509609398301816515251) (P 46))

(138 221 (12421 136483 60520729 410426457447957171102446964089227683799) (P 48))
(138 268 (277 829 1554244829750059 508504161601204299821910180359317) (P 54))
(138 355 (32707 86113 2847769 12982896343 106021498893573608349694249967659028698351) (P 46))
(138 759 (2038180237 31449044251 108472936931481375661 335433117197286677763649967389) (P 58))


Nov. 25, 2000.

By David A. Miller (Nov. 24, 2000)

(75 304 (60606151 237410549470961621477450648251) (P 63))
(75 504 (1616551 3639693164718614047848451) (C 78))
(75 519 (4951 6301 6451 298651 2629433814001915324601321659651) (P 62))
(75 728 (205470414010876801 5249036302454814120799966051) (P 70))
(75 770 (2851 324283460667257933204214301) (C 86))
(75 948 (151 751 1863397307027623335613818430801) (C 84))

(110 634 (11 1237897280805145899874321 2116818363892239853371756432991031) (P 54))
(110 763 (9545030772770256478747028454753575831) (P 79))
(110 800 (11 331 72722330619854891450940994089589051) (P 78))
(110 805 (11 19544644901 1637584094433512963070736852818931) (P 72))
(110 806 (3631 18371 246391505056015027878568704170581) (P 77))
(110 814 (881 972366153881 198884553639569381 4491038417255827951229226809667489121) (P 48))
(110 815 (661 45615901 112433812591 189050510784395301567315589141) (P 66))
(110 845 (72161 290669872353637632511126901 3389647562610648703253275875551921) (P 53))
(110 850 (331 66221 2234262057940615532546887466939007311) (P 74))
(110 915 (11 10560329419124522916332863070491318363315211) (P 75))
#(110 972 (1015081 1971091 1394118571186111) (C 93))


Nov. 24, 2000.

By Yasunobu Torii (Nov. 23, 2000)

by SNFS

(126 723 (396411768247581083792113931916384319) (P 68))
(63 819 (41138097836031058944250429871910257074075637203) (P 59))


Nov. 21, 2000.

By Katsuyuki Okeya (Nov. 20, 2000)

by snfs (specialized in 88-series, by Prof. Kida)
(88 304 (2729 23761 4852295822632958988190269068208497) (P 58))
(88 316 (15401 14723096580416430945915339922703965377750361) (P 53))
(88 326 (89 617 19452418886751538133454145065842610640724881) (P 53))
(88 377 (551675081 123587632267638910446078003119066793737) (P 57))
(88 384 (89 12542113 2709093692384194472197732183292353) (P 61))
(88 450 (1409 6337 61684657 15405815902405088383983757533899089) (P 58))
(88 477 (10334926220945102886076355437457 197996744764818922219243218786977) (P 44))
(88 499 (89 27287643306801388413885170880041721499217) (P 66))
(88 515 (89 11021240289494930987579639890537) (P 76))
(88 520 (89 616956358541155501250357440215388541848495156533049) (P 56))
(88 538 (2729 4239861141621522323644676171628570327126072554033689) (P 55))
(88 562 (89 46993 42504824333917642724255994484514550262883849) (P 60))
(88 571 (617 866213611512805287392364350898329643684089609) (P 63))
(88 581 (5281 1232429870303067214058887833457796804713) (P 68))
(88 600 (89 2729 91873 808938638556549388196684405530422913) (P 65))
(88 624 (204324340762491491110087553 46217271266409250298673193841960921) (P 51))
(88 644 (16688502175973411567793140984601357768778873) (P 70))
(88 646 (89 617 6453133259809710869177950665836327534968074323150777) (P 56))
(88 702 (1321 7311271379782881224721978650485299358027660020039585169) (P 56))
(88 703 (1321 90641 543929 87407055203291299398275077195110198335657) (P 60))
(88 705 (89 367259699735604113730003770895102123669393704497) (P 65))
(88 714 (353 3433 20714084609217730695673338650610716017) (P 71))
(88 803 (911092374989404187210192836889704209509489) (P 75))
(88 993 (89 312878743419328937127344947712733587971016129) (P 74))
(88 996 (1321 5677024786340464701059553484386745959869845623697) (P 69))
(88 997 (2377 3697 23057 15611369300260796187970837388525537) (P 75))
(88 999 (6181160129 15882108900442447759914729615127517544637561) (P 67))


Nov. 20, 2000.

By Masaki UKAI (Nov. 19, 2000)

(100 515 (10108927213788827027737785901) (P 81)) 
(100 922 (5 81401 12842273066501 113008428369499558898920746401) (P 71))

(82 749 (83 24109 571049 1744950756612010081744517490299 1322734972856541920785406328331567) (P 40))

(86 821 (9983861573477395199739055739 7636693261978713861688094256612504631) (P 58))
(86 872 (1010107294086952456052387 1204929555559679171542568201 2397030776126002884688428148010663) (P 40))
(86 921 (173 5591 6709 234597509 543063292672073160059 542170895464210436155259551) (P 59))
(86 926 (1191068796973938337849 24977229842908299262018866001) (P 76))

(94 426 (2451239358301 19536486250066503573254598673 984586339051311188579813970846034059487) (P 42))
(94 637 (105716408284536768010083269) (P 103))
(94 699 (8419234724371 31248248605873218995995650221869111) (P 84))
#(94 974 (283 1649419 20886049578920604271 55028009941525090752141378373) (P 81))
(94 988 (148700419725071798892282507053) (C 109))

(98 671 (7 9544194521 13667841832285597804829549 602664845187481335475936651) (P 56))
(98 999 (3137 12906307 511338510969023603847078274922666881 3120252389757674311671598459447391977453) (P 41))


By Takahiro Nohara (Nov. 19, 2000)

(69 438 (3282145081 1093506863415967218713959090171 1265644362572919966507278435519606173) (P 41))
(69 478 (2698506511 1672836881163673 76809865726318445254309609603182954729427) (P 53))
(69 665 (829 147661 45909928137553696792489 1574372189604147109138049499663510267642031) (P 52))
(69 932 (8436217 636762044472888601005589 330940596362818545588368196679) (P 71))
(69 956 (139 37155005323 88395369383180554779607 7721988907225106612304517099) (P 68))
(69 997 (139 11317 189337 3610476863445194907880986248208673 646702600328681867965065503287918306561981) (P 46))
(69 998 (139 14442876647574057654804885259) (P 102))


By Tetsuya Kobayashi ("Hamayan") (Nov. 18, 2000)

(150 394 (6151 17372177702312401 44487839316043871005459105376763901) (P 50))

(138 104 (139 461836975072196304978929422199219745259) (P 48))
(138 150 (3283808257 1052935821697841820613181285322984160921) (P 48))
(138 180 (10627 168232489 93528516974406068950523324281) (P 59))
(138 650 (146615758969 5920699715145180553222070503 3230937305913608072576293273337594800309) (P 46))
(138 793 (139 102576919 12090835982726623 19637841480938017 1226749093468067043234994980671270767) (P 49))
(138 955 (76350991252621116208314487933939) (C 100))


Nov. 19, 2000.

By Jun Eto (Nov. 18, 2000)

(92 308 (1381 51145216852455492297232471697) (P 78))
(92 565 (831699559484051381 3317910700561105641444421) (C 79))
(92 672 (277 461 26277409 482010649916908666612356437) (P 86))
(92 789 (277 6073 94526455198209248913628259398853) (P 90))
(92 875 (553256261 60293767097853582756398371053337) (C 89))


By Yasunobu Torii (Nov. 17, 2000)

by SNFS

(126 705 (4223086560723282689095605222356706064510933) (P 60))
(126 715 (399537137790098648011526267742972386563) (P 65))


By David A. Miller (Nov. 15, 2000)

(110 380 (11 2630233211 44037782175249247494738217947610684258531) (P 53))
(110 415 (11 141131 1358274846914014502098535628042281) (P 66))
(110 476 (331 1321 1258646401 143873269155883672591690965516035287121) (P 55))
(110 608 (215161 933919278623087461 249424794311824397348311105146557353344191) (P 47))
(110 855 (11 47923465281035366066103833401 1018143185193988015340705677549838616101) (P 49))
(110 858 (3728561 29767321 135822299685058161341 109381984079300077606478773967260061) (P 49))
(110 867 (331 11551 319143661 49567410329702431 1789775670615409925704346829421) (P 56))
(110 869 (8581 35059421 42959467651 2544852211441 713404185340479414104353885777707740671) (P 45))
(110 883 (14081 39161 352441 41195374107166773673543955762872023731) (P 66))
(110 884 (701581 1191278441 3932165785513764846429149793213761) (P 70))
(110 886 (11 1886611 251225730070261 126319591173359583164998118213805006691) (P 59))
(110 888 (11 331 23297341 916049084252993066158994518699252961) (P 72))
(110 895 (3301067551 32889700035288087027682691 595346271011616666938753162590594261) (P 48))
(110 897 (11 331 4951 1381225193763255704428455759635251 50936923403505627680353381016583821) (P 44))
(110 902 (1321 7128292856213387035299323600741) (P 85))
(110 912 (4290560891 31040218952241106631 293623156662412749844839760687500671) (P 54))
(110 913 (186477147425141 717951052090397401 14776463010046039554498700388762499422741) (P 47))
(110 918 (273640291 84195609024341 26628011053449435225528358263641) (P 65))
(110 922 (1321 18041 1388082575490141060576924590456110291) (P 76))


Nov. 14, 2000.

By Aiichi Yamasaki (Nov. 13, 2000)

by ppmpqs(ubasic)

(63 575 (379 41389031677561686362721670936425305927893) (P 57))
(126 773 (66898567 2924536290003406468519106380195210527525697) (P 54))

by ppmpqs Ver.2.71

(92 996 (6805495950246893 21408504212377007281 35807649231738062653558433 10928040030287528889588122406684313) (P 38))

by GMP-ECM4c

(63 885 (3830527 5617144285426699498951223614471) (P 69))


By Andy Steward (November 12, 2000)

by ECMfile2 (Ubasic - KIDA/steward)

(43 866 (431 7730197 2096005390889 11454910939127190885308657) (P 77))
(43 869 (421138217 3027508139 8538034118659346604141938873) (P 78))
(43 952 (13331 78062725011459885230738026314601) (C 90))

(47 428 (941 545483 4552523069309 1798713352413482875849 35055741765972801135593) (P 56))
(47 949 (8461 8782174903450713374059 9827977809800053552292759906867) (P 81))

(49 866 (331241 1579412982613166524374597207637589513) (P 82))
(49 940 (13624549 2994215071 1836450112324715441 14647966245292278689425738923569) (P 59))
(49 960 (7 197 226381 2610663122957 5513994369004686189952216079) (P 77))

(53 456 (743 277398490449798079729022087) (C 109))
(53 515 (107 892627 10754426112416606155597169) (C 109))
(53 915 (6679 106637 77351699 541872855622947787995051427) (C 111))

(59 130 (2802973 38046569963 474637073892550047723163) (C 82))

(65 470 (131 521 162919430441 5371204697849375321 87157557561683185745024611 6146030544598355648933080711) (P 40))

(67 126 (2339325513793 25508505485171321594684539) (P 101))


By Henrik Olsen
(49 659 (7 15575533 105015746486778743689815558608673718453) (P 73))
(49 684 (601674529 10198470047958952912801835968097) (P 80))
(49 811 (197 7057 67745044166410129608099324354807640428076524980431002851) (P 61))
(49 913 (92594179492697 49010960450523970413381625776137) (P 79))
(49 978 (197 2647 158813999 925077281613497498002529920473622527606029473827782563) (P 58))

By Joe Leherbauer
(43 795 (1033 15739 96493 1534069 6063689 16144550424803892984020723763026787738547) (P 57))

By Robert Backstrom
(43 427 (173 410491709599988166210358026180726614858161347993604423) (P 55))
(43 428 (338497 713831578470463526715132762720786511) (P 70))
(43 440 (431 10145209074785199337300310638683869423267) (P 69))
(43 456 (85660903 2649407938198768282373323528736789653488605691647) (P 56))
(43 461 (1233941092819376906193195966054233281) (P 76))
(47 267 (4231 20117 35983859 415639532701177772390148538005589589) (P 61))
(53 112 (1061 93493 142497491761 163189396275929952142565305037975099125483) (P 47))
(53 118 (107 2028629 6177413303165648875435757955466681939009290421) (P 54))
(53 122 (248783 11697949 19577205280753854143065245105296840225796974713) (P 50))
(53 126 (107 910746265372042482829 21457486121289629665591599528299890559) (P 49))
(53 130 (107 19314049 29835821 804786098932378853779680439462114028670361) (P 52))
(53 133 (131759 637909 63456367911827212314118728866209922247371) (P 59))
(53 138 (8408391493535390279309906228581 20257994203650571510038321186907) (P 50))
(53 138 (8408391493535390279309906228581 20257994203650571510038321186907) (P 50))
(53 146 (107 1234183441 3708820289487118309521979369077885615524497) (P 59))

By Sean Irvine
(43 730 (1757121557 1590001033547 14989286861925561410236129323504832451125584159613) (P 50))
(43 820 (1721 10378173497 32927792747 627478319138314182507864317663192309460226591) (P 54))
(47 515 (521231 143365961876938353431 53942239899468702652684610576052631) (P 65))
(47 603 (17092662397 24561601288057538311 396721202398101128286522451271603049574193) (P 57))
(47 629 (5077 10534487 54368137628830004699 9065672707727006973536195529053) (P 68))
(47 846 (3761 8322587041 710905670949152161919257 927034960129247611945549507111019817192859) (P 56))
(49 549 (1539890018764409327 806804538066581403203937449726378388597315348731) (P 49))
(49 794 (141709 343618969 1372964713 767420488045893192571334134717986245451298321) (P 55))
(49 880 (16073 1572202180183816986743 6398918393782894130281788336674523809005313) (P 56))


By Takahiro Nohara (Nov. 12, 2000)

by PPMPQS Ver2.71

(69 622 (139 5521 1387872892476047491 1442872523873133965540500623769) (P 69))
(69 760 (121579 232669 562351 82965739 2514725839 161577955354667766499820672449202540174413) (P 53))


By Masaki UKAI (Nov. 12, 2000)

#(110 974 (11 35064371 152876252958671292414541) (P 88))
(94 325 (6967601293 72565163055049438978033387973 476606803379280470690938083422450269) (P 42))
(94 470 (30073375847955167218765987) (P 98))
(94 566 (6727050518125936069245039703) (P 99))
(94 820 (283 15626618830689883 7896259565813204252857617487) (C 88))
(94 867 (72492836958894824638649071 2351824791256239291577394188069 115351623662855465505397864965326284033) (P 41))
(94 974 (283 1649419 20886049578920604271 55028009941525090752141378373) (P 81))


Nov. 12, 2000.

By David A. Miller (Nov. 11, 2000)

(110 253 (176568701 14704534362208416131199246202672934331036641) (P 45))
(110 363 (78541 3367093773182240440126255887187328341) (P 61))
(110 368 (768606613055904481 1169633236214467636010183342473450046903161) (P 43))
(110 390 (661 463986176675911995025599368080981481) (P 66))
(110 392 (11 10891 53681 3410441 35484647696996129949169350309123356820344801) (P 44))
(110 401 (189156776099420105914728709881553141) (P 69))
(110 414 (11 9241 1196049351970520322156681691) (P 73))
(110 422 (5281 351341 117554719811 243075619306618890645698705746271) (P 53))
(110 440 (881 1321 5281 1616453411909370425785848047765161) (P 63))
(110 483 (657581 191295136292737400605776781831) (P 73))
(110 492 (11 241132321 4956475637603393145955855638298991) (P 65))
(110 504 (21182478196346837301533009638231) (P 77))
(110 534 (11 9296607256454765375670413533572602346571617361) (P 63))
(110 540 (143012761 1113554876095465329454538548951) (P 72))
(110 557 (11 331 661 2971 256408298763717385281719911229800771) (P 65))
(110 559 (11551 9483101 141228455831 3951677830779308466366167317158249385781) (P 49))
(110 564 (4079573851 223920125286475261828834831675609831) (P 66))
(110 573 (2399656278656109134903643433431685231) (P 74))
(110 574 (11 3211849961 9137961911699410489506449541964231) (P 66))
(110 580 (11 103859251 910476652972151 8846683447959873958748899231) (P 59))
(110 590 (11 392841149251 2888648702088497931321302809038826561) (P 62))
(110 606 (331 11551 3684671 329301315701045648867769341522891099891) (P 60))
(110 956 (1840515407611 2799547703371 88072444725478234532851244758519809991) (P 57))


By Tetsuya Kobayashi ("Hamayan") (Nov. 11, 2000)

(138 162 (691 2347 319561753852726190663882371) (P 65))
(138 175 (23707839131878255743822463 71003855807889394115581976047) (P 45))
(138 284 (277 477411001 306584032099 44319600458247833007517758911001739) (P 51))
(138 287 (19174841675552621448480889639 1229873201163677672785883436240872521201) (P 41))
(138 403 (1618051 18453810157 229650825479923830406919707) (P 72))
(138 407 (277 1761884975888531019477130567 2046612553206707520490333491786041329) (P 49))
(138 446 (8971 20149 491166979 138123177927703 8373809755258340264725330823341) (P 55))
(138 570 (691 1138867001051443 381546534661392283619123707) (P 77))
(138 578 (139 3313 918015193 2866754041 1060501855867 106219006095642291370824661171) (P 57))
(138 635 (39414642971464237327367208164286937) (C 89))
(138 650 (146615758969 5920699715145180553222070503) (C 85))
(138 737 (2347 1393939 1838299 15476977 2643882937 105443354917 159995034544775556081702215167) (P 54))
(138 752 (277 758499097123 3927600506397798026201353469221 341321721153286297239724998524041) (P 50))
(138 754 (8215969 555329113 982978381924369531325284873 212230172245061742819255271217251) (P 52))
(138 820 (730573 1185006001 42031431283 15559485031765013780411401) (P 78))
(138 870 (277 30628227126352116898235337355777) (P 96))


Nov. 09, 2000.

By Satoshi Tomabechi (Nov. 08, 2000)

by PPMPQS Ver. 2.71
(132 909 (5500837 34459546621501 224887498385097599674099472702557727082272221) (P 54))


Nov. 08, 2000.

By Aiichi Yamasaki (Nov. 07, 2000)

by ppmpqs(ubasic).

(57 988 (198341781433 6494659194669150880884644952122681450293) (P 57))
(126 832 (2521 218737 2210294063664126027428653711030289347) (P 61))

by ppmpqs Ver.2.71.

(49 524 (6763 7796044406026235442427210022087 899904267228937460542008975806663) (P 47))
(98 428 (234613 15306092632515958754335541 46943418281601106895179434533777647) (P 46))
(49 916 (883 93493 130378711 6373081929469859592392388293 1006508927890347043537810750945997720501) (P 42))
(49 657 (132414906667 19747432924766773972887667 106779872951518240558075634173679) (P 50))


By Katsuyuki Okeya (Nov. 07, 2000)

by ppmpqs ver.2.71 (by Mr. Tomabechi)
(88 931 (89 353 7131427935078322617002449 501918935063965711744645063554651089) (P 54))

by snfs (by Prof. Kida)
(88 406 (1012556727127032517813823876478141181633) (P 66))

by snfs (specialized in 88-series, by Prof. Kida)
(88 260 (89 258408482954525270507945157621313) (P 63))
(88 282 (89 617 91597744229159556982959267864852845417) (P 56))
(88 285 (353 1321 379250280054750917140702193285439881513) (P 54))
(88 287 (6337 44617 4236673976595418709355770890095137) (P 57))
(88 294 (89 235654057122247403955440768506619801) (P 62))
(88 303 (551824417 50531841409905064172963528062601) (P 59))
(88 355 (353 617 2887557682858609075256249723257867201) (P 61))
(88 363 (89 8101694412161571572350619611142009) (P 67))
(88 391 (89 2377 1930350625312443439687203481475606175038432393) (P 54))
(88 408 (17907833459564340750148154370865671837480929) (P 62))
(88 456 (6073 5318614753 1165989302715144069061859723633) (P 63))
(88 465 (1009809057689640082536069051953) (P 77))
(88 466 (29452373216337384722036793052916638913249) (P 67))
(88 574 (14659332142645865358662660124355793) (P 77))
(88 577 (89 1019228566231540653242135851440830850351697) (P 67))
(88 660 (484505229315206947844749450796732551850417) (P 72))
(88 719 (89 38928042018196407369187751731145342496441899500249721) (P 60))
(88 984 (47242932924788350862262335093833) (P 89))


Nov. 07, 2000.

News !

David A. Miller found a 50-digit prime number for phi(110,966) with GMP-ECM 4c.
In detail,

Input number is
74194667582610928530465974089022931930644715291020872723107468379542134\
85498912763247896138332430895021 (103 digits)
Using B1=3000000, B2=964863900, polynomial Dickson(30), sigma=2072145647
Step 1 took 189480ms for 39070093 muls, 3 gcdexts
Step 2 took 119960ms for 19340869 muls, 63342 gcdexts
********** Factor found in step 2:
30594391662286892147783273883147685710094959898591
Found probable prime factor of 50 digits: 30594391662286892147783273883147685710094959898591
Probable prime cofactor 242510681047694251842661133307111942122159357207775731 has 54 digits

(110 966 (14032591 2410037741 30594391662286892147783273883147685710094959898591) (P 54))

By David A. Miller (Nov. 04, 2000)

(110 248 (11 136701401 285061634472184114903699268090553721) (P 52))
(110 274 (881 649001 120568370212342571245346075580943831) (P 54))
(110 339 (991 24048911366740325158247580844921116571) (P 61))
(110 946 (158071 699593401714752260943682669391 10027735166074406061676745317977751501) (P 47))


By Takahiro Nohara (Nov. 05, 2000)

(69 674 (139 15197169409 7854692884303 92624854819527381732716120299) (P 71))
(69 815 (139 232301611 149962931857 16418085363937 3840180902441385685804908884323074628531) (P 54))


By Satoshi Tomabechi (Nov. 05, 2000)

by snfs
(75 230 (1081700300990857386464754417329325876001) (P 56))
(75 236 (35545788664216328851721367633665963334001) (P 55))


Nov. 05, 2000.

By Tetsuya Kobayashi ("Hamayan") (Nov. 04, 2000)

(82 909 (83 422137 9103763411 8011118618238352515227199349 4311798885228038862665030058123953) (P 40))

(138 226 (691 56167 128269524919 17452230260396661282799532289616649732149) (P 45))
(138 436 (139 8971 23587099 1020836284202430517 5970070940891821959901551598865540431) (P 48))
(138 450 (8221876264929931 345597302777946298266720499 487906751634306386518012762476363979) (P 39))
(138 698 (139 20847535976651317 413663160047531999071627 6107624166146624849733794021628277) (P 50))
(138 705 (691 66607357 4927006687 12732610595041414626667 32006408148585879254756960806483702849) (P 46))
(138 754 (8215969 555329113 982978381924369531325284873) (C 84))
(138 781 (3851443 14878333 16452361 4461414421 180667374928021 24078803830223133117993143009877541) (P 49))
(138 917 (277 691 2551069 107230141 2694354263540268162629439417083071351) (P 75))
(138 934 (691 9661 335341 344587 177183859 1116720875905271783233 317282277678208247503809763419817) (P 52))
(138 939 (5107 181422742453 638862903257143999221182110087) (P 87))
(138 981 (565111 16166413927 511974231049 1073244839052631991923 64224086651637599258789872156064276589439) (P 43))

(94 291 (283 8179 4199999762858197464543712871 9126749635299117186196500468001) (P 49))


By Jun Eto (Nov. 04, 2000)

(92 259 (652511085740903949278070804553) (P 77))
(92 371 (144349 13781693 7052097036997 8239554627794334960774313) (P 63))
(92 664 (698557 294749969 14884729356093357554809861121) (P 82))
(92 996 (6805495950246893 21408504212377007281 35807649231738062653558433) (C 72))


Nov. 03, 2000.

By Kunihiko MIYAZAKI (Nov. 02, 2000)

by GMP-ECM 4c

(49 596 (7 45552906103737719857401211) (P 91))
(49 682 (12646313 2559842340568484257885789) (C 88))
(49 704 (15877 4135929379 711304867722611 169723480114350423206142417388393) (P 59))
(49 744 (46747 15947639 17916147796656236969602531) (C 84))
(49 855 (7 29288477 2897705505768214547068433) (P 91))
(49 864 (197 291520171202797142947874779 395659280360300052974264759) (P 68))
(49 916 (883 93493 130378711 6373081929469859592392388293) (C 81))
(49 952 (4372242413401074837864004741116079) (C 92))
(49 969 (15289 92446243 32901929291944450609114352789) (P 85))
(49 973 (17837 1500479 2493709 377204900840939479137408119143) (P 80))


By David A. Miller (Oct. 31, 2000)

phi(110) series
282 13092695315602637159686764493180301
330 7971794099124263693853085829776631
355 662760807255809475221646410238841
378 2780093769698829214196921488454861
749 95486089757004066032030670483381011

(110 282 (11 331 2531 381371 13092695315602637159686764493180301) (P 52))
(110 330 (234781865231 7971794099124263693853085829776631) (P 56))
(110 355 (881 3651063791 662760807255809475221646410238841) (P 57))
(110 378 (5171 2061482831 2780093769698829214196921488454861) (P 57))
(110 749 (316083917911232308405639691731 95486089757004066032030670483381011) (P 51))


Nov. 01, 2000.

Yuji Kida (Oct. 31, 2000)

by snfs
(88 213 (89 88563832174417061115779768549534409497) (P 54))
(88 219 (89 915122662834535475455005717039336396177) (P 53))
(88 236 (89 54725143789758303436139963201) (P 65))
(88 246 (2017489 67563881153420345888021213631697) (P 58))


By Masaki UKAI (Oct. 31, 2000)

(82 909 (83 422137 9103763411 8011118618238352515227199349) (C 73))

(86 375 (27091 288440389 1290720006951376441456779443 1868417033074274053912551962656667) (P 35))
(86 671 (7741 571471 2300290365560641 1706206415863820286270721881659) (P 64))
(86 767 (422452631919328616245887238447) (C 92))
(86 902 (43 173 64713109 62250774652377039976837855239253 5392961405851536119098796913554317) (P 47))

(88 713 (32471125395814172513597933497) (P 86))

(94 291 (283 8179 4199999762858197464543712871) (C 80))
(94 356 (12973 1172933 7541142293 629651716041990311338613353) (P 71))
(94 464 (210467 375841533575581555217 73831625778600666992986405155137) (P 65))
(94 520 (659 1098203 38935459 132477703828975318938315122924467) (P 77))
(94 714 (10529 10167381409 10093559287293855518343347) (P 93))
(94 723 (1693 1924570144319614917945315127 8877996027238829523051017941) (P 74))
(94 894 (1129 398853857783668568749546601) (C 107))

(98 204 (197 10120951 1797993824478671931814361) (P 64))
(98 770 (11263381029711004692510853) (P 97))

(100 668 (5 1601 72208094080903725212838701) (P 84))
(100 746 (291695755269526662340575835082101) (P 83))


By Katsuyuki Okeya (Oct. 31,30, 2000)

(Oct. 31, 2000)
by ppmpqs Ver.2.71 
(88 434 (353 881 123289 4579586969 97226584503423497590027604739106013801) (P 48))

by snfs
(88 376 (269746656659605612696327144438574999814677185201) (P 56))

(Oct. 30, 2000)
by ppmpqs Ver.2.71 
(88 390 (6337 11144962767929 726971085302152982302737398901915333593) (P 48))

by snfs (Kida UB ver1.8)
(88 186 (1969663199443300869417261824744261767273) (P 52))
(88 278 (14188359640019673263528755206583528793) (P 61))
(88 279 (111334369700833202774294675605172076433) (P 60))
(88 338 (4441387604034538881526278258641) (P 71))
(88 367 (7854752390915921859173071025826948605761845490321) (P 54))


By David A. Miller (Oct. 29, 2000)

phi(110) series

286 4943271086900861525504988035648731991
946 699593401714752260943682669391
949 269407231541015648035350456064631
952 86710746770780195913342628448318171
954 21017422647702836776974130054621
993 638487146315933487687583344518501

(110 286 (661 2971 2077351 4943271086900861525504988035648731991) (P 49))
(110 946 (158071 699593401714752260943682669391) (C 84))
(110 949 (269407231541015648035350456064631) (P 87))
(110 952 (11 337005645425867229153537691 86710746770780195913342628448318171) (P 57))
(110 954 (11 263355480961 21017422647702836776974130054621) (P 76))
(110 993 (9901 638487146315933487687583344518501) (P 84))


Oct. 30, 2000.

By Aiichi Yamasaki (Oct. 29, 2000)

by ppmpqs(ubasic)

(126 929 (135829 505513 366915695677891043408249745615697205649185833) (P 52))

by ppmpqs Ver.2.71

#(110 366 (1176121 13158158323032416851219788881 9498051319378776821449378745829461) (P 35))
#(110 438 (5171 5281 71309259095313106926480995101 1481984917535647913769336605190421) (P 37))
#(110 511 (186712901 2876906284910473442666381 282808094111585241596298099176221) (P 44))
#(110 979 (209863832054762512001 3103971985234063606368421 449964968527422325343328127111) (P 46))
#(49 724 (197 11369 30577 8152817 5623193941 51729279720440256007529 138426248912598844502243298942583) (P 38))
#(94 301 (6269707 338752323780627227159669067679 1855633345636348218860088610441771) (P 45))


By David A. Miller (Oct. 27, 2000)

phi(110) series

228 880551506983796366873698069021
409 191559737381278045149838196181751
473 322192845196015990714703791
496 45952107456266593990650661
518 1645608667525599889179984861121
586 51674866807263519324259108751
604 66851253969189789435052528681
618 9193716744944946048983210869181
694 309040857920581810282124733121
705 561141038827519893125543896322376571
749 316083917911232308405639691731
768 786269745292687624402184580275491
825 1491809613343541801074067701741
984 19872951465247586385284247281

(110 228 (11 8526101 880551506983796366873698069021) (P 57))
(110 409 (11 331 191559737381278045149838196181751) (C 69))
(110 473 (331 1375219147730011 322192845196015990714703791) (C 63))
(110 496 (14741 18701 36397122822061 45952107456266593990650661) (P 61))
(110 518 (331 267404281 5414883431 1645608667525599889179984861121) (P 58))
(110 586 (51674866807263519324259108751) (P 83))
(110 604 (843848281 66851253969189789435052528681) (P 74))
(110 618 (11 881 1202830757453597298071 9193716744944946048983210869181) (P 56))
(110 694 (148171 778660888572798551 309040857920581810282124733121) (P 62))
(110 705 (13041802037495659925604493541 561141038827519893125543896322376571) (P 51))
(110 749 (316083917911232308405639691731) (C 86))
(110 768 (331 859981 359529061 128064757591 786269745292687624402184580275491) (P 55))
(110 825 (661 1491809613343541801074067701741) (P 84))
(110 984 (28051 19872951465247586385284247281) (P 87))


And I factored,

(110 409 (11 331 191559737381278045149838196181751 7775473416434285989187000862588781) (P 35))
(110 473 (331 1375219147730011 322192845196015990714703791 77904992542379175086105553461) (P 34))


Oct. 28, 2000.

By Tetsuya Kobayashi ("Hamayan") (Oct. 27, 2000)

(55 783 (351483221 222825016693938781 711515425368417331873612842470357131) (P 55))
(55 898 (97963998250849752690268957171 76890391505950524554091759642062052551) (P 52))

(110 366 (1176121 13158158323032416851219788881 9498051319378776821449378745829461) (P 35))
(110 438 (5171 5281 71309259095313106926480995101 1481984917535647913769336605190421) (P 37))
(110 511 (186712901 2876906284910473442666381 282808094111585241596298099176221) (P 44))
(110 979 (209863832054762512001 3103971985234063606368421 449964968527422325343328127111) (P 46))

(49 724 (197 11369 30577 8152817 5623193941 51729279720440256007529 138426248912598844502243298942583) (P 38))

(138 498 (10656192281701 779432292336097 770627704244784331690325011) (P 64))
(138 526 (139 277 3203027913793680681534753890491) (P 85))
(138 610 (601543 20470844943534048961517055739) (C 89))
(138 696 (7867 65827 499127199973651 8936432733950096371 103440616382736580802655273079079964481) (P 45))
(138 969 (139 26495311 6348668749 103954922704371447611471774929) (P 84))

(94 301 (6269707 338752323780627227159669067679 1855633345636348218860088610441771) (P 45))


Oct. 27, 2000.

By Kunihiko MIYAZAKI (Oct. 26, 2000)

by GMP-ECM 4c

(49 423 (197 822907 136155641145858391 1339312142677899811346341501) (P 58))
(49 524 (6763 7796044406026235442427210022087) (C 80))
(49 651 (197 2647 176989 1073507779 1034611101858924472768047113239) (P 69))
(49 871 (31477492103 412109361021023 8230161402304761069950875807271) (P 68))
(49 928 (7253 305369 7129998037 38121518856311353 3678547478545771589310239) (P 65))


Oct. 26, 2000.

By Andy Steward (October 25, 2000)

by ECMfile2 (Ubasic - KIDA/steward)

(47 218 (928849718741133999062699) (P 84))
(47 412 (8214678698990654018587931239) (P 93))

(49 814 (7841 248137 517931 345515563 141975087064189 180989054350054699929707213) (P 59))

(53 302 (5690611 20180201773 55189162196948191 754005003804727347059) (P 75))
(53 575 (107 18978833052224800278463787) (C 117))
(53 669 (107 814823 2149510507 53057129104024228381313 3041106950636979885057976509503) (P 77))
(53 867 (107 26304215286719 15616393176896125330429) (C 116))
(53 879 (107 8162138734718851704527) (P 130))
(53 976 (107 31907 50033 611939 51993743 45736962787 127070578461274734875027 150684428951307572243185273) (P 71))

(59 210 (1063 549591491 62743336067 408897510321556965307 78661255048758130120695341 5476939709332158991737230933) (P 38))
(59 228 (297077509 289358688124236966448177 81452320251879591453769871) (P 79))
(59 879 (709 101363 2411449 611271003844468819 561190487351904892645395467) (C 112))

(61 395 (122080033 160607023 177911297651 810292959717585329214517) (P 105))
(61 572 (2424358492363 2983198485215479785781) (C 132))
(61 976 (367 5457265695723319 67354186397494018557763) (C 139))

by PM1file (Ubasic - Steward)

(61 228 (2138797861 22949038284744412787 19850775185368826639293) (C 91))

by GMP-ECM4C

(93 970 (6883 328339700247391669 434570540075869745158201) (C 135))
(89 790 (179 9257 121658551284187235341) (C 229))
(195 115 (197341 12632881 1056100705921 47866886546701 74387100246034291 1778353224801512971) (C 125))
(101 167 (607 203213 47891203879037 29370912936774195727) (C 182))
(206 170 (1031 1977709000064244143) (C 207))
(113 688 (227 71336455007 6834723687461 117182358166120337213) (C 272))
(308 674 (9857 165089 3209998177 1734290175576421 19157064395615917 32241796141927373) (C 273))
(372 970 (373 1861 169973676031377553 364141735542699768889) (C 315))
(384 390 (1153 3457 160033921 453507376751109074689) (C 297))

By David A. Miller

(43 545 (354647343258258984481608518199003127) (P 80))
(43 861 (43 173 58394793007 29741039792837366285496880426319) (P 78))

(47 753 (47 37845991497621349269040974252779) (P 100))
(47 814 (1693 864707 277501349 544766093281744097 107733345641915486998453329194137) (P 67))
(47 857 (1895981 19078711 25992391033346259411771553499449157441) (P 84))
(47 940 (1787 2069 3761 48197843 17231840841034847141972589989461 50724300233102613022362191024043599425510121) (P 44))
(47 960 (283 2351 3393830210369500085737946203) (P 104))

By Henrik Olsen

(49 525 (24267238499447608778624871443954494286714691436298136937) (P 59))
(49 541 (13618157505932751276418046829841380078528912001152178403) (P 60))
(49 572 (491 9833197350982134418038604394703683170756604087) (P 68))
(49 590 (1467367769863244485656024026889507939424837957633121) (P 66))
(49 633 (197 8431234017870714226141397474915633279) (P 79))
(49 688 (657091 240598356818377046157062551345123175298067871) (P 69))
(49 722 (7 9311 8078504851372096904516199264914216914737449) (P 73))
(49 781 (197 6763 3226859680566790562462340837892682243111) (P 76))
(49 867 (491 122212273 2586053727102470958558639648085069079) (P 77))
(49 879 (2646981079 1927735998141259869023298854032147411673) (P 75))
(49 976 (197 3606503489 64188010213730696934054627085531) (P 82))

By Jens Franke

(47 736 (7333 13537 781669127 2056989499 11718991469 239330730313546305833609504632318293456976852231) (P 49))

By Jo Yeong Uk

(47 891 (283 659 1465367 430492768483 20713284811117905311 10075228441208247614794665297223770343) (P 57))

By Joe Leherbauer

(47 974 (66621401250062243686217586551758475202925903) (P 94))
(47 991 (23932490351407939678014858223494279241439570026442141091773405680031) (P 71))

By Robert Backstrom

(43 302 (43 3613 11173929538762680439876772366495332403) (P 62))
(43 394 (11783 246410995169991481034292872081131125637583621) (P 61))
(43 402 (15435023 2332620307597303900517595408082926745510110489077) (P 54))

(47 248 (941 164730113 517345328316305533793879084372397974378024617297) (P 52))
(47 254 (8110568537 13509565711663410856913183507922559501) (P 64))
(47 265 (12503 26227 539607954980008749302513556814357888550153558041) (P 56))

(53 108 (26183 43476911013936800913532329485540074377973) (P 61))

By Sean Irvine

(47 609 (659 565020468192119 5353202331283777 2665268401992327580585045830255557951851769) (P 53))

(49 669 (491 796017449758403454583 25244769617437619920451307040116472304432117) (P 52))
(49 773 (197 126732131 12618822899453 2495290020456418542852776464463910156290453201) (P 53))


By David A. Miller (Oct. 25, 2000)

phi(110) series
366,13158158323032416851219788881
438,71309259095313106926480995101
511,2876906284910473442666381
629,11010122778216169667385827103048757301
690,93119250406836472891595216783101
764,4042662658244031070733881
854,2266668366718891371965411
854,9060103509233400019521279551
895,32889700035288087027682691
948,6766964086198866266341489591
959,73329714767837638808588359205968661
974,152876252958671292414541
979,3103971985234063606368421

(110 366 (1176121 13158158323032416851219788881) (C 69))
(110 438 (5171 5281 71309259095313106926480995101) (C 70))
(110 511 (186712901 2876906284910473442666381) (C 76))
(110 629 (11 331 501289250853929158312561 11010122778216169667385827103048757301) (P 48))
(110 690 (11 881 1871 339566701 93119250406836472891595216783101) (P 66))
(110 764 (12153571 274694971 817571591 4042662658244031070733881) (P 67))
(110 854 (11 991 2266668366718891371965411 9060103509233400019521279551) (P 61))
(110 895 (3301067551 32889700035288087027682691) (C 84))
(110 948 (11 18041 278741 6766964086198866266341489591) (P 81))
(110 959 (11 372461 73329714767837638808588359205968661) (P 78))
(110 974 (11 35064371 152876252958671292414541) (P 88))
(110 979 (209863832054762512001 3103971985234063606368421) (C 75))


Oct. 25, 2000.

News !

The factorization of phi(41) series have been finished by Tetsuya IZU !!!


By Tetsuya IZU (Oct. 24, 2000)

by ecm (Kida, L1=1000000)
(132 898 (1453 7789 2839315249 22903139238922391608042509676110457) (P 68))

by snfs (Tomabechi, Ver1.10)
(132 607 (10429 1574238087167883511505609533569658606026077377829581) (P 57))
(132 615 (190895103691856514340509627147497353) (P 77))

by snfs (Kida, Ver1.8)
(41 866 (83 16073 10690332207897690120026251179885497910833063582449) (P 63))
(41 869 (739 18287 167117 535596989986839203861115625930417718967701) (P 64))
(41 876 (24109 14079680581745962544460300179943274207847) (P 74))
(41 887 (31892753 614867093607792603414941763102157964137) (P 72))
(41 904 (13121 264697 218728438184071422291376042172166715300913638244987443) (P 56))
(41 915 (88643 8873928348465337914766942395682558290451) (P 74))
(41 949 (83 2953 5327916286277302994782275399474656373823045474861) (P 65))
(41 952 (7494719 9524219 48419664600298898111066514804139083800833) (P 65))
(41 957 (83 6017489 722353390284142214263234401551464035824197) (P 69))
(41 972 (83 16811 742021380496831542617004641070602016969419) (P 72))
(41 990 (83 6151 16073 71341 15170468881127850112304182750801335836240303946739) (P 56))


By Jun Eto (Oct. 24, 2000)

(92 888 (1234995673 15179755413401 121247849805486953 493120504941715053219281449) (P 64))
(92 527 (12098469043826689 65233476091000082977946273) (P 78))


Oct. 23, 2000.

By Robert Backstrom (Oct. 23, 2000)

N = 412^43 - 1 = 3 * 137 * 947 * C107

C107 = 70857934499028481426835723567674185094510375350475809791868\
       400896673502167711182818850687531610418174708831

     = p53: 28449712870241406162594128570608614696087039272320187
       p55: 2490637948516744593678318676765057515870208789491607213

(43 412 (947) (28449712870241406162594128570608614696087039272320187) (P 55))


By Takahiro Nohara (Oct. 22, 2000)

(69 604 (568177327 393748452840546905287 3216534826181047010921082698581176165847) (P 54))


By Jun Eto (Oct. 22, 2000)

(92 957 (480181727684617177 109527440205291176455277789) (P 88))

Oct. 22, 2000.

By Jun Eto (Oct. 21, 2000)

(92 629 (2470930811753 178941511615605469806604901) (P 85))


Oct. 21, 2000.

By Aiichi Yamasaki (Oct. 20, 2000)

by ppmpqs(ubasic)

(63 724 (5419 8821 1318141515371332960219023582873862985569) (P 57))
(114 945 (14479 10064149 113391840105993114254637922558442758764654727) (P 52))
(126 531 (127 268289620261061448141065687302172406110508298891) (P 49))
(126 540 (631 5659449674556895356732732545024316614869) (P 56))

by GMP-ECM4c

(114 902 (229 44234755987578680316494072061124686853) (P 67))


By Kunihiko MIYAZAKI (Oct. 20, 2000)

by GMP-ECM 4c

(49 398 (1373 407420987 158148394303845132669382279) (P 72))
(49 412 (83987 27926066808941281 8538349703295088433359 9434161679973300731289288167) (P 39))
(49 483 (4163497001254863097720651 428182259428921202396735419) (P 62))
(49 498 (7 883 81047 39192863641 10468067942506531404360811) (P 69))
(49 694 (7 491 268053044447161 129723175287450592872255169) (P 76))
(49 724 (197 11369 30577 8152817 5623193941 51729279720440256007529) (C 70))
(49 816 (197 5406398537 234875915058430363726324919) (C 84))
(49 948 (27058156547110175079885633139) (P 97))


By Katsuyuki Okeya (Oct. 20, 2000)

by ppmpqs Ver.2.71

(88 319 (2729 70753 83777 1345032905008419206981528984806540537) (P 51)) 
(88 375 (89 14660517295513 119655118310373684343746761) (P 62)) 


By Tetsuya Kobayashi ("Hamayan") (Oct. 20, 2000)

(75 462 (2153496187513429501 436585772911974969898566647537690177934151) (P 47))
(75 562 (51001 2949901 54750047551 847571649439044110981789551) (P 62))
(75 846 (1548474103801 11752953434073601 114789268623887867914706968347165242148901) (P 48))
(75 867 (1801 103801 16232401 24172583370301 825903498081146041434141307393120676701) (P 50))

(138 114 (139 25117 3901381925735580437240782502712561103) (P 48))
(138 122 (11615384351773181313994136896519) (P 61))
(138 200 (139 1657 236688769 1892118105118781451982078435872979) (P 55))
(138 219 (7591 6725372172814485142425511 46228286172680627783636072157253) (P 43))
(138 360 (277 1903251790459 715209851414649403510371253 45219097899698619713484515557) (P 43))
(138 550 (97111291 125241369667 307789666291368680319692883181) (P 73))
(138 565 (20011 36709 174157 502597 317812268377 7919930939345108236899369319) (P 62))
(138 591 (189061 8086249 3152237625518095497981106148486971 302933807150565930836763991849122961) (P 41))
(138 831 (74383 1752763343759145907915730569) (P 97))
(138 897 (606315935293 108390598116914652490400089) (P 93))


Oct. 19, 2000.

By Jun Eto (Oct. 19, 2000)

(92 669 (1477337 162791701 19595584185365032643508961 5179844541370976328818302229) (P 57))


Oct. 19, 2000.

By Yasunobu Torii (Oct. 18, 2000)

by SNFS

(63 659 (1723745426395251592278157051072784321347396429) (P 57))
(63 688 (276554181620467707864704815128487835806585149067) (P 55))


By Satoshi Tomabechi (Oct. 17, 2000)

by SNFS 
(49 446 (169645419031367785095608232360449352143302072823687) (P 62))

Oct. 17, 2000.

By Katsuyuki Okeya (Oct. 16, 2000)

with PPMPQS Ver.2.71 

(88 387 (89 4662223703308513 9889600354332994175257615517299802497) (P 49))
(88 453 (8537 576987207494809 55217789391857510565163431447627409) (P 53))
(88 497 (58169 792188541688721 2831944926831192517948218672929137) (P 55))
(88 532 (20252259193 14944081462553 12241011828292024402605100854946873) (P 52))
(88 536 (41871253337 3356979084449 7972210534595323280752247558657) (P 56))
(88 560 (89 1112921129 2846661688993 2002002696763005426399146880809) (P 57))


Oct. 16, 2000.

By Takahiro Nohara (Oct. 15, 2000)

(69 302 (139 92843355395977 94315080964214754843626812516950277) (P 59))
(69 526 (1531111 969161141264761971499 70528798727953720042690356529513351) (P 58))
(69 871 (139 967 588019 13486753856998892399696846744881) (P 88))


By Masaki UKAI (Oct. 15, 2000)

(100 391 (608863289905103201 3256611938705726119317029954201) (P 56))
(100 867 (5 101 1071601 80372975298179410854701) (P 86))

(110 793 (279511 30845312885190080856785471) (P 86))

(75 582 (3001 48687451 63355154060655817455895771457851) (P 68))
(75 590 (151 340968387713176651 606398431209446857673256885161251) (P 59))

(82 616 (83 780113775788167 13469816490691827037311797 87670216558474306332827639150977) (P 38))

(86 226 (3536698201801934366085973398947) (P 69))
(86 274 (2063897271950887 2750632838186880257115049031) (P 60))
(86 424 (173 947 1721 4817 62351 98729 1799005074722541873321894596503) (P 59))
(86 500 (1721 4129 2120603567 14096356367581588545236953593667) (P 67))

#(88 882 (353 113909993473 517288231347986742337 54449671332628143849440293153) (P 55))
(already found)

(94 194 (2579653939 3760723003286575556549220613 21205767905316359696862523877) (P 40))
#(94 258 (62944967950939 10460129367191438225092807 22226013122677619415686013773) (P 44))
(already found)
(94 358 (144667 2905823 10361687117 18454523335114761115542843479) (P 68))
(94 526 (18804854465009204578153 775568190201607989829497149677) (P 74))
(94 656 (22937 53840569 1864043468699 21276844964937775916581145963) (P 77))
(94 804 (659 268888975603338309225056145829) (P 102))
(94 835 (1129 1787 283928422185360986453762962625521) (C 96))
(94 898 (12973 5260428659 192750355084822961295706567) (C 96))

(98 436 (18131 1046053 1218043 685433953 2790262114766067733162909344269) (P 56))


Oct. 12, 2000.

By Tetsuya IZU (Oct. 11, 2000)

by snfs (Kida, Ver1.8)
(41 791 (83 18451 213611 77047192691003374416467648820303546294476231) (P 61))
(41 811 (83 695957371 3318267323678437999096186052364208674107405679127) (P 58))
(41 823 (1559 5659 114883 5432121114364901840947287157028607090732697) (P 62))
(41 844 (7873 1234705817 57164309718583433578569933317899163) (P 70))
(41 918 (35226053 38039063 488992818286948574003172043775783853748506783191) (P 56))


By Andy Steward (October 11, 2000)

by ECMfile2 (Ubasic - KIDA/steward)

(47 371 (772570867 76011087931 1435021432601534693567) (P 78))
(47 376 (554524111857363524099055549000881) (P 86))

(49 833 (883 38501699531 1650403669363 2943634625359102917327821) (P 73))

(53 647 (68477 1782459957668830698467047) (P 118))
(53 789 (107 140124822637465640666158583) (P 123))
(53 808 (743 4241 51517 209669 239137 1790633413118311337 12576761564866549789) (C 92))
(53 910 (683701 6539777 255864557234913135116819) (P 118))

(312 873 (1410553 296165644517527469257 527636805277053586871329) (C 232))

(218 703 (265961 136163439182977) (C 288))

by PPMPQS (Tomabechi)

(47 833 (55931 1621031 5077494977 36012646903421 587979777278683 18464822588581326477544310632049076097) (P 49))

(49 451 (30085710831980122330799632573 8242316851796322931056821341346050381) (P 47))


By Henrik Olsen
(49 575 (7 3407719708862408471749547191196135355657313) (P 73))
(49 639 (376942376290745995857787474385341) (P 86))
(49 721 (1373 750007811906367291489423700332090685136609) (P 76))

By Joe Leherbauer
(41 759 (83 739 5279243 5858016736231850853701391573168943821652328771856517) (P 52))
(117 125 (7655311 6475711850365695029787483033056414199292785571 1489161023006154219903790225805356280792802449809) (P 51))

By Robert Backstrom
(43 371 (1840281164196808442931387185667153374339478711736931) (P 57))
(43 376 (1977743 816046517807146280267811439754247181171) (P 63))
(43 399 (22977739 1078238019292819567508210940446892551536600158829) (P 54))
(47 226 (813025606311895227958537352795132742413882716889) (P 61))

By Sean Irvine
(43 765 (2207601871889 275706419852770427 419309666228659112022028340085133858470444479) (P 47))
(47 395 (2129648053004048920593769 472567092730725415033560059527286985641426213) (P 51))
(49 789 (5783 792821 9324278774668439 44234315812578331025614769902303217328174103309) (P 50))


By Tetsuya Kobayashi ("Hamayan") (Oct. 10, 2000)

(75 192 (601 1945519747254125642872766395273423501) (P 53))
(75 244 (28404451 369321506835816730558852899836547301) (P 53))
(75 753 (112447501 13583712891838266901 911823636180885235939409389765491566401) (P 49))
(75 765 (151 11012851 6414707953296866401 1240187830722421001309321018889372001) (P 52))

(92 161 (26673819383074298148219601) (P 72))
(92 163 (552939895503274266157712879460224165032249) (P 56))
(92 195 (277 113161 3223488383845301432606888848709) (P 63))
(92 368 (115475041289899451834562137) (C 87))
(92 432 (324476722553480867147105243549) (P 87))

(138 246 (37687840335770497 503608033548907166905422577) (P 62))
(138 711 (1372411 2121463622539 2424856807397302038562904083) (P 80))
(138 995 (139 15999584347 243234980825157935454498577) (P 94))


By Satoshi Tomabechi (Oct. 10, 2000)

by SNFS 
(43 218 (12817417344404995623669883614240092866032455209) (P 53))


By Kunihiko MIYAZAKI (Oct. 10, 2000)

by GMP-ECM 4c

(49 346 (69541487 780247872943025785133203243) (P 72))
(49 410 (197 1471 179283553 116903009468769159769183) (P 73))
(49 459 (491 25524689 8518779557 2236013800868575980585089) (P 68))
(49 483 (4163497001254863097720651) (C 89))
(49 657 (132414906667 19747432924766773972887667) (C 82))
(49 787 (24559857100093705896661 87954371115257392629310783028303) (P 68))
(49 799 (7 224437775196097 85935299460243769747) (C 87))
(49 820 (7 24178161492536777587 40540671421787388391 363616794171481957794895453) (P 56))
(49 826 (3529 5632051279 151303824449 5736526081230792359) (P 80))
(49 830 (197 883 5790229213763 69537212430543103 8098911887034778495589) (P 66))
(49 833 (883 38501699531 1650403669363 2943634625359102917327821) (P 73))
(49 837 (197 85370741 28250037229 56138601163 7365811327193139076103429) (P 67))
(49 864 (197 395659280360300052974264759) (C 95))
(49 931 (22639 22453663 441758214159119571044522381) (P 87))
(49 984 (15289 220198553 13795733471774425947203) (C 92))


Oct. 10, 2000.

By Takahiro Nohara (Oct. 09, 2000)

(69 350 (6073 14996248435229101 245339894220103407776610538101044370092563) (P 51))
(69 564 (277 23266249 441664208779 113324601635567985548656983019) (P 71))
(69 615 (111229 996361 38116755021139637461 11281499063705651856670461859295251129) (P 56))
(69 709 (132711366000820070428549873) (P 100))
(69 711 (139 418944403 245699342779619346221623 148588398493299196641377042288133706381) (P 54))
(69 819 (139 277 7232581 46064852505108718356196837 733558581213702702969694925341) (P 62))
(69 879 (277 10390274227220431 398946716170050091 1586864838077678855091366972691) (P 64))


By Katsuyuki Okeya (Oct. 09, 2000)

(88 310 (89 617 10622447089 6957659476912060647381344489715304793) (P 49))
(88 378 (881 152417 12492849953 648593117779714129517102381250342361) (P 50))
(88 427 (152123401 9279603605977 443880386103805412526066353827914296956073) (P 43))
(88 588 (89 617 1184721777531714187921 287283147433947744093060816076561) (P 53))
(88 627 (617 1014641 31373761 319797686561 760314084640719238653905521306917798857) (P 46))
(88 636 (89 259714092933301039475641 8294770949253497013383134230245219809) (P 50))
(88 645 (353 68238123557260543962241 9802672423014032166927563152038021137) (P 51))
(88 655 (169753 213794505128786169457 49718230260327904837829904530925769) (P 53))
(88 680 (1946509779742765312395051073 8024872829424010560794170609) (P 59))
(88 753 (89 10634844001 9616038581205688633 14939794055238550626239089327801) (P 53))


Oct. 09, 2000.

By Masaki UKAI (Oct. 08, 2000)

(100 669 (101 22986001 71073185200088289561836201) (P 78))
(100 833 (5 56501 177887701 5688532369359019530968548914301 10894710639392718966136316635054901) (P 39))

(110 334 (3169211 19340642059477822805417304852431) (P 64))
(110 501 (11 286964145176790181 72320501341410185606031631) (P 64))
(110 837 (2311 1235131076134056570726054098401) (P 84))

(75 506 (9113851 137863128888840682951027951) (P 76))

(86 382 (15945929118973946974411 2140136966359154774470038623) (P 59))
(86 403 (947 42743 221539337804831279786684251) (P 76))
(86 447 (913737359 163770863724436600722820313) (P 77))
(86 554 (173 1033 17019487 26695261 1881603582121 2702573962046310161772962581) (P 56))
(86 662 (2237 12041 90963491 1627965543415438807 7272733497046911209420691281) (P 58))
(86 998 (2237 863315506446836463388324753957) (C 93))

(94 237 (18143 207547019 396246745996812651993111377 2619325935640936260209996912937323) (P 37))
(94 301 (6269707 338752323780627227159669067679) (C 78))
(94 437 (10529925299447 19056351072581 7670279031899108775613312667) (P 68))
(94 595 (13943160578725741835781965699549567) (P 94))

(98 287 (88388450352441667 180250148882284759286219821) (P 61))


Oct. 07, 2000.

Data from Prof. Brent (October 01, 2000)

(75 839 (29101 523801 5449747910909410194204305945212201) (P 74))
(82 919 (83 17586564812910679862433675582856349 330194148094652933183881651679472863) (P 47))
(82 929 (1231 40869457 11088919989620299429924073873) (P 80))
(88 617 (89 1526314922089 158628895760779582189165677026034312017) (P 60))
(88 947 (140452281091400923773201925397127807193) (P 81))
(88 983 (3837329 20764921 4665263705966526190652769226033) (P 76))
(100 769 (6664557553225027701164273536901 15573840272925719289400945950553501) (P 51))
(100 997 (5 1008901 6097646209091733882775853061301) (P 83))
(110 337 (11 14411 119767371062486450902137873649150580141) (P 58))
(110 821 (11 331 811479036123455041 1782316913773678210031623867966212353951731) (P 53))
(110 839 (881 6330860189597107231 770477998971707297342353025202656191805659201) (P 51))
(110 859 (904531 29566681 4610809541712537969611307040111 8615600802941728015694842342561144601) (P 37))
(110 911 (1136081 26626711 348076360406431486488403818073661 2629022321118840691785294650999431) (P 39))
(132 883 (1706629 5117824010173167478710876164868084097) (P 75))
(132 971 (107565638329354356916897036707736915873) (P 82))
(150 769 (151 2321213182938509495462568849883051) (P 80))
(150 787 (9146101 19603651 20158922058318130967212548169951) (P 71))
(43 272 (7131379 233746561149053103370505649627515261324900513) (P 52))
(43 276 (7007969 15094916548284444459670475643815027) (P 62))
(43 581 (2362608934959067112359 1012493836230466195277529336132206753) (P 59))
(43 891 (82900607974677320235812940889 332269229521682988020653579326869332878042187) (P 51))
(49 451 (30085710831980122330799632573) (C 83))
(86 733 (173 1033 1291 1287722268422478487444224416141261) (P 79))
(86 907 (22877 50311 1303331 64168206687424779214848127571) (P 81))
(98 401 (197 37339 3037217 60846221365707755147663109109014879728827) (P 56))
(98 419 (7 197 33811 163420078150381544550870430074546791) (P 68))
(98 673 (883 3228023 1749220444483 5173344679363817297340568686587) (P 67))
(98 947 (29303 46747 75853 2722147 114244460126017421431554088067) (P 76))
(69 479 (277 57449223419954107039 308967770993094088612457414555808367297) (P 58))
(69 857 (89622626613671563165450738411 2565780300351853018663743326844397) (P 67))
(69 919 (277 55339 3682703265211 2074150204783567 26857510826214001408277097598339857697) (P 58))
(92 347 (45817 315945187383006788530000185697) (P 78))
(92 359 (277 7334333 41295673 1322405705779526469775918077071825643643000217) (P 51))
(92 439 (46093 1479178407458875402704677053729) (P 82))
(94 727 (1496381932365993314104879937429) (P 102))
(94 839 (601883 1339341250331065276591 26533066346313132436325089303991) (P 77))


Oct. 06, 2000.

By Andy Steward (October 04, 2000)

by ECMfile2 (Ubasic - KIDA/steward)

(47 654 (499805103919322074083817 2019399338685613306644294599) (P 79))
(47 981 (52268158858878369886343271599679577) (P 103))

(49 315 (84967 1790629825361992545214650409) (P 73))

(53 237 (107 6345198502169 9606706878368423 1641442617282066152310853569791) (P 63))
(53 334 (107 152641 21973173917139782640205008919) (C 96))

(55 637 (850301 35274074174681 5695193821411600408155672404701) (P 62))

by PPMPQS (Tomabechi)

(43 910 (431 1033 5849 98041 1246829 22470441239857217 471509929690155522360009620280335826115159) (P 46))


By Gerhard Niklasch
(59 190 (2833 28793 3103813903747841 13894916546506714831512181 18907985677490327178909915953844529169911) (P 44))

By Henrik Olsen
(49 599 (15703585553397010273662172591083827) (P 83))
(49 611 (3720191411482589268114400341461 55884536220553179309562782486870971) (P 52))
(49 647 (1672729945343546442757975382133186107820809) (P 76))
(49 716 (1227884296218040072243133307216160233355015439) (P 75))
(49 808 (1667 47381570848352888002597158651804040581976181563129) (P 70))
(49 909 (6763 842857240394319270001537539785853367215934204384777) (P 70))
(49 966 (30881093626856638830365569013219638531073) (P 85))

By Richard Brent
(47 691 (205921276909 8301146118368402173009 810939432247741328260303007456596109) (P 62))
(53 389 (471331969 4897704115627013 5606413578029052920924140429486841) (P 77))
(53 419 (655059443209 13929370998479 36340173180797709265945770712099 165512740070119784086498717945989170249) (P 42))
(53 419 (655059443209 13929370998479 36340173180797709265945770712099 165512740070119784086498717945989170249) (P 42))
(55 883 (11 881 3301 136128283484994022964337498976618222261) (P 73))
(59 137 (766132767348481122361 212289276062402139772211570413414979299) (P 65))
(59 317 (62423 2168977774990401210131 465976860193301513586443 927881990773974822938936748096822678306481) (P 54))
(67 103 (2011 2824721 2986645633827767432534353 3499141812858116773430449 687068824676412113785067977635287) (P 42))
(67 103 (2011 2824721 2986645633827767432534353 3499141812858116773430449 687068824676412113785067977635287) (P 42))
(71 94 (1279 174095854921003 10718654388185066639 3563282386965235728008912656147288391843156009369) (P 54))
(71 96 (13344280181326306472697457 16001866111300325156620312720684759347799513) (P 71))
(73 93 (1607 69497 508916329903 30755637033697 56893991911245960534837462399054561065035043) (P 65))
(73 97 (28909 65701 541369 2075560967 406200032183433943894585200505966442183) (P 81))
(77 98 (617 1902671 104058263 83059113467384133713328522990316865667727) (P 62))
(79 99 (3319 6637 428023 853429417 274512778508464216268280437477 27100756722615202899087603064941702173) (P 67))
(89 42 (179 1069 18698582905289477 14444379222199215931 5735037882936470515855886923634466519997049) (P 60))
(106 289 (1061 1494286214623237388491714984882811051550425483917) (P 77))
(122 169 (8626498609074269149060403255784440097670457) (P 91))
(184 100 (120553054891405588545727822543281066162803459003848166118314367809) (P 111))

By Robert Backstrom
(43 331 (173 3527 8360328172538087146885001752781474857075583) (P 58))
(43 334 (675230446912198502282605386988121364131419650110399) (P 56))
(43 338 (2856641341587453066243714532518460057634180064176503) (P 55))
(43 355 (1291 363854322088920980507105264299706872275855537487) (P 57))
(47 200 (108689358325701068460477953173552987178257) (P 65))
(47 207 (283 659 11617483359408784780615313788867307) (P 68))
(47 210 (659 8461 886103501968718576423590960995700318155337) (P 59))
(47 228 (9234749 1069889600383903148532840889588409471) (P 66))

By Sean Irvine
(47 633 (1693 359161511593551687140416447093 18181770105343298843129696846354166682500250799) (P 50))
(49 215 (8429 36542395919 38888116983012514051604518694856181319441) (P 43))


By Sean Irvine (Oct. 04, 2000)

(88 306 (1321 58554673 2897343605848012193188147141287357128057) (P 50))

Oct. 04, 2000.

By Aiichi Yamasaki (Oct. 03, 2000)

by ppmpqs(ubasic)

(63 741 (12337419403 583892219542647885918676360834092769) (P 58))
(63 979 (315030957171967 1038524489121015565964245766580409) (P 61))
(63 531 (757 3240406753749104220259843370185746795317023) (P 53))
(63 628 (127 1009 986185639124248139264509976668801862585557) (P 54))
(126 612 (63127 8287732727132109032872792449738300519792215767) (P 50))
(126 747 (127 724879 3464693969360513023408219475607465393177019) (P 53))
(126 767 (539243713 1388005628632966508790078639726607207) (P 59))


By Tetsuya IZU (Oct. 3, 2000)

by snfs (Kida, Ver1.8)
(41 736 (309653971327 17879298915164704651757825274066615127) (P 66))
(41 825 (83 23973878805201741171296353434144839) (P 81))
(41 842 (83 113489 470059097 512795140453389517998833816961100052141685623) (P 57))


By Sean Irvine (Oct. 03, 2000)

(88 272 (353 1703857 3928590684207080177515463743717872839473) (P 50))


Oct. 03, 2000.

Many data arrived from Prof. Brent on October 01.
It takes a little more time to update all.
If you want to see latest results before I update, please see the following URL.

http://web.comlab.ox.ac.uk/oucl/work/richard.brent/factors.html


By Takahiro Nohara (Oct. 01, 2000)

(69 119 (23225194550138086141524974609216297641) (P 54))
(69 166 (4492591 350035372237857522574648448437) (P 62))
(69 385 (139 10903 171811 131470963873 4689869484299334708985270039) (P 64))
(69 450 (94677754529420758151553062839 56313161723908229446403018561084809591) (P 51))
(69 612 (1021753 12565153324589233910921557 21416735542682452922729292165256367021131) (P 52))
(69 955 (139 401354790211 44590710741679 845299096103094472037032981) (P 77))


By Tetsuya Kobayashi ("Hamayan") (Oct. 01, 2000)

(75 186 (2851 1817077926628739859511786343422878363151) (P 49))
(75 513 (2009860935372062663251 344454819941519801862983817943848151) (P 52))
(75 736 (2551 182269951 6699993616175551 296008881961911455477369449707822901) (P 52))

(92 418 (129376274612989 11932583606479101730553460229) (P 74))
(92 465 (829 547093223181121 1238111659961857 9040949276189910723334849) (P 60))
(92 550 (253334789 1400877377 59982690089039359989596230829) (P 75))
(92 609 (460367021447127933997 341869470246300075423522447533321) (P 70))
(92 846 (277 33589753 743802689689327134265284706253) (C 89))
(92 999 (277 5950146423387182160329621) (P 105))

(94 161 (665897 2738211581657565245535241) (P 72))
(94 570 (4231 90715077317 905308941044236661582148607) (P 86))


By Katsuyuki Okeya (Oct. 01, 2000)

by PPMPQS Ver.2.71

(88 674 (89 353 8677515786820180972849 36602718679022811505791262553) (P 59))
(88 710 (1409 18041 30757431644003729592049 588708649670251058362592515810001) (P 52))
(88 726 (89 5470169 385614241 239597569817 703329921500160025417518735837610905670993) (P 44))
(88 737 (2113 35439939231841 113731862198329 11841522106905324242086695161) (P 56))
(88 772 (89 10643031222683414140254800561 1161979747647905651253143947090050757657) (P 47))
(88 791 (82633 465869030881 985932601505809 7649880677072844164885860976901105593) (P 48))
(88 882 (353 113909993473 517288231347986742337 54449671332628143849440293153) (P 55))
(88 936 (89 155849 3544171489 90245966659553 113526031315766204335316912592536081) (P 54))
(88 951 (89 2315897 4073873 83416916446117511401 731674885808953598236326254753) (P 55))
(88 990 (3433 123113 59651586457 494885026625089 77607890004437244028091592793) (P 57))


Sep. 28, 2000.

By Igor Schein (Sep. 27, 2000)

(47 372 (622187 54999589 48746733050677902834259 3418865270894062610783458777950389804749) (P 43))
(47 963 (659 83003 3749849 3676787441 1465642542361 4182182154386187169 2469699119291260170721682389) (P 56))
(75 893 (151 5701 5381251 622403310022569555965238451 562626071413871781943556187350401) (P 46))
(94 615 (659 84319 224014622207586961999 4464369043860443795752783 44172168486915502770011310058791007) (P 41))


By Tetsuya IZU (Sep. 27, 2000)

by snfs (Kida, Ver1.8)
(41 833 (83 14473792400571857 383523492909322910280707577323604263) (P 64))
(41 870 (83 28824116102809259 7684406313633315393246034202043128177608783) (P 57))
(41 896 (1559 374741 4954257551 681144238385886378240278771797434646812539) (P 58))
(41 930 (83 739 18451 60210503753 4826141464098515935997759275370582761) (P 63))
(41 953 (83 821 93692918938277 11525552573833333858409352279851362309) (P 64))


Sep. 27, 2000.

Many errata.

Mr. Ukai's results,

(98 435 (197 27007334352841808914229) (C 87))
should be
(98 435 (197 712247311750896260221 27007334352841808914229) (P 66))

and Mr. Tomabechi announced,

(86 842 (173 639637074528877661423269547 1187484451618335944507743) (P 70))
should be
(86 842 (173 1187484451618335944507743 639637074528877661423269547) (P 70))
(This was already corrected in the main table.)

Dr. Morimoto announced,

(88 762 (2532926673024001 331009814490904682184041 560387592505828515827081 368789623321663051667268121) (P 27))
should be
(88 762 (2532926673024001 331009814490904682184041 560387592505828515827081 109513626719223673295491561) (P 27))
(sequence of factors)

(86 830 (431 39336793781810554258693 5273387144197256873311231 147596327565826398515920951515451) (P 41)
should be
(86 830 (431 39336793781810554258693 5273387144197256873311231 147596327565826398515920951515451) (P 41))
(missing right side parenthesis)


By Tetsuya Kobayashi ("Hamayan") (Sep. 26, 2000)

(75 494 (80799751 68779309149601 392761208800802394358607395809601) (P 54))
(75 959 (19297355532001 81791273235292012201 12611291281106164640176720501) (P 58))

(138 600 (65756206839162172752553) (P 100))
(138 603 (227011 636207279166009 9544504712825591812326089250169) (P 72))
(138 802 (829 96596827 27428592763552298327507413) (P 92))
(138 803 (139 277 5659 11037258881989 3407602897162789438408938913) (P 79))
(138 813 (2823330055441046937662287 36395614715028982740003694458139 121645589131294565658267443940871) (P 40))
(138 879 (1240002690181531280733535487911) (P 100))
(138 899 (691 967 10508748853 12276809037664351627295317297) (P 87))
(138 933 (5107 9168277997194576898108143) (P 103))

(94 258 (62944967950939 10460129367191438225092807 22226013122677619415686013773) (P 44))
(94 554 (1100554684092733 27706996206916674708324191) (P 86))
(94 692 (1223 405893 508375587403964447 12086971136226243654198671 555881782385859824534452554634662863839) (P 41))


Sep. 26, 2000.

By Yasunobu Torii (Sep. 25, 2000)

by SNFS

(63 609 (7967484196362325872251812662476163924079) (P 61))
(63 643 (36489282152512737218795515043456802680405747220121) (P 52))


By Andy Steward (September 25, 2000)

by ECMfile2 (Ubasic - KIDA/steward)

(47 191 (5730395978260105084320676489373993) (P 72))

By David A. Miller
(43 814 (8581493489 7313769598303849905224114867461) (P 82))

By Henrik Olsen
(49 792 (7 101985209258811186816237753581039728680386935579759) (P 71))
(49 914 (192548009052200878786140729885334557727) (P 87))
(49 954 (236663944289405323039485059392572086758274040867047) (P 75))

By Robert Backstrom
(43 315 (173 947 3846532981106046411215288649572310195626107) (P 58))
(47 188 (36110088525892641105803232160535249) (P 71))

By Sean Irvine
(43 215 (556045443520631724638374376010196604281) (P 60))
(43 267 (42829 38610177425107812887428333466287031) (P 63))
(43 561 (1291 11305532498399357 159486341376679618721229003027167060976345096349) (P 50))
(43 609 (947 10837 3623334811181549 25978872928813245496309213993468107746677268921) (P 48))
(43 654 (173 261085665463377777097 159127870436042011762792303690316454191699047) (P 52))
(47 451 (283 5077 69915227 434772234069289 489918164130310135838763197226110854135951) (P 52))
(47 692 (20399 28817470021 57398661023281785967927 1414410917836445347996507867835044298963353) (P 51))
(49 717 (1366121 485347199266401661625143 4740263378803011494779928747237465273) (P 54))


By Sean Irvine (Sep. 25, 2000)

(88 232 (89 26086321105814746857480705504937) (P 62))


By Masaki UKAI (Sep. 25, 2000)

(75 893 (151 5701 5381251 622403310022569555965238451) (C 79))

(86 460 (26579926826880696766261) (P 90))
(86 821 (9983861573477395199739055739) (C 95))
(86 842 (173 639637074528877661423269547 1187484451618335944507743) (P 70))

(94 458 (445091 3898838631769922862611559329) (C 90))
(94 559 (14759 54719657 14141654966196074059 131103283712550842880119 311509924486789012915560248275044767) (P 37))
(94 615 (659 84319 224014622207586961999 4464369043860443795752783) (C 76))
(94 645 (283 659 11657 7040475391546275883423783) (C 96))
(94 692 (1223 405893 508375587403964447 12086971136226243654198671) (C 80))
(94 723 (1693 1924570144319614917945315127) (C 102))
(94 777 (659 1223 47189 58657 13793722489452658911649213) (C 93))
(94 825 (941 140813 19707383 44051597 186791271767 2620875958915791896866727 9284688404364227026073210159) (P 48))
(94 981 (283 46061 226561351180048354761049961149) (P 102))

(98 201 (197 87312023 211284620328291044140733) (P 64))
(98 428 (234613 15306092632515958754335541) (C 80))
?(98 435 (197 27007334352841808914229) (C 87))
(98 454 (7 491 59642634773 13843200529308611729899) (P 76))
(98 558 (124446967 100211006612450902561 50142896320331473390527013 879399608106084591437201637551) (P 32))
(98 614 (16073 59798294641 226976359481929 12769429888017889217279311619) (P 60))
(98 781 (11180233 7137785411 1334287420021846764923 3865276096084117241835825637) (P 56))


By Takahiro Nohara (Sep. 24, 2000)

(69 320 (176779 99072911978071 59539984670934454114154190688542333146371) (P 51))
(69 334 (277 20149 409861 275670457 1180921431936585911538875409114578553813883) (P 49))
(69 480 (290228028294493924148623681684927) (P 86))


Sep. 24, 2000.

By Sean Irvine (Sep. 23, 2000)

(88 164 (89 1109487470158773166595562144835494661802177) (P 45))
(88 214 (25873 5211451501659993534944890241941294710457) (P 50))
(88 266 (597521 699073 1453675779206584151158369845648000649) (P 50))


Sep. 22, 2000.

By Sean Irvine (Sep. 22, 2000)

(88 194 (353 544721 52843291823865257450394378935326313079329) (P 43))
(88 412 (89 617 58585592258837689 187478237215289542697092916298775345817) (P 45))


By Tetsuya IZU (Sep. 20, 2000)

by snfs (Kida, Ver1.8)
(41 765 (2543 197621 3216287 172140127897751887259889120675571637437920427) (P 56))
(41 910 (30341 107049671174841727 7469265193098879592111519478222078891) (P 60))
(41 981 (83 5741 8398277 742825537 463216320920650614220072603471251156520943) (P 57))


By Andy Steward (September 12, 2000)

by ECMfile2 (Ubasic - KIDA/steward)

(43 657 (173 1979 3623353 1764990693343 802908550344321492171109802161711567) (P 59))
(43 722 (3307777109301953478433 13008012841465732286754247) (P 74))

(47 722 (703950487593353821122043426703 63367344460466786207475444483231473737) (P 64))
(47 891 (283 659 1465367 430492768483 20713284811117905311) (C 94))

(49 282 (197 17250059 9597905399785811252209951953677) (P 63))
(49 717 (1366121 485347199266401661625143) (C 91))

(55 998 (26885730712434544134039131) (C 95))

(61 116 (70639 3149112313 111060576033955721 349199329183950889991145581) (P 66))

by ECM and PPMPQS (Tomabechi)

(47 581 (283 5641 797309 36575401 52557073483 531334014235628578666822133 60425909817275165175689704567471) (P 39))


By Henrik Olsen
(49 601 (1096318308043173566491865636430796489125914723017) (P 69))
(49 711 (17740451 251170516549331 121162768710725239178281231382360701) (P 64))
(49 804 (197 2549 649053607108790496430378593777717075760952495856209) (P 66))

By Sean Irvine
(43 272 (7131379 233746561149053103370505649627515261324900513) (P 52))
(43 276 (7007969 15094916548284444459670475643815027) (P 62))
(43 581 (2362608934959067112359 1012493836230466195277529336132206753) (P 59))
(43 891 (82900607974677320235812940889 332269229521682988020653579326869332878042187) (P 51))
(47 326 (104999 78879371011438103 208690848895182491612361883691513604069253519) (P 50))
(47 385 (13362007 1300163489316743 4684523780055844465406459104003224420348247) (P 55))


Sep. 20, 2000.

By Igor Schein (Sep. 19, 2000)

(138 387 (139 26497 39607 20390162531909249333951611 14428165422215629352247638767) (P 50))
(138 830 (139 2347 31787473 1235093345134264864790029 2522169809725476765422683051 973201335524819299344154545169) (P 34))
(75 640 (151 8065930708384208451071569942351 430071577805369552514206960538597601) (P 44))
(86 300 (43 583799654870052513496704619 2722648914778214894173371493) (P 49))
(86 634 (2237 169642397 225390544055202632011173811 11217548867562000791685832049821) (P 49))


Sep. 19, 2000.

By Tetsuya Kobayashi ("Hamayan") (Sep. 18, 2000)

(75 143 (140938492767894574841088547720116451) (P 52))
(75 416 (216438451 13223231551 180219210454358537496996072685501) (P 55))
(75 674 (384751 17989172014883549429701 70147497123268282592982547235207851734151) (P 45))
(75 892 (151 397051 17222347715363145934687351 144885128867323562857141442180386869423901) (P 44))
(75 917 (151 144856801 37440232291645951275601 24120881585878608321304437458508451) (P 52))

(138 352 (277 559177 120227712181771 1785936163877701351131784442311) (P 60))
(138 374 (691 4441531 7095961 1241256158328676142113780135963) (P 67))
(138 380 (139 765128719 13609236834499 86354014265873999590547678287) (P 61))
(138 390 (91035013 148357974293569 214361504562066991184127151 39320276300005184650376268696067) (P 34))
(138 406 (139 1933 37537 21714802784242489 88425247136510462070987979) (P 63))
(138 407 (277 1761884975888531019477130567) (C 86))
(138 598 (82775477633939484441428640643) (P 94))
(138 764 (277 1657 25639270207842542365583205829) (P 93))
(138 791 (41904006431935535542557837223) (C 99))
(138 888 (14767 1041833004019441 268949526124334624119 2618160226214324911260157 27030309142559426242695847) (P 41))
(138 890 (139 829 1853479 3471031952079170210338843 1809574807313975587633285123) (P 67))
(138 898 (89594560411 8580745664075059 111241818022505850394660938845857 40063329948565082838583171384768549) (P 37))
(138 996 (3037 1171194372197660206322453563) (C 102))


By Satoshi Tomabechi (Sep. 18, 2000)

(100 295 (101 701 38501 355231443537596759748158016800423403062378201) (P 45))
(86 268 (25166574913 48160240882348820299277256017) (P 63))


By Masaki UKAI (Sep. 18, 2000)

(82 524 (821 3527 159737 912892963 16532735945678777789375669) (P 63))

(86 338 (947 169249 11707737292406816603834347 220188003503058223002995577091) (P 44))

(88 318 (89 3944368845451087087754895473) (P 71))

(98 294 (197 2549 83497 1791343 17675748987295732883411) (P 65))
(98 392 (9190702465860959299789387) (C 84))
(98 838 (3529 19699 86143 2323777 25250681 363275304830382925763506991 340270438959392712954675987097) (P 41))
(98 886 (4999 1997339 258425333425511359943221) (C 91))
(98 957 (197 2420993 13662999879966975925129) (C 95))


Sep. 18, 2000.

By Takahiro Nohara (Sep. 17, 2000)

with PPMPQS Ver2.70 by Tomabechi
(69 567 (139 243607099093 2274155191618341637 1086980313514291969492545946903) (P 60))

(69 304 (23100849207584643654906892801) (P 81))
(69 420 (6022321 2191646173 11622217861 19206221167804424781735660106757091589) (P 52))
(69 432 (1381 1657 630029893 1366421404286158772341236035041 254423626011726820788282120319957) (P 39))
(69 920 (139 436357 243819091 80994140574118473576020743 788196911779039339896942607) (P 62))
(69 988 (7039 26497 13581851809 2256429568418146060692673 667814634681236953738174263792103) (P 57))


Sep. 15, 2000.

By Sean Irvine (Sep. 14, 2000)

(75 143 (140938492767894574841088547720116451) (P 52))


Sep. 14, 2000.

News !

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


By Tetsuya IZU (Sep. 13, 2000)

by snfs (Kida, Ver1.8)
(41 657 (41 48961463 2147779463049415250172798887343312892393571677) (P 59))
(41 717 (1231 131447 1620734367792779281208112436643549870093) (P 67))
(41 722 (2806256178274236100929149822832824164771607) (P 72))
(41 893 (83 5167 2891704490131117 6531819467707574815952837894527208705249) (P 58))


By Andy Steward (September 12, 2000)

by ECM (Ubasic - KIDA/steward)

(41 974 (83 2953 5413 3592383507059554173535906684655432699) (P 74))

(53 119 (107 4365325442784952501 34806581017194680158522793119) (P 59))
(53 135 (697766504985676091265043 90325061235847260974258084041) (P 58))
(53 989 (309509719 568663819 137021641695462001 379568401656209023963) (C 101))
(53 998 (107 1061 33472720069 106898302101596031715901) (P 118))

(59 523 (1181 1771261228005476743 75043097494911440279357237) (P 111))

(61 119 (1709 9151 662339 13411339 254291076927534839596719877 970318876608092774226205349) (P 52))

by Pollard's p-1 (Ubasic - Steward)

(59 290 (122839 23854007810900680594705217) (C 113))

by PPMPQS (Tomabechi)

(49 290 (2647 711988858565027 120253906289907875872649332708769111023) (P 48))
(49 330 (7 197 10487 17053 1042819 505178003292118021359180909793733) (P 56))


By Henrik Olsen
(49 510 (3217243 301494630784859652746167677753330351703927) (P 66))
(49 906 (7253 25540833313451446151648386696331835583770907603) (P 74))
(49 998 (3529 72031 625743721 175359645014006313621704733431901113) (P 74))

By Jo Yeong Uk
(49 989 (1937156887 1167904756649 1419949720967 3040772786842166770935043803467305956011041) (P 50))

By Joe Leherbauer
(41 717 (1231 131447 1620734367792779281208112436643549870093) (P 67))
(41 722 (2806256178274236100929149822832824164771607) (P 72))
(41 728 (83 41939115595062427823777842482128120272980984146683) (P 63))
(41 760 (172320042605341671122971639240091732967223267444215801301) (P 59))
(47 282 (941 281539914909622748689785747814480687153) (P 72))

By Sean Irvine
(43 286 (2274271 10564908546156018061657228191086818672710288721) (P 51))
(43 442 (173 18061 7136302361 8532953941834494182612832540174737) (P 61))
(47 556 (12409 18049 60913 3873647 148713165677 70355240154139683820414180616323) (P 64))


Sep. 11, 2000.

By Tetsuya Kobayashi ("Hamayan") (Sep. 10, 2000)

(75 378 (751 20895451 590055451 40410505953461250188188158936112723651) (P 47))
(75 458 (151 1201 9528751 34718283601 10759002725419893832043691150497551) (P 50))
(75 558 (2038280569505949305044201 2383265433107044419577958101) (P 59))
(75 646 (151 5490879380423262257688301 489756777862288528469247115215920354101) (P 47))
(75 776 (151 157322198029951 4104246467120251 22777868967855433061323599737886485871901) (P 44))
(75 785 (348451 1259701 105664651 4435030252951 75587535933451058047394029772401) (P 52))

(138 387 (139 26497 39607 20390162531909249333951611) (C 78))
(138 536 (139 7242241 4875889141 649043119028929 9455492350062997501396651951) (P 59))
(138 621 (155502225981015847675741) (P 100))
(138 800 (2347 6073 784651914159143299 119886770661175660382347) (P 80))
(138 814 (139 1657 1659451 648508104275736267284696539) (C 90))
(138 830 (139 2347 31787473 1235093345134264864790029 2522169809725476765422683051) (C 64))
(138 890 (139 829 1853479 1809574807313975587633285123) (C 92))
(138 892 (139 9780715757509 15699576303060439 125681038076683201021691079097) (P 70))
(138 912 (4003 259383335654231917 122912613004119811200152462647) (P 81))
(138 965 (61422007 2583965959 112679537959 7799892388858526841484111) (P 79))


By Takahiro Nohara (Sep. 10, 2000)

(69 497 (691 393577 31550899767327675234880153 6759533266873872274268491841563159) (P 51))
(69 678 (139 3313 296563 1251109 51952704422540675473 2208289782376399576802178416864944008043) (P 49))
(69 702 (139 5521 978973 237535261 227047826724500503 2100723159573957653896823407) (P 61))
(69 721 (691 1238137 497144163169 344230303046050963 3983394262130490100801718727778869028102777) (P 45))
(69 818 (14629 1658761983209869 1708636298122309974793 7519097139048468074845644567744289) (P 54))
(69 876 (109297 7812119961092487243906433 8691491930963470290222821417923) (P 69))
(69 894 (1381 24151 147661 2751334153 217118452485056787949 13032630419920010619805289864322756828069859) (P 45))


By Masaki UKAI (Sep. 10, 2000)

(110 516 (3291638794523641 13882081174022263666630088561) (P 65))
(110 615 (205151 17293135091 2324421235125883833231919537389931) (P 63))

(75 640 (151 430071577805369552514206960538597601) (C 75))

(86 300 (43 583799654870052513496704619) (C 76))
(86 634 (2237 169642397 225390544055202632011173811) (C 80))
(86 657 (276849739 7140656036907397 249478788676424169558155917) (P 68))
(86 703 (2237 12745401963858097063 4325804779641790198624417) (P 73))
(86 728 (2789239 743780663522977640612753 8253463708591235320937117) (P 65))
(86 758 (22535415319 342592924766300077577) (P 91))

(98 791 (24006923704616698099786127) (C 97))
(98 430 (17142259 2030623752529 186442724260843489409573 178126034838362971681003401811) (P 39))
(98 435 (197 712247311750896260221) (C 88))


By Igor Schein (Sep. 07, 2000)

(138 250 (139 480598249 3669567375583 7553423112114742696965407993641) (P 52))
(138 510 (139 29836086680867239 375207121123610287 168717455196988389609753581958973) (P 51))


Sep. 07, 2000.

By Yasunobu Torii (Sep. 06, 2000)

by SNFS

(63 548 (36723143843623164192267030200473501994138353) (P 56))
(63 572 (3081276074791940795576456775726172168015434415261) (P 51))
(126 541 (1158060712056153539662760621158215840979) (P 60))


Sep. 06, 2000.

By Igor Schein (Sep. 04, 2000)

(98 692 (7 5828849293 266420756603 251517907954811 8563943192361557761222651230077) (P 52))
(98 745 (79670963 632963834435899 4976632069364453 10580697557182433776903227615200511955597) (P 43))
(92 494 (4049 987308213 254107244405130708328421 90325328995204321893860467614535428841) (P 45))
(138 140 (303187 1881907 4191589659463097244134437) (P 59))
(138 573 (139 93979 371083 1096625281 630469838049503303378407 16197185817494336494612012867722076171) (P 39))


Sep. 05, 2000.

By Takahiro Nohara (Sep. 04, 2000)

(69 342 (20287 52579 831156954856171 1392321108272931837227247600975939001830817) (P 46))
(69 440 (2196183119341 10193098299128792965312306609) (P 76))
(69 497 (691 393577 31550899767327675234880153) (C 85))
(69 554 (139 967 1053079 777270153489495727334921431621) (P 80))
(69 558 (829 372196294186882687237 16462779565511276130169843 22875850938436681984529611264591) (P 41))
(69 886 (277 2602003119568805559591151) (C 103))
(69 926 (2347 12007 32188903927 231270332901672414817 222203533442399155416955111 13380808324013541655370431267) (P 38))


Sep. 04, 2000.

By Tetsuya Kobayashi ("Hamayan") (Sep. 03, 2000)

(55 722 (19801 1192951 6251521 210653081 1012022333987465895468438027828651358001) (P 50))
(55 979 (4164354176071 1943836830144191951 1237144431348572608996286685820621181) (P 53))

(75 352 (11527651 149167196701 16152147614979490097922494551) (P 56))
(75 430 (1201 3506636694105685801 61137523663240388698111913964380760151) (P 46))

(92 246 (20149 147425857416101987469222941) (P 75))
(92 584 (1289 26497 83439894407488229271389) (P 92))
(92 638 (4139881054739364149 2893684042490008477199600407993) (P 75))
(92 801 (20333 433229 35367193 24445896268480168356428664961) (P 82))
(92 931 (882707801 13021055850523492570992397) (P 97))

(138 106 (277 102146464622724736872571 789660278032611478228531) (P 40))
(138 165 (139 11990026639 72886881866760301850076781) (P 60))
(138 210 (277 967 5388110381430813837595723) (P 73))
(138 522 (967 2109538243 632239818052271407010491) (P 84))
(138 532 (139 829 153457 8619855611023 47440267646335842390257492181139) (P 66))
(138 573 (139 93979 371083 1096625281 630469838049503303378407) (C 76))
(138 688 (139 30416719 22517760289 18039443133277311833539 726288180786926987317134049) (P 56))
(138 715 (829 78010711 410193118854535879001929) (P 92))
(138 850 (1230035736442442360467 2057683338323585608993057 2479857374605072621885393) (P 60))
(138 963 (7867 334426717 25741590423981437667577 2975289412187009111136744541 3125664824636471367630767860549) (P 39))


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