29w = { 2, 29, 299, 2999, 29999, 299999, 2999999, 29999999, 299999999, 2999999999, … }
3×100-1 = 2 =
definitely prime number 素数
3×101-1 = 29 =
definitely prime number 素数
3×103-1 = 2999 =
definitely prime number 素数
3×106-1 = 2999999 =
definitely prime number 素数
3×107-1 = 29999999 =
definitely prime number 素数
3×108-1 = 299999999 = 13 × 23076923
3×109-1 = 2999999999
<10> = 16937 × 177127
3×1010-1 = 29999999999
<11> = 2113 × 3767 × 3769
3×1011-1 = 299999999999
<12> = 7 × 683 × 953 × 65843
3×1012-1 = 2999999999999
<13> = 359 × 8356545961
<10>
3×1013-1 = 29999999999999
<14> = 19 × 1578947368421
<13>
3×1014-1 = 299999999999999
<15> = 13 × 107 × 33203 × 6495563
3×1015-1 = 2999999999999999
<16> = 83 × 103 × 227 × 1545895313
<10>
3×1016-1 = 29999999999999999
<17> = 100126307 × 299621557
3×1017-1 = 299999999999999999
<18> = 7 × 157 × 3257 × 6961 × 12040213
3×1018-1 = 2999999999999999999
<19> = 61 × 3145189 × 15636684431
<11>
3×1019-1 = 29999999999999999999
<20> =
definitely prime number 素数
3×1020-1 = 299999999999999999999
<21> = 13 × 23076923076923076923
<20>
3×1021-1 = 2999999999999999999999
<22> = 17 × 191 × 757 × 11059 × 110363948159
<12>
3×1022-1 = 29999999999999999999999
<23> = 167 × 311 × 337 × 1559 × 1099432012969
<13>
3×1023-1 = 299999999999999999999999
<24> = 7 × 50367072601
<11> × 850896044657
<12>
3×1024-1 = 2999999999999999999999999
<25> = 23 × 130434782608695652173913
<24>
3×1025-1 = 29999999999999999999999999
<26> = 23057 × 10833241 × 120104713180327
<15>
3×1026-1 = 299999999999999999999999999
<27> = 13 × 59 × 71 × 5508933654075692748407
<22>
3×1027-1 = 2999999999999999999999999999
<28> =
definitely prime number 素数
3×1028-1 = 29999999999999999999999999999
<29> = 47 × 638297872340425531914893617
<27>
3×1029-1 = 299999999999999999999999999999
<30> = 7
4 × 29 × 4308549598586795731663531
<25>
3×1030-1 = 2999999999999999999999999999999
<31> = 19441 × 45949 × 671304589 × 5002728961799
<13>
3×1031-1 = 29999999999999999999999999999999
<32> = 19 × 16187 × 546924986987
<12> × 178350167647709
<15>
3×1032-1 = 299999999999999999999999999999999
<33> = 13 × 146437799 × 157588568214707166713677
<24>
3×1033-1 = 2999999999999999999999999999999999
<34> = 113 × 149 × 34303 × 5194269029314101397578509
<25>
3×1034-1 = 29999999999999999999999999999999999
<35> = 46811 × 51047 × 12554606696004419459257547
<26>
3×1035-1 = 299999999999999999999999999999999999
<36> = 7 × 478631 × 3887236453
<10> × 23034640168453340899
<20>
3×1036-1 = 2999999999999999999999999999999999999
<37> = 193 × 2347451 × 6621668120347220058071014093
<28>
3×1037-1 = 29999999999999999999999999999999999999
<38> = 17
3 × 6106248727864848361489924689599023
<34>
3×1038-1 = 299999999999999999999999999999999999999
<39> = 13 × 2423 × 9524111876567510079685069367281501
<34>
3×1039-1 = 2999999999999999999999999999999999999999
<40> = 20474512935513701
<17> × 146523632061420300823699
<24>
3×1040-1 = 29999999999999999999999999999999999999999
<41> = 1316507 × 13940701 × 24313333578409
<14> × 67230905546473
<14>
3×1041-1 = 299999999999999999999999999999999999999999
<42> = 7 × 42857142857142857142857142857142857142857
<41>
3×1042-1 = 2999999999999999999999999999999999999999999
<43> = 9063097 × 331012677013166691253552731477992567
<36>
3×1043-1 = 29999999999999999999999999999999999999999999
<44> =
definitely prime number 素数
3×1044-1 = 299999999999999999999999999999999999999999999
<45> = 13 × 594332567 × 10550048513531
<14> × 3680390637464286032999
<22>
3×1045-1 = 2999999999999999999999999999999999999999999999
<46> = 499 × 6012024048096192384769539078156312625250501
<43>
3×1046-1 = 29999999999999999999999999999999999999999999999
<47> = 23 × 1304347826086956521739130434782608695652173913
<46>
3×1047-1 = 299999999999999999999999999999999999999999999999
<48> = 7 × 1404819661871
<13> × 30507220264887130087041437378722567
<35>
3×1048-1 = 2999999999999999999999999999999999999999999999999
<49> = 443 × 757 × 334127 × 26773803868940651228170563387195934487
<38>
3×1049-1 = 29999999999999999999999999999999999999999999999999
<50> = 19 × 103 × 1321 × 665293 × 17442737999925077569064711017059757319
<38>
3×1050-1 = 2
(9
)50<51> = 13
2 × 431 × 4118672689081398701245212042998942874009802441
<46>
3×1051-1 = 2
(9
)51<52> = 1066480229
<10> × 1356476046074293
<16> × 2073749608604567097036502567
<28>
3×1052-1 = 2
(9
)52<53> = 390621169 × 72645380763102632869
<20> × 1057200780089282053600259
<25>
3×1053-1 = 2
(9
)53<54> = 7 × 17 × 6132679193
<10> × 679927496140561
<15> × 604590671733065589907762577
<27>
3×1054-1 = 2
(9
)54<55> = 3217 × 1390016294869897
<16> × 670888430310272971761577811789656151
<36>
3×1055-1 = 2
(9
)55<56> =
definitely prime number 素数
3×1056-1 = 2
(9
)56<57> = 13 × 83 × 4331167543529607187088879
<25> × 64194057375964295426367330839
<29>
3×1057-1 = 2
(9
)57<58> = 29 × 1136834253520662461
<19> × 90996797063160225886700832599613151271
<38>
3×1058-1 = 2
(9
)58<59> = 6686869667
<10> × 52776674411
<11> × 626931419603
<12> × 135592709679897593746997509
<27>
3×1059-1 = 2
(9
)59<60> = 7 × 19531 × 641317 × 3421574356367246644163949706650392458891569799391
<49>
3×1060-1 = 2
(9
)60<61> = 743 × 808716498647
<12> × 1057972676861663008729
<22> × 4719127225971742808162711
<25>
3×1061-1 = 2
(9
)61<62> = 71 × 422535211267605633802816901408450704225352112676056338028169
<60>
3×1062-1 = 2
(9
)62<63> = 13 × 23076923076923076923076923076923076923076923076923076923076923
<62>
3×1063-1 = 2
(9
)63<64> = 1728967 × 7703231 × 1605051241
<10> × 140337174186780324552365181567296961903007
<42>
3×1064-1 = 2
(9
)64<65> = 277 × 108303249097472924187725631768953068592057761732851985559566787
<63>
3×1065-1 = 2
(9
)65<66> = 7 × 611704123343575338233723
<24> × 70061883223682835822554541457490468968459
<41>
3×1066-1 = 2
(9
)66<67> = 503 × 15763439 × 50162659539371570232061
<23> × 7542611608385988025064828485248227
<34>
3×1067-1 = 2
(9
)67<68> = 19 × 107 × 15920843 × 10644771958592162966987
<23> × 87072588295411188803975078531858983
<35>
3×1068-1 = 2
(9
)68<69> = 13 × 23 × 1003344481605351170568561872909698996655518394648829431438127090301
<67>
3×1069-1 = 2
(9
)69<70> = 17 × 36493 × 329860332209700670780056854383
<30> × 14659956248770104285450993620607013
<35>
3×1070-1 = 2
(9
)70<71> = 661 × 434132891 × 637935136493979035228233
<24> × 163877972349517148682713565578488753
<36>
3×1071-1 = 2
(9
)71<72> = 7
2 × 2371 × 2582222260477366821886915879806161182313498997237022181289217500581
<67>
3×1072-1 = 2
(9
)72<73> = 4188054211417
<13> × 4267778689730745828517
<22> × 167844482547367204773786131605885255691
<39>
3×1073-1 = 2
(9
)73<74> = 373 × 275676723385625913658191645377
<30> × 291750980771364417216161647598876663509219
<42>
3×1074-1 = 2
(9
)74<75> = 13 × 47 × 1069 × 367823 × 90855262284385309
<17> × 13744007092186107278415663200174774248999883123
<47>
3×1075-1 = 2
(9
)75<76> = 757 × 51378297061009
<14> × 1405847460733497973
<19> × 54866526792220496038143451174747976388551
<41>
3×1076-1 = 2
(9
)76<77> = 2402214527
<10> × 135999956282039
<15> × 91827063621559306927394843586328922240326571839259783
<53>
3×1077-1 = 2
(9
)77<78> = 7 × 23677 × 4275127 × 4369427 × 3621327289
<10> × 247502724582139745843
<21> × 108112340743472502401674533227
<30>
3×1078-1 = 2
(9
)78<79> = 61 × 1427 × 2713 × 5410076687
<10> × 4849502882804430492203
<22> × 484191331287271863114267578513481652669
<39>
3×1079-1 = 2
(9
)79<80> = 293611531788139
<15> × 102175823331241199704581398426177346644437517656619757456424151741
<66>
3×1080-1 = 2
(9
)80<81> = 13 × 109 × 502441 × 394460147 × 121000994263045222745790261071
<30> × 8828242660013348139969025855696091
<34>
3×1081-1 = 2
(9
)81<82> = 198347 × 580610829637
<12> × 546035880317951
<15> × 47707790680126762810965842706145250687293836957191
<50>
3×1082-1 = 2
(9
)82<83> = 3623 × 1179592811783
<13> × 81901814233106783
<17> × 85709168379882713447112804288382078260973732635217
<50>
3×1083-1 = 2
(9
)83<84> = 7 × 103 × 2917 × 2092564310751650241184817
<25> × 55817750862408931155328183
<26> × 1221232670144955999083128837
<28>
3×1084-1 = 2
(9
)84<85> = 59 × 3037200296737
<13> × 16741555597023462687292691535071815284183972598585064174887691519199853
<71>
3×1085-1 = 2
(9
)85<86> = 17 × 19 × 29 × 223 × 977 × 6563 × 14653 × 152859471551123480004843160977546975097365506330010478081244364258113
<69>
3×1086-1 = 2
(9
)86<87> = 13 × 17309375399
<11> × 1207510782643354586857133772644363
<34> × 1104092571873395520541318241400785866473479
<43>
3×1087-1 = 2
(9
)87<88> = 2741 × 964927 × 394211670918873961
<18> × 2877320783415929720655717276789004987147764455948869723172437
<61>
3×1088-1 = 2
(9
)88<89> = 1304488873
<10> × 3300924483140581825965792499050421
<34> × 6966991598609698357143166308824300493706869803
<46> (Robert Backstrom / GMP-ECM 5.1-beta for P34 x P46 /
May 2, 2003 2003 年 5 月 2 日)
3×1089-1 = 2
(9
)89<90> = 7 × 12594245972471028228269
<23> × 186182086789309759054543090955981
<33> × 18277346698490628671886518504139713
<35>
3×1090-1 = 2
(9
)90<91> = 23 × 416998450980192814055629
<24> × 312794405595744596969514780116162611260899355352176462266677835197
<66>
3×1091-1 = 2
(9
)91<92> = 1597 × 184553 × 446028257 × 14076488831
<11> × 16212071708719648632278491157629276678664053603353596806375780717
<65>
3×1092-1 = 2
(9
)92<93> = 13 × 2473 × 8354651 × 1116928758657913030746751251796032617863380560312387775178668625667297149218675001
<82>
3×1093-1 = 2
(9
)93<94> = 503699641 × 48503123144589502741752878729057
<32> × 122794781146491779173462117695893007175726748617613527
<54>
3×1094-1 = 2
(9
)94<95> = 97 × 380774519116859555009563691113510103
<36> × 812234892273730400146403072480506371926158526721772968889
<57>
3×1095-1 = 2
(9
)95<96> = 7 × 157 × 7544219843
<10> × 14044244326009837
<17> × 2576385525477167077559755888656850563188888467559516732456150855611
<67>
3×1096-1 = 2
(9
)96<97> = 71 × 225175496540201364974370054300058530191
<39> × 187647065404458407478575579255133377195945562460800825959
<57>
3×1097-1 = 2
(9
)97<98> = 83
2 × 1129 × 6823 × 23264344193
<11> × 18929164970412319489
<20> × 1283729395505707376279023867054907059411215130486873257049
<58>
3×1098-1 = 2
(9
)98<99> = 13 × 1019 × 187379 × 376657 × 2065995084482425229722350759373801066391
<40> × 155312880582011749094355956606205409844262829
<45> (Robert Backstrom / PPSIQS Ver 1.1 for P40 x P45 /
June 8, 2003 2003 年 6 月 8 日)
3×1099-1 = 2
(9
)99<100> = 345221647 × 477752776081611404646500077456166023
<36> × 18189468758616411279538180668857592713662364213329197479
<56> (Robert Backstrom / PPSIQS Ver 1.1 for P36 x P56 /
June 13, 2003 2003 年 6 月 13 日)
3×10100-1 = 2
(9
)100<101> = 30908839729
<11> × 52687875503
<11> × 18421621929042446518945642871526259144172571872058046358421612697832167819925377
<80>
3×10101-1 = 2
(9
)101<102> = 7 × 17 × 461 × 42703 × 128060437587372995319339355138356780636701102819820530493717889157422282840645351747588735187
<93>
3×10102-1 = 2
(9
)102<103> = 757 × 341667013 × 11599047429948021078058597960005614850022606973185675972655317149495105361550724254328327239
<92>
3×10103-1 = 2
(9
)103<104> = 19 × 60083 × 23917741750007011930592110720920008759435096557
<47> × 1098742369919843494185783706649927078558709517031491
<52> (Makoto Kamada / SNFS for P47 x P52 / 5:47:41:70)
3×10104-1 = 2
(9
)104<105> = 13 × 347 × 1321 × 133881109 × 2813505323
<10> × 15058978723753
<14> × 8380200882966911
<16> × 32926128941294964210169
<23> × 32165325017020156619259454561
<29>
3×10105-1 = 2
(9
)105<106> = 69233 ×
43331937082027356896277786604653850042609738130660234281339823494576285875232909161815897043317493103<101>
3×10106-1 = 2
(9
)106<107> = 218279 ×
137438782475638975806192991538352292249827056198718154288777207152314240032252300954283279655853288681<102>
3×10107-1 = 2
(9
)107<108> = 7 × 35491 × 132967 × 3286888271596093
<16> × 2762969980683717258321223144209234268699368337958266176306842668501370570391151817
<82>
3×10108-1 = 2
(9
)108<109> = 479 × 1537022713
<10> × 12042349012118749379843
<23> × 5580815161537522052816552016371
<31> × 60631261945090711190778038575214536541054929
<44>
3×10109-1 = 2
(9
)109<110> = 941 × 60259 × 78121 × 524086391 × 14770997282202389
<17> × 26506062415929309987997152493
<29> × 33005323977166274796073777418225748488133943
<44>
3×10110-1 = 2
(9
)110<111> = 13 ×
23076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923<110>
3×10111-1 = 2
(9
)111<112> = 966767341958861
<15> × 3103125095145859264337050293405093023943285127966189415280642637135368146774978576169338417355259
<97>
3×10112-1 = 2
(9
)112<113> = 23 × 181 × 3407 × 127103 × 3483791461
<10> × 954027040968047
<15> × 5006959449134196242766265868072792925075855906976643628238419170429812879439
<76>
3×10113-1 = 2
(9
)113<114> = 7
2 × 29 × 8139497 × 183196997235114666313664862887412748867877758421
<48> × 141583048280838478129901762617470802340141205501351431287
<57> (Sander Hoogendoorn / SNFS for P48 x P57 /
June 8, 2004 2004 年 6 月 8 日)
3×10114-1 = 2
(9
)114<115> = 171141301 × 5078181337
<10> × 3451900116240059527310349962515641788338540306292431489892874508205404626512683628520178446569627
<97>
3×10115-1 = 2
(9
)115<116> = 66935581832507131
<17> × 448192115145409256752005959887688729242511151091393953380282171310853902822633424231824418287457229
<99>
3×10116-1 = 2
(9
)116<117> = 13 × 191 × 419 × 342803 × 3080389672652381470662675187786673261869
<40> × 273073929335371915922432805053316071687914686044309883829457031841
<66> (Sander Hoogendoorn / for P40 x P66 /
June 8, 2004 2004 年 6 月 8 日)
3×10117-1 = 2
(9
)117<118> = 17 × 103 × 7717 × 1343893 × 698810987349616407838127758561787
<33> × 236408012483724037920438356017353423704940485863994051049626928720839267
<72> (Sander Hoogendoorn / for P33 x P72)
3×10118-1 = 2
(9
)118<119> = 1801 × 2322347 × 269136729617782632743
<21> × 525337354976588234359540934329
<30> × 50730503927128935534261432720820845779278829698082773940411
<59>
3×10119-1 = 2
(9
)119<120> = 7 × 7141775796359
<13> ×
6000908468590146007802970302085578213299657647019234436854511092567500093029441038440754743913961970037423<106>
3×10120-1 = 2
(9
)120<121> = 47 × 107 × 587 × 44209021499
<11> × 11890818970927053203
<20> × 2047296729179266187110579273833644931841
<40> × 944274051192262206631103925845322418206838969
<45>
3×10121-1 = 2
(9
)121<122> = 19 × 695084724889
<12> ×
2271589796011125260933021182971065840770325771072812443357936760347860632353214061224348430869129003298879789<109>
3×10122-1 = 2
(9
)122<123> = 13 × 2294796717664213509541276266917758467689777187014509
<52> × 10056194912293669804719011098323636255061719884507348567986171070655047
<71> (Makoto Kamada / GGNFS-0.70.0 for P52 x P71 / 3.39 hours)
3×10123-1 = 2
(9
)123<124> = 2990366970937067399
<19> ×
1003221353484891513387954898308810381727983558088177158306275171844453418150696067538783658365482703827401<106>
3×10124-1 = 2
(9
)124<125> = 2602864396977816164601828457
<28> × 11525763706642949500110430345615582532053120160077139973457388941551304686760716557918497750074407
<98>
3×10125-1 = 2
(9
)125<126> = 7 × 3599650081
<10> × 31612646761
<11> × 3876544332029444008036492867365402990466431683
<46> × 97153246083586305759374376504412500632762391535023918322219
<59> (Sander Hoogendoorn / GGNFS for P46 x P59)
3×10126-1 = 2
(9
)126<127> = 179 × 2927 × 292983186719575321
<18> × 5647443464815144203568297
<25> × 3460596075084905650466669068797064557997911238583417117155774526018030889091019
<79>
3×10127-1 = 2
(9
)127<128> = 148738622029916094823
<21> ×
201696100115584238393124824460099143584753960141821190136295028657532443918821279751573958245772262039795113<108>
3×10128-1 = 2
(9
)128<129> = 13
2 × 227 × 541 × 601 × 148983787999561869461523139665361324139
<39> × 161435091255666683067612614137458155297916999164385294636452087869504653287195627
<81> (Makoto Kamada / GGNFS-0.77.1 for P39 x P81 / 3.83 hours on Pentium 4 3.06GHz, Windows XP and Cygwin /
May 5, 2005 2005 年 5 月 5 日)
3×10129-1 = 2
(9
)129<130> = 757 × 3862845783794364415817
<22> × 4154462659947867699343214598881767
<34> × 246946653468267095788453656414425393826920686199248335419564218437793213
<72> (Makoto Kamada / GMP-ECM 5.0.3 B1=400000, sigma=2577217194 for P34 x P72)
3×10130-1 = 2
(9
)130<131> = 176410843726584853883407743387462128062837
<42> × 170057573368314684049302929168844425493413216950195208787238174395441995530703625941928227
<90> (Sander Hoogendoorn / GGNFS for P42 x P90)
3×10131-1 = 2
(9
)131<132> = 7 × 71 × 2281 × 151813 × 977057 × 18215699449
<11> × 168678924343
<12> × 85892292823905156190531
<23> × 546893930756919181751220197647
<30> × 12360804653411226627683395388566345189673
<41>
3×10132-1 = 2
(9
)132<133> = 1823 × 751446263 ×
2189962393226079924195568697698785877427193914407518505622793919738599146505349576421961755644686047247091066773551414951<121>
3×10133-1 = 2
(9
)133<134> = 17 × 277 × 947 × 63911747 × 284800447 × 1908595079
<10> × 308272668350011
<15> × 628163081468531196471678625762635108684284589253543477082381703073219111516811871677753
<87>
3×10134-1 = 2
(9
)134<135> = 13 × 23 × 131 × 50237491883
<11> × 74611295693503631
<17> × 6270336254236758322137851221
<28> × 325878274972959912313450677639337986912758521683301002776370480401214035687
<75>
3×10135-1 = 2
(9
)135<136> = 9661029311
<10> × 2737810280944238993239874575304072948881248252017519
<52> × 113421269769628317461074177992926273808105712904085317777627767022874178511
<75> (Makoto Kamada / GGNFS-0.77.1 for P52 x P75 / 5.63 hours on Pentium 4 3.06GHz, Windows XP and Cygwin /
May 6, 2005 2005 年 5 月 6 日)
3×10136-1 = 2
(9
)136<137> = 835817364193303896837129099287216945204282453961493
<51> × 35893008790209509851297098644911189995904355230294598135551859369093208362424725320643
<86> (Anton Korobeynikov / GGNFS-0.72.10 for P51 x P86 / 16.41 hours)
3×10137-1 = 2
(9
)137<138> = 7 × 487 × 1050233 × 6621524008283
<13> × 42100336899241
<14> ×
300583449314555435059595288664414400507392811785133653676322034725504693698971499976681413695127808189<102>
3×10138-1 = 2
(9
)138<139> = 61 × 83 × 2617 × 58211 × 123215977 × 18301389014578223
<17> × 1879512152331664267523
<22> × 413385011612455959639469
<24> × 1643961787701703715784696623
<28> × 1350398306002428325645695676549
<31>
3×10139-1 = 2
(9
)139<140> = 19 × 233 × 18257 × 3189010880100257960332198816490123216053698925938885318275266097
<64> × 116392853688224551320628030044644926368910927741779050815872100922653
<69> (Makoto Kamada / GGNFS-0.77.1 for P64 x P69 / 11.04 hours on Pentium 4 3.06GHz, Windows XP and Cygwin /
May 6, 2005 2005 年 5 月 6 日)
3×10140-1 = 2
(9
)140<141> = 13 × 1043951 × 26883947 × 182071650990950202615387530626934743348640561028796729
<54> × 4516088321889703271038563016128691273952825632884219310105789502309547671
<73> (Makoto Kamada / GGNFS-0.77.1 for P54 x P73 / 8.19 hours on Pentium 4 3.06GHz, Windows XP and Cygwin /
May 10, 2005 2005 年 5 月 10 日)
3×10141-1 = 2
(9
)141<142> = 29 × 12049787588762983115267162180707134919286653
<44> × 8585070491909711967989582026822386992430936673986287924871109410890430123873686351241585281361127
<97> (Makoto Kamada / GGNFS-0.77.1 for P44 x P97 / 7.74 hours on Pentium 4 3.06GHz, Windows XP and Cygwin /
May 10, 2005 2005 年 5 月 10 日)
3×10142-1 = 2
(9
)142<143> = 59 × 1667 × 93717112244395171896790558091
<29> ×
3254728338396397350299417788498932335144337966986383779784082085195537945799463747173648638531505035959656813<109> (Tetsuya Kobayashi / GMP-ECM 5.0.3 for P29 x P109 /
February 24, 2004 2004 年 2 月 24 日)
3×10143-1 = 2
(9
)143<144> = 7 × 368161095989
<12> × 2773039137463081
<16> × 24566776282235900088908433900766498349491
<41> × 1708760320079077756989239124726576953642075628982585485036155402183550090703
<76> (Makoto Kamada / GGNFS-0.77.1 for P41 x P76 / 14.68 hours on Pentium 4 3.06GHz, Windows XP and Cygwin /
May 11, 2005 2005 年 5 月 11 日)
3×10144-1 = 2
(9
)144<145> = 114960971 × 2213287753
<10> × 108090137887270909297090797793
<30> × 109080439628348269202774046214310086366771298172396864071466868126105645656536199141927505676107861
<99> (Tetsuya Kobayashi / GMP-ECM 5.0.3 B1=1000000 for P30 x P99 /
August 14, 2004 2004 年 8 月 14 日)
3×10145-1 = 2
(9
)145<146> = 113 × 1051 × 115336553 × 2287852509381529362215874023304871802874572090778188945277943
<61> × 957293486672798203907184531262070219175708798167529171237812739812913587
<72> (Makoto Kamada / GGNFS-0.77.1 for P61 x P72 / 11.34 hours on Pentium 4 3.06GHz, Windows XP and Cygwin /
May 12, 2005 2005 年 5 月 12 日)
3×10146-1 = 2
(9
)146<147> = 13 × 493573 × 18325201302275702459091151740961
<32> ×
2551395316378933371196249242159398075810419408174368073290161677105829014102810175513071204192402345218026591<109> (Makoto Kamada / GMP-ECM 5.0.3 B1=450000, sigma=3350150933 for P32 x P109)
3×10147-1 = 2
(9
)147<148> = 2515313 × 4380884647177105247767
<22> ×
272249694675382115672371457148969342652091706433155665804841695191724637927901103092611354783625552190520929023861944169<120>
3×10148-1 = 2
(9
)148<149> = 5698826293
<10> × 120232877212186884433
<21> × 123074961607917110161534951484159374642729
<42> × 355748343355447265512908734948080985968709118990801171190063642693710339565499
<78> (Makoto Kamada / GGNFS-0.77.1 for P42 x P78 / 28.55 hours on Pentium 4 3.06GHz, Windows XP and Cygwin /
May 14, 2005 2005 年 5 月 14 日)
3×10149-1 = 2
(9
)149<150> = 7 × 17 × 1249 × 3803 × 29983 × 47363 × 59021 × 25970585924786847027298660631
<29> × 243827637273805306729808414600327800876310711471007497576365833251559647434564618561961895558734917
<99> (Tetsuya Kobayashi / GMP-ECM 5.0.3 for P29 x P99 /
February 24, 2004 2004 年 2 月 24 日)
3×10150-1 = 2
(9
)150<151> = 383399 × 23802994718148901
<17> ×
328729499631075215103914984155771879133819146534222325019886723795831518647675685691088397349572871406691314755646056939225744501<129>
3×10151-1 = 2
(9
)151<152> = 103 × 15607 × 35159 × 14094323 × 803919452098002873794823857201688324440053056001
<48> × 46845872075351073831628759072931045137614880228706167557837224075618406020863534117667
<86> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 for P48 x P86 / 32.36 hours on Pentium 4 2.4GHz, Windows XP and Cygwin /
June 15, 2006 2006 年 6 月 15 日)
3×10152-1 = 2
(9
)152<153> = 13 × 263 ×
87744954665106756361509213220239836209417958467388125182801988885639075753144194208832992102954080140391927464170810178414741152383737935068733547821<149>
3×10153-1 = 2
(9
)153<154> = 72019 × 1472927109551
<13> × 6437899768974245773
<19> × 45425367911692522245626027985214885364243
<41> × 96705293648696981037155654696825961344230797647139452351613239823428072265389
<77> (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=4238945311 for P41 x P77 /
September 6, 2005 2005 年 9 月 6 日)
3×10154-1 = 2
(9
)154<155> = 169973521 × 3541566709633
<13> × 62282513633822346544465252554897044469175211
<44> × 800162926125406274759982565017119197917086497848155175255046781462749015168218472947165613
<90> (Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 for P44 x P90 / 63.81 hours on Pentium 4 3.20 GHz, 1 Gig RAM, Windows XP and Cygwin /
March 17, 2007 2007 年 3 月 17 日)
3×10155-1 = 2
(9
)155<156> = 7
2 × 844643 × 159010443754010418818537
<24> × 5423853441107577188852485479594908047413233
<43> × 8404625993321570476494919510450078586561494231252473102406403901939727050282602317
<82> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P43 x P82 / 27.74 hours on Cygwin on AMD XP 2700+ /
March 16, 2007 2007 年 3 月 16 日)
3×10156-1 = 2
(9
)156<157> = 23
2 × 757 × 37958325803
<11> × 34508927160252119290871470429799344288040408510935452205656946628557
<68> × 5719146168209700929932117892283471025039070385347664045593119483067546173
<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P68 x P73 / 29.42 hours on Cygwin on AMD XP 2700+ /
April 14, 2007 2007 年 4 月 14 日)
3×10157-1 = 2
(9
)157<158> = 19 × 409 × 8669 × 1478382377561711
<16> ×
301223302549621999298659687439059017007707324952067882550054765883129452999327273835105189723866856348822058327855755819455471102120191<135>
3×10158-1 = 2
(9
)158<159> = 13 × 8713 × 5289083 × 695325459814498871
<18> × 8252373899553049676093269
<25> × 998030902239641757418958240703001
<33> × 87441739575224379973751656500118777910978931283986448286477478905281163
<71> (Anton Korobeynikov / GGNFS-0.77.1 gnfs for P33 x P71 / 13.78 hours /
May 27, 2005 2005 年 5 月 27 日)
3×10159-1 = 2
(9
)159<160> = 1321 × 6967 × 398760584767619777
<18> × 1365996837467415111026906770750469
<34> ×
598426350404332450433128876484310209991358869759713755798077815328602741567697247226824883321819832989<102> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, sigma=2625841172 for P34 x P102 /
July 11, 2007 2007 年 7 月 11 日)
3×10160-1 = 2
(9
)160<161> = 3119 × 62171 × 716003 × 80479894854409
<14> × 22773127470380768369771978355584433053642892841637684786821
<59> × 117894381311324651726376382743763178993218466198694259251340381195966953253
<75> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.28 for P59 x P75 /
November 2, 2007 2007 年 11 月 2 日)
3×10161-1 = 2
(9
)161<162> = 7 × 445307 × 12654241 × 4753427389819
<13> ×
1600002742222315874207495930489789942851093204466890859980649901635579490615534553038031986322050491140769704228139579001336217079639569<136>
3×10162-1 = 2
(9
)162<163> = 1586308304691323221318531843777
<31> × 152512406662190891155427973892329217
<36> × 12400194079641198397538641885769926694273799859212033454948583982801438301040530455353496340235711
<98> (Makoto Kamada / GMP-ECM 6.0 B1=36000000, sigma=757237952 for P31 /
March 19, 2005 2005 年 3 月 19 日) (Wataru Sakai / GMP-ECM 6.0.1 B1=110000000, sigma=1534915970 for P36 x P98 /
January 4, 2006 2006 年 1 月 4 日)
3×10163-1 = 2
(9
)163<164> = 997 × 2287 × 45747879641691574163746483574403221719068934066339
<50> ×
287600053136766851692762111657822054428122201049566171614253119368688303514147608918518033049860541686054719<108> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P50 x P108 / 63.42 hours on Cygwin on AMD 64 3200+ /
July 24, 2007 2007 年 7 月 24 日)
3×10164-1 = 2
(9
)164<165> = 13 × 2591 × 20864331285956384714363476632186247632145067881
<47> × 16745773198975668201316866017478902963614694091371
<50> × 25491818321127692702503378138106307806982680946323585329451086103
<65> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 for P47 x P50 x P65 / 125.82 hours on Pentium 4 2.4GHz, Windows XP and Cygwin /
July 7, 2007 2007 年 7 月 7 日)
3×10165-1 = 2
(9
)165<166> = 17 × 563 × 10366352216620195513339
<23> × 32537822232223537739373298666992795881162109492993066147359
<59> × 929286216648341931114487283109312466413415118752186358498797622230367374713700369
<81> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.33 for P59 x P81 /
February 6, 2008 2008 年 2 月 6 日)
3×10166-1 = 2
(9
)166<167> = 47 × 71 × 2667289 × 10991159 × 627960539 × 2137781721901653563
<19> × 10345389693582740479529989859541374220406006881752101849
<56> × 22080500640751102476087504432625828948573909939464280318314247588489
<68> (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=3068145495 for P56 x P68 /
September 14, 2005 2005 年 9 月 14 日)
3×10167-1 = 2
(9
)167<168> = 7 × 7643 × 5308447 × 22854213927330216399615920416772214007
<38> × 39688758719895871031552328771144713882109670630545445702193
<59> × 1164549798963657623144995222566231913164712125722393092919267
<61> (Wataru Sakai / GMP-ECM 6.0.1 B1=110000000, sigma=2117868705 for P38 /
January 4, 2006 2006 年 1 月 4 日) (Sinkiti Sibata / GGNFS-0.77.1 gnfs for P59 x P61 / 127.93 hours on Pentium 4 2.4GHz, Windows XP and Cygwin /
March 9, 2006 2006 年 3 月 9 日)
3×10168-1 = 2
(9
)168<169> = 1812361 × 130589868517
<12> × 5316091494767
<13> × 175320276174094299158123
<24> × 14218271534104519162365193
<26> × 7346438825607067443755539899769423966309
<40> × 130202342717147930171665152085069493289786784935131
<51> (Makoto Kamada / msieve 0.87 for P40 x P51 / 3.4 hours /
December 11, 2004 2004 年 12 月 11 日)
3×10169-1 = 2
(9
)169<170> = 29 × 257 × 1187 × 893281 × 162352619114966156197
<21> × 2228251805235709353313536175233325312147783871786905403
<55> × 10493678433883386533453073734793889071910451026636427224419520005990497132630462879
<83> (Sinkiti Sibata / Msieve 1.40 snfs for P55 x P83 / 59.94 hours /
July 13, 2009 2009 年 7 月 13 日)
3×10170-1 = 2
(9
)170<171> = 13 × 5783 × 173013747441272949252140271307882198468644836377812061
<54> ×
23064502808650629916626080541133445738284945384523360813873885767965239712427790623664167124028559969692067948321<113> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P54 x P113 / 83.81 hours on Cygwin on AMD 64 3200+ /
May 26, 2007 2007 年 5 月 26 日)
3×10171-1 = 2
(9
)171<172> = 727 × 111443 × 75309234594877
<14> × 1030775741943931673
<19> × 203808353944020828211710001231914168129351013132544641
<54> × 2340451493876462621104078626827590279589654809102234493298958220750325105388919
<79> (Sander Hoogendoorn / GNFS & msieve with the factmsieve.py (python script) for P54 x P79 / 25.57 hours on Intel Core 2 Duo 2,2 GHz using 2 cores on Windows 2003 /
January 27, 2010 2010 年 1 月 27 日)
3×10172-1 = 2
(9
)172<173> = 38122987748499595028686163894145203
<35> × 144305979336767394731126911499701100363397016943877899
<54> × 5453182077435764716694269821536175903777022858744153878594451246373586312292773813167
<85> (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=111443754 for P35 /
September 1, 2005 2005 年 9 月 1 日) (Wataru Sakai / Msieve for P54 x P85 / 3.49 hours /
January 13, 2010 2010 年 1 月 13 日)
3×10173-1 = 2
(9
)173<174> = 7 × 107 × 157 × 3013176114760906824959
<22> × 3438554741560059188437
<22> × 30644010457996651884427900089832310981
<38> × 1965123061305630337817335362597030221689
<40> × 4088876295547466384808084321913583821345407444169
<49> (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=1547437923 for P38, Msieve 1.01 for P40 x P49 /
August 30, 2005 2005 年 8 月 30 日)
3×10174-1 = 2
(9
)174<175> = 166087909788096950834522423
<27> × 8463645713858598762260867888847965297310229007204191808496082691
<64> × 2134154023417552716331724005141659076217090584552967921447661573925237208250265541843
<85> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P64 x P85 / 47.56 hours on Core 2 Quad Q6700 /
February 27, 2010 2010 年 2 月 27 日)
3×10175-1 = 2
(9
)175<176> = 19 × 1358197 × 127908438358629022538945818383105074917390387700273693347951544125819
<69> ×
9088782074048181389749646028623925455114377328452874707792183747630337777668429784177679834126974147<100> (matsui / GGNFS-0.77.1-20060513-prescott snfs for P69 x P100 / 170.28 hours /
May 27, 2008 2008 年 5 月 27 日)
3×10176-1 = 2
(9
)176<177> = 13 × 58742557 × 57269690852172211230698590365937264946108274851869337123769319131139186850180629
<80> × 6859622507929484284606361644307751405797667931674866097064318293703456089128520372145691
<88> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P80 x P88 /
March 2, 2010 2010 年 3 月 2 日)
3×10177-1 = 2
(9
)177<178> = 311 × 116471 × 1402627451282133493
<19> × 6212798730210408050381624569671817339
<37> ×
9504153515554352849906622482432664871708559936002497935758971157239414990468164783447373021653755199704052528655977<115> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=6359294935 for P37 x P115 /
February 21, 2010 2010 年 2 月 21 日)
3×10178-1 = 2
(9
)178<179> = 23 × 28871 × 950809 × 3670957 × 6486841 × 20123971618573
<14> × 15822535005390769197619578154346714884187993498909473
<53> × 6266658034440589293040361904117425689899050899063420689751835198468171995771249785353879
<88> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P53 x P88 /
March 4, 2010 2010 年 3 月 4 日)
3×10179-1 = 2
(9
)179<180> = 7 × 83 × 269 × 8731 × 81853 × 116981 × 341557 × 12603850771
<11> × 40741126949
<11> × 135924365039
<12> × 65229101266939367735801851025243606155752420471073669310383
<59> × 14765247618055126790247356701740302955486828755600519733418471207
<65> (matsui / GGNFS-0.77.1-20060513-pentium4 gnfs for P59 x P65 /
February 16, 2008 2008 年 2 月 16 日)
3×10180-1 = 2
(9
)180<181> = 572624573272440906246891681503
<30> × 18430490162974811893591210694438204036249222668991102941368207733
<65> × 284259107445064507092201327543954373371556380517472751352150669366327959473078731952701
<87> (Makoto Kamada / GMP-ECM 6.0 B1=16000000, sigma=2663771591 for P30 /
March 20, 2005 2005 年 3 月 20 日) (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P65 x P87 /
March 4, 2010 2010 年 3 月 4 日)
3×10181-1 = 2
(9
)181<182> = 17 × 149 × 67651 ×
175070045379264539259437251461445348065890039216448801818566940450735222120090896600987641321136218833541784373309607529547899173169269046904608994971714020303094918024122353<174>
3×10182-1 = 2
(9
)182<183> = 13 × 1307 × 3253 × 15313 × 30483181 × 712236001 × 217790685050910667548997
<24> × 18282126687045549663745432739326772351099604880474511
<53> × 4100225547077532938162524694413091222368841653737008072666860688562574061951363
<79> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P53 x P79 /
March 8, 2010 2010 年 3 月 8 日)
3×10183-1 = 2
(9
)183<184> = 757 × 705259 × 94685971491169408238495197
<26> ×
59345951695499727131645089060192058135909213873136735226382733194452511684809704681156559640467203767085254024562482893630526915384657525961066917309<149> (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=517744189 for P26 x P149 /
July 21, 2005 2005 年 7 月 21 日)
3×10184-1 = 2
(9
)184<185> = 10073641022189321360228001328707180659381468877455557544719139
<62> ×
2978069194040036330503581914737461793403041082476154833888528931755723356899703483852214198475678536123147506448805613562741<124> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs for P62 x P124 / 343.63 hours on Core 2 Quad Q6600 /
September 12, 2007 2007 年 9 月 12 日)
3×10185-1 = 2
(9
)185<186> = 7 × 103 × 5419 × 40859069 × 34405086211
<11> ×
54620506344778751196212174083932539853598979159171505198079512296438983419526842906298190446596589467895874271186208542033563390832223006082042424056219876319739<161>
3×10186-1 = 2
(9
)186<187> = 1000926126622857454738657
<25> × 169578631674993232722608070359
<30> × 5038740629385387262999058978219
<31> ×
3507729531114303162480919388024654186192017726789378826407554907313223454226891369837005953138455530667<103> (Makoto Kamada / GMP-ECM 5.0.3 B1=400000, sigma=2779326909 for P31) (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=1358866576 for P30 x P103 /
July 30, 2005 2005 年 7 月 30 日)
3×10187-1 = 2
(9
)187<188> = 337638313967807182936900258849
<30> × 99433004049017708218656527004744377
<35> × 47527930809248160978423930812756482163
<38> × 18801394593718690635972065355070083787495002798358052698294076860191499763907183853901
<86> (Makoto Kamada / GMP-ECM 6.0 B1=11000000, sigma=588872100 for P35 /
March 21, 2005 2005 年 3 月 21 日) (Makoto Kamada / GMP-ECM 6.0 B1=13000000, sigma=2468554643 for P30 /
March 21, 2005 2005 年 3 月 21 日) (anonymous / GMP-ECM B1=1000000, sigma=2711386167 for P38 x P86 /
January 27, 2007 2007 年 1 月 27 日)
3×10188-1 = 2
(9
)188<189> = 13 × 109 × 167 × 769 × 25375234751
<11> × 5153248863097
<13> × 3749089470469489319
<19> ×
3362726945702192537278270379287745910169270402907379473520095703855904159132288646009078852590438801004689733992343446479621750210601907473<139>
3×10189-1 = 2
(9
)189<190> = 467 × 53231 ×
120681235922282410424252068989278960590214915983533769445820098792073350698826821501228716003542718361734522440414343737249273167086349073612617335851494820140105283114760171990070187<183>
3×10190-1 = 2
(9
)190<191> = 97 × 29924824213
<11> × 247984694771318430568948981693
<30> × 7668447060104434870881489582121
<31> × 512358733922895524489343752888689
<33> × 10607461577425281731753905244766737614406396259890391295260540539167282031764330723127
<86> (Makoto Kamada / GMP-ECM 6.0 B1=4000000, sigma=2904675407 for P33 /
March 28, 2005 2005 年 3 月 28 日) (Makoto Kamada / GMP-ECM 6.0 B1=4000000, sigma=3586049989 for P31 /
March 28, 2005 2005 年 3 月 28 日) (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=2685518144 for P30 x P86 /
September 12, 2005 2005 年 9 月 12 日)
3×10191-1 = 2
(9
)191<192> = 7 × 359 × 1301 × 281993 × 2790288133
<10> × 23268995217971929
<17> × 13515484787040813847
<20> × 9986328167407533917958306774605218725739829
<43> × 37132056081125955472819112147087747804782221939881071336471506401331809870109280710565214621
<92> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=11000000, sigma=7007836905 for P43 x P92 /
March 6, 2010 2010 年 3 月 6 日)
3×10192-1 = 2
(9
)192<193> = 179209 × 592154051319954517820401873
<27> × 294029254151558642128613500432031
<33> × 9740471141873076715269094836964843996395634689724625712596839367
<64> × 9870888065300008002666195086781466583752845796759751444217049391
<64> (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=53705871 for P33) (Jo Yeong Uk / GGNFS/Msieve v1.39 gnfs for P64(9740...) x P64(9870...) /
March 1, 2010 2010 年 3 月 1 日)
3×10193-1 = 2
(9
)193<194> = 19 × 1882472591
<10> ×
838762474401972650861798055481516772627977863833371814325102897830745962547163252918274564975563762894145974622026976657878272172382120181983904157118943370077801881231942155301549131<183>
3×10194-1 = 2
(9
)194<195> = 13 × 1744151 × 2118866528953
<13> ×
6244392889110125089580580780440747420845559279279194303632447024695108721938978055392965370236240048699212656733908110604978637693204515295186661381098719191277421837118682341<175>
3×10195-1 = 2
(9
)195<196> = 12377 × 26641 × 4242465959
<10> × 2549430086848235938069023022334565304647820249008607
<52> ×
841189548672696590223631459471770406069927514620180520789383724252020064883602521044531561533541571410124284972274340308388639<126> (Justin Card / ggnfs/msieve for P52 x P126 /
April 7, 2010 2010 年 4 月 7 日)
3×10196-1 = 2
(9
)196<197> = 122344767534061284667205826233542620221024729103782351
<54> × 349916959335497159053279727421119255555113601555011417
<54> × 700762515289784210874039143325825539548489780330736974377987653994531387998577206825482297
<90> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs for P54(1223...) x P54(3499...) x P90 / 516.20 hours on Core 2 Quad Q6700 /
October 3, 2008 2008 年 10 月 3 日)
3×10197-1 = 2
(9
)197<198> = 7
2 × 17 × 29 × 310459974207253356569798917
<27> × 68053976324751545794284630967427895603244001434280187721763258182322358947
<74> × 587785857793798607044597286642006113609085738682247451587060917433885743162793893936656523493
<93> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P74 x P93 /
April 6, 2010 2010 年 4 月 6 日)
3×10198-1 = 2
(9
)198<199> = 61 × 7304109398819
<13> × 245186388835201614679588776888220094897052023
<45> ×
27461723689325607345365923884323524383870179087245314211471108082418732281332903742131945838261002031868993262649351286813848647212990461807<140> (Robert Backstrom / Msieve 1.42 snfs for P45 x P140 /
March 20, 2010 2010 年 3 月 20 日)
3×10199-1 = 2
(9
)199<200> = 112403 × 277334011 × 1601852971
<10> × 252830208606500054458883
<24> × 747259820832076009467740924242262873561358607
<45> ×
3179925708804289450372549233037593965881328406446880827201957011485530677908247685109118491928166361686144753<109> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=7401064585 for P45 x P109 /
February 28, 2010 2010 年 2 月 28 日)
3×10200-1 = 2
(9
)200<201> = 13 × 23 × 59 ×
17005838671277138484212913100164389773822345672014058159968255767813616008162802562213026472422198288078907091434725922566747916784762768550535683918145229862252706762655178277875403888668442832039<197>
3×10201-1 = 2
(9
)201<202> = 71
2 × 274818953 × 1154915948058749
<16> × 45592979882964819734189
<23> × 4198545201102514144301929
<25> × 51680027931445099736270712486418113352984366948483125672373
<59> × 189534357475685771189652977002654801785730673893347954721465838236699
<69> (Erik Branger / GGNFS, Msieve gnfs for P59 x P69 /
October 1, 2010 2010 年 10 月 1 日)
3×10202-1 = 2
(9
)202<203> = 277 × 360959 × 1489398605083370326967975894222389
<34> ×
201452503151630272092171137067216064475573143899301503387898381245497334238104480994753555248962880536691887832549083203575674684283685304601450640255059157512937<162> (Wataru Sakai / GMP-ECM 6.2.3 B1=3000000, sigma=908324205 for P34 x P162 /
September 25, 2010 2010 年 9 月 25 日)
3×10203-1 = 2
(9
)203<204> = 7 × 296047 × 195439185049
<12> × 5911299004317409433064334686882431
<34> ×
125304878537135736559526197866845333384642570946536343308979146223992751323209664439152035917197388371173912085442221646664802334553324599448976142255649<153> (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=4160805105 for P34 x P153 /
November 8, 2010 2010 年 11 月 8 日)
3×10204-1 = 2
(9
)204<205> = 1085374429
<10> × 4865205201866784469055303560140189723401751827411
<49> × 17201334856843872792091840415632047084927184520471936483205241911287
<68> × 33027701925539102191885887797543028799413573668100232754515284004933008970778783
<80> ([GPU Force] Robert 7NBI / GMP-ECM B1=110000000, sigma=750827538 for P49 /
December 17, 2011 2011 年 12 月 17 日) (Dylan Delgado / msieve v1.53, ggnfs, factmsieve.py v0.76 snfs for P68 x P80 /
March 6, 2019 2019 年 3 月 6 日)
3×10205-1 = 2
(9
)205<206> = 379 × 529749497444143
<15> × 167600016483650028459421539216317068402628490727
<48> × 5643409327877686865675323356436413413687355359135162301043505206904279
<70> × 157977734941873640075507850668289158160299711451325582398769107983884099
<72> (Dylan Delgado / ggnfs, msieve v1.53, factmsieve.py v0.76 snfs for P48 x P70 x P72 /
March 9, 2019 2019 年 3 月 9 日)
3×10206-1 = 2
(9
)206<207> = 13
2 × 26283540729538778269
<20> × 189346637458613088402776207
<27> × 1021828675072250135587964288654831275335642902205599
<52> ×
349071986346124370311964251579663214438523292674438408864698510831591803568951831593803689621187774672568163<108> (Bob Backstrom / GMP-ECM 7.0.4 B1=48250000, sigma=1:142020064 for P52 x P108 /
June 1, 2022 2022 年 6 月 1 日)
3×10207-1 = 2
(9
)207<208> =
definitely prime number 素数
3×10208-1 = 2
(9
)208<209> = 13883 × 98193131 × 489483369480799681873165359859227605279010625360148675273962137695042497
<72> ×
44959231787070252937151747295347879448217753675962434119898768511186356218314659414429845460707928579018149806800998239751079<125> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs for P72 x P125 /
April 21, 2020 2020 年 4 月 21 日)
3×10209-1 = 2
(9
)209<210> = 7 × 1747661 × 4891355507
<10> × 272169036755873
<15> ×
18420358354564417017849878330782298558113545462340294123133168425830643649462789809665306769555825852572778532343313379921358047457980863518068457902537737631893938810610967605567<179>
3×10210-1 = 2
(9
)210<211> = 757 × 36263 × 39261367232392369
<17> × 54773739454063334542547
<23> ×
50818733134845399004857583515009494891738906885537809922619055051051744548567230947396508666826938743615478468388554605159866505649927500437383887193986349471755223<164>
3×10211-1 = 2
(9
)211<212> = 19 × 191 × 4399667 × 23471920759275827668858758489201611273405477544273283955881
<59> × 701301841443020897685416688374061205424850638583113743670131900388387
<69> × 114146045393689588744555368567781509029088868161603599183595448958757109819
<75> (ebina / Msieve 1.53 snfs for P59 x P69 x P75 /
July 13, 2023 2023 年 7 月 13 日)
3×10212-1 = 2
(9
)212<213> = 13 × 47 × 27316646893
<11> × 275304983921517806903
<21> × 20975006445313415306232251
<26> × 2932138393579874431181967347
<28> ×
1061578256042879534892931314264450816128500117873330246121049342968047659102482672078662722328086068788629637212004699432078943<127>
3×10213-1 = 2
(9
)213<214> = 17 × 1553287 ×
113611063657452948262013925005109657587993946348084076277104806850020027737005081330562788688079650747471803532842061421246382292367544363889571712420556043599230307765933487766114508060875383091772858612281<207>
3×10214-1 = 2
(9
)214<215> = 1321 × 694381 × 51700214952073
<14> × 95030588319999601
<17> ×
6656789768401722637374672011092358566245481684417596914862082726978087245450004988692807331971873956471416540034155654065083427486911332392774104470484098863847009857794583163<175>
3×10215-1 = 2
(9
)215<216> = 7 × 474819775515343
<15> × 21653669935445881
<17> × 135069937014825408795388841396935613723
<39> × 570851018157094747039977245744874086515128563
<45> ×
54060670324271450418193984895009035869320119837249970916079791611665274741622296069799206552538924671<101> (Youcef Lemsafer / GMP-ECM 7.0 B1=3000000, sigma=3:3642554675-3:3642556274 for P39 /
December 19, 2013 2013 年 12 月 19 日) (Robert Balfour / CADO-NFS for P45 x P101 /
April 7, 2020 2020 年 4 月 7 日)
3×10216-1 = 2
(9
)216<217> = 137469623 × 7100763731
<10> × 30684681107
<11> × 687751284877
<12> ×
[145631870002781454717561682762880626089322799700979310229236886473776340441637327653247393670147665933591499388303122901639997221078477495535277351822564540046749106190357910357<177>]
Free to factor
3×10217-1 = 2
(9
)217<218> = 4423 × 6619 × 1542213691
<10> × 51021602449586267694017733429293415506756956519079808475739087810633
<68> ×
13023067318631122348557103888630650700446941612605094117352079694456660978800505690045749506045121566785337486300651991346814028979209<134> (Bob Backstrom / Msieve 1.54 snfs for P68 x P134 /
September 12, 2019 2019 年 9 月 12 日)
3×10218-1 = 2
(9
)218<219> = 13 × 11114641 × 1347678337
<10> × 166672864679
<12> ×
9243390811052682914271373889884578065723515716762589375390038238632098241288138699398805222911352206004217198555203792735963983033031506922365884079289647046633215863750058117512362752097661<190>
3×10219-1 = 2
(9
)219<220> = 103 × 21734061113
<11> × 8524390652898344180739943187
<28> × 51537980707374859288465624373661565777383269
<44> × 78968497606560052814333700965974749136904008185517
<50> × 38627671356147142887904952437828881669989202768143263641330016660368569254577218482091
<86> (KTakahashi / GMP-ECM 6.4.4 B1=11000000, sigma=1583749019 for P44 /
March 14, 2015 2015 年 3 月 14 日) (Erik Branger / GGNFS, Msieve gnfs for P50 x P86 /
April 21, 2015 2015 年 4 月 21 日)
3×10220-1 = 2
(9
)220<221> = 83 × 63647 × 253439 ×
22407416051217670255681525212768052854628254507021109065627944404868096201952445779664049591134394209771679259800355858603594584010379212530418393662879196712128973750947991222167705176569823030302270844630341<209>
3×10221-1 = 2
(9
)221<222> = 7 × 19470966117578317283
<20> ×
2201079422476709293304102934147095472613875263572223075854430954205168767071205736987199625637800238788499729721152926076158382902561089699675242864606921379659475025620454582645811204442672322265892579<202>
3×10222-1 = 2
(9
)222<223> = 23 × 383 ×
340560790101033034396639800204336474060619820637983880122601884436371892382790328073561130661823135429674196844136678397093881257804518106482007038256328754682710863889204222953797252809626518333522533772278351685775911<219>
3×10223-1 = 2
(9
)223<224> = 8011 × 339735653858118751669853297
<27> ×
11022837278281468177184019681753494721420578660597187554220606694881660653433616079669970432650594458607139878955994963621056524432298086584868774567736696863915794172175888499022700746086140397<194>
3×10224-1 = 2
(9
)224<225> = 13 × 1597 × 14759 × 34154509247514536194799
<23> × 43092828909137488757879
<23> ×
[665216478586907855339972747484555374250749668841598036191771671137679236270989472674109002982763554683333874059637778491788808949793207676841176175320873503227364076562681<171>]
Free to factor
3×10225-1 = 2
(9
)225<226> = 29 × 506449 × 332202603809371025659
<21> ×
614871702854921063581311595907749137038892782594239054812685270254519780265744700639026451609314841883703454384490985711907084212877323225678717366919402117773934880419297963490175523476599113521441<198>
3×10226-1 = 2
(9
)226<227> = 107 × 5903 × 18301 × 67189 × 17992383975144400018112539343077
<32> ×
2146856343293436332976432901719291039559467373504861438399416545721553677474102024253775003565260475976479068611061707728189411944382135346998937655661055842674313223981050711561623<181> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=3230293330 for P32 x P181 /
June 2, 2010 2010 年 6 月 2 日)
3×10227-1 = 2
(9
)227<228> = 7 × 1327 × 67915519953890986840301
<23> × 20344927471173334979349573079769558971349
<41> ×
23373681181395635316839983302967007703902506110568886227014358845303531417267938147068218935705923260423482835638272708535773508269840735220618226559712321989559<161> (Florian Baur / gmp-ecm B1=11000000, sigma=2006884560 for P41 x P161 /
June 16, 2022 2022 年 6 月 16 日)
3×10228-1 = 2
(9
)228<229> = 193 × 304682332763
<12> ×
51017206379564777667944771877960688781577730637545661430297880536631723098875906132218302504946101189368190917319084295394703279581161326848527759552581494971662628894914130993316338286988242241010590075456432586861<215>
3×10229-1 = 2
(9
)229<230> = 17 × 19 × 3083 × 4806377 × 56289821727331
<14> × 25558887279658179925339
<23> ×
[4356678967073131699922919238013195777268404683816329412282933395427914670466940368270959639305823432531294732744114567989001133102965833856075412728110445335868062963377998453577527<181>]
Free to factor
3×10230-1 = 2
(9
)230<231> = 13 × 10333 × 42731687 × 5205770389515937
<16> ×
10039600362922126506165694235549489901072609873947685746719477823037447110911886829953173365984406297217145461904123277565988103852836822351737903034548608586270178347348299167115051110532408257075660049<203>
3×10231-1 = 2
(9
)231<232> = 3049 × 3833 × 32421121 ×
[7917662474182316214227603643169139421570856799921026888010388859387406485741797396717628609075723138663392672268035950746935123514655318934038254620922525714676970209930134476969171144513307411981009875618829118031007<217>]
Free to factor
3×10232-1 = 2
(9
)232<233> = 229 × 150551 × 12314386787
<11> × 28101802461565621
<17> × 298363907844779350307048893453665107
<36> ×
8427696243327701015938935430022630937488867323174880941163956638487776713388125224527233959937892819820286832747140750154647858167538283583428483700883633002034329<163> (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=2457181535 for P36 x P163 /
November 12, 2010 2010 年 11 月 12 日)
3×10233-1 = 2
(9
)233<234> = 7 × 189463425949411434003748743265533094404392834958315942679047997
<63> × 6937859318682358619779711655390966130774663036538025305503447222060484081
<73> × 32604109221823010620391224287664218577256270072051779328401086054283813766714696419408318931140301
<98> (matsui / Msieve 1.51 snfs for P63 x P73 x P98 /
September 14, 2012 2012 年 9 月 14 日)
3×10234-1 = 2
(9
)234<235> = 1093 × 9949 × 352043 × 7270063305596659597
<19> ×
[107792304307139560210666335830848687978750752449830788691580353046844516595060078066677756466921413394857447882633792760092630660543544064791722379156530851262917123495944561541496798422416709220741501217<204>]
Free to factor
3×10235-1 = 2
(9
)235<236> = 2143011373
<10> × 28210233977
<11> × 852999186877
<12> × 264076233311743
<15> × 2136402331008922147165389780849956832607
<40> × 1594264654009345926779168497144420365135920494761720601213
<58> × 646798041172415267289633787963704266787787379285930212171336658990155749445764798817046701819
<93> (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=3576123916 for P40 /
November 10, 2010 2010 年 11 月 10 日) (NFS@Home + Lionel Debroux / ggnfs-lasieve4I14e on the NFS@Home grid + msieve for P58 x P93 /
August 2, 2013 2013 年 8 月 2 日)
3×10236-1 = 2
(9
)236<237> = 13 × 71 × 3381553657046207
<16> × 30764637576691042201
<20> ×
3124290925678702176243531096564451212258787328924578058773843423403842515900528302292941663485427408464992830488479676992630513214967568597682900875679076836617267488933612077777757703700315115811659<199>
3×10237-1 = 2
(9
)237<238> = 757 × 87629 × 5758947332450579298247
<22> × 979344090486010814933143639196331587
<36> ×
[8018610266659686546645654000385995234265376666722739667470794883946905113756811628514863257406251781280851390981204234613914060239590544033769436639667734592286755819943347<172>] (Serge Batalov / GMP-ECM B1=3000000, sigma=790511631 for P36 /
September 23, 2010 2010 年 9 月 23 日)
Free to factor
3×10238-1 = 2
(9
)238<239> = 3637 × 13043 × 253304171 × 733094246271381527872270076511379937952520383863
<48> ×
3405636622252819807336572127265585521853216537017929000577864261466477647604929352437610101401770682143725979360760998613859997748731422133742453790114651694810530194462925093<175> (Florian Baur / gmp-ecm 7.04+ds-6 B1=11000000, sigma=620034157 for P48 x P175 /
June 19, 2022 2022 年 6 月 19 日)
3×10239-1 = 2
(9
)239<240> = 7
2 × 19391 × 374639 × 77203796737224443766710102182926132323
<38> ×
10916246254259329875940527696399155789884824127541558495304859754181264740404524607872548942516259298620753621206702100588140627958595463239342669014541036268439465523024466804909854179973813<191> (Serge Batalov / GMP-ECM B1=3000000, sigma=3856446914 for P38 x P191 /
September 24, 2010 2010 年 9 月 24 日)
3×10240-1 = 2
(9
)240<241> = 60527 × 417133 × 8612983311914710449432234585981951050033163457717503080226681247987264415833
<76> ×
13795706659228618195322438459544243347989247229848777018474606399282338997390472414635229090167824493337681234778725030255806805084989944559370201803717533<155> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P76 x P155 /
April 24, 2023 2023 年 4 月 24 日)
3×10241-1 = 2
(9
)241<242> = 227 × 4880774711228399
<16> × 23322340571998966245463
<23> × 22880312729166736787542428497
<29> × 695741014426238161421383101413887
<33> × 7259452327746521153190995373860628441589099
<43> × 229285497603320667207077634519116727893380825579
<48> × 43817187363491904946764333609605587734192812331979
<50> (Serge Batalov / GMP-ECM B1=2000000, sigma=4080826854 for P33 /
September 23, 2010 2010 年 9 月 23 日) (Wataru Sakai / GMP-ECM 6.2.3 B1=3000000, sigma=458411955 for P43 /
September 26, 2010 2010 年 9 月 26 日) (Dmitry Domanov / Msieve 1.40 gnfs for P48 x P50 /
September 27, 2010 2010 年 9 月 27 日)
3×10242-1 = 2
(9
)242<243> = 13 × 4130334436471098719
<19> × 325604793963376923442516447201
<30> ×
17159391921704221233397448886585956653327687159531128913980146763772696050869104925233975758559439909831461606154328293077690950760879505172935739075402946024822168031615996367553533451071374917<194> (Serge Batalov / GMP-ECM B1=3000000, sigma=561220683 for P30 x P194 /
September 23, 2010 2010 年 9 月 23 日)
3×10243-1 = 2
(9
)243<244> = 40706647 × 73280611 × 926940776073990033225313348679
<30> ×
1084962817215187500354747332697493900314682405003802303136902959791211670985589587208290809529514856971511927982385959707922331227570374226472022335751556553231608324376982822961551342678226949391893<199> (Serge Batalov / GMP-ECM B1=2000000, sigma=2462459920 for P30 x P199 /
September 23, 2010 2010 年 9 月 23 日)
3×10244-1 = 2
(9
)244<245> = 23 × 12491 ×
104423010654627853793862015433720974753996790732805881103960068640725670308709227165298145099254071627223775031065845669751786503673949591531989989314045243009749628428120420615886916840995081676198167028086309099073071742089086751156484843<240>
3×10245-1 = 2
(9
)245<246> = 7 × 17 × 877 × 3065243 × 7561187 ×
[124028020298159826909478862678703486017987474148853830173622993600839418469848645573751360701236893222794428896737010022306531909832922641384840829331594853253330125535001203914851531537824260502880310212948224997567767453170253<228>]
Free to factor
3×10246-1 = 2
(9
)246<247> = 3853 × 43787 × 138637 × 9225404519
<10> × 2940488297028181
<16> × 144006707690744099
<18> ×
32832980392171410858940949160132475920882282111599718233331910455910220813852141246171785548588173194211897149622631194584602611789103747750774223496616306611669223931006970221775539164394237<191>
3×10247-1 = 2
(9
)247<248> = 19 × 3137 ×
[503330369276714259349361609314967367414391893025518849722329412949012633592268845527909668976393805680922101236514940523128030468265020217103165948022750532691307484522591144741036525007130513564753452007449289465295371038370551817861517037733<243>]
Free to factor
3×10248-1 = 2
(9
)248<249> = 13 × 5231 × 46051493207244966325278220810248409
<35> ×
95796461103603119871604838434486717700243417657696515920803485868215910956344736478763290580783516682187399019799924476121631939704185675070918276440320191932973270470220436196777055717660460074352138830963837<209> (Serge Batalov / GMP-ECM B1=3000000, sigma=3783953849 for P35 x P209 /
September 24, 2010 2010 年 9 月 24 日)
3×10249-1 = 2
(9
)249<250> = 360461 × 14274265427
<11> × 1726063437369789654448846178369596291661
<40> ×
[337794403708670653416593235656564566384717438342157284566726726000475319090394272283672990642619382693244597730757769829442822175463072436346392471826660197601711855162362683994360044079523320797<195>] (KTakahashi / GMP-ECM 6.4.4 B1=11000000, sigma=4190689324 for P40 /
October 13, 2014 2014 年 10 月 13 日)
Free to factor
3×10250-1 = 2
(9
)250<251> = 491 × 203589548174855797
<18> × 278984038634718404823349055784265724393081891
<45> ×
1075734078846116826565575685145514189316212622504364684610726258420057585321791181765414619843667387655848719019083328558662837515216264295032917669234263799379404741177389335548295053507<187> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=1225193389 for P45 x P187 /
July 22, 2011 2011 年 7 月 22 日)
3×10251-1 = 2
(9
)251<252> = 7 × 157 × 823 × 9810373128146159410841244364459
<31> ×
33809457437605620451313519682836038864936868779214640560935095050861588240131319458653089032139770531125376321938627058190130151956558179379351873615333457736245639284910430377028606031721217678473477772435283844193<215> (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=968664949 for P31 x P215 /
September 14, 2015 2015 年 9 月 14 日)
3×10252-1 = 2
(9
)252<253> = 1103 × 167087 × 4447019 × 6368470185841
<13> ×
574776463405835502002879432403362519141068734377527378424436389333517326800244431479099567490399280128306676254243144238086357880126381580781082979381599880792503555878291270559119311459873346970719540777933706195366314742221<225>
3×10253-1 = 2
(9
)253<254> = 29 × 103 × 821 × 943219 ×
12969712061432565787650413608082285516021982044487878427871739388972578299712341946993086990640060424132256857610713308260732448422058143166131332393462177930082411421928883851549676188657487247618356779334619052998090538685910373092503134323<242>
3×10254-1 = 2
(9
)254<255> = 13 × 15527 × 52200134711
<11> × 307719686123
<12> × 21802069806605651
<17> ×
[4243905638787949384663828328592955185506026898991670618849869185658285372328512845058139212076375355053406042013500764639216677462822614069220243077742717156140096252756144860191755652275886802290799890162655883<211>]
Free to factor
3×10255-1 = 2
(9
)255<256> = 5297 × 1377791 × 3165311 ×
[129864829971838041085624128957898621981599168578722458624082152515250670680189240672666982644243242746416468066110961347320093868040631097671098394462804886622205439254963578422474041344708873450926808441503597125283917181575416210247512367<240>]
Free to factor
3×10256-1 = 2
(9
)256<257> = 313 × 6073 ×
[15782421433790900802746562194051184497032641730090080800736933864815143128149579477380896641448110817850339506189076565261101749797064364397172000511350454454825186008988615087258377703857592054918617943876657220010637352046375067141051182918790498351<251>]
Free to factor
3×10257-1 = 2
(9
)257<258> = 7 × 113 × 389 × 571 × 2731 × 62549 × 73598297 × 358165651 × 1918260791
<10> × 585689203642621693
<18> × 84466016020313605155542793133
<29> × 31171197226311395570049869722472441520374169867277
<50> × 2406643285962096341272041895466642897001048567538429589
<55> × 53265156365744056575082514085847115301971800009032820222428212741
<65> (Florian Baur / GMP-ECM 7.0.6-dev B1=43000000, sigma=4227195106 for P50 /
September 4, 2022 2022 年 9 月 4 日) (Florian Baur / for P55 x P65 /
September 6, 2022 2022 年 9 月 6 日)
3×10258-1 = 2
(9
)258<259> = 47 × 59 × 61 ×
[17735422960278564376629441984475593102102829982323695116255697504625989488805992208237512784284050534131821487056097142823361099123278924996896300981951251234089847652716771207132004753093353354655252936690451839458951363558435262750291156526931239765183<254>]
Free to factor
3×10259-1 = 2
(9
)259<260> = 373 ×
80428954423592493297587131367292225201072386058981233243967828418230563002680965147453083109919571045576407506702412868632707774798927613941018766756032171581769436997319034852546916890080428954423592493297587131367292225201072386058981233243967828418230563<257>
3×10260-1 = 2
(9
)260<261> = 13 × 18539 × 1841296467185422441
<19> ×
676032971789130536380734020793785435567612218211955330375719922563276137625614539981611247756094072753015917122859646976560458006888677571458560715134867709490576745522151837618998632779464198440215925416318804898419715186038217951947977<237>
3×10261-1 = 2
(9
)261<262> = 17 × 83 × 30859 × 319288564304741
<15> × 355959485721696996870222685848276298889302372613659
<51> ×
606217484095065893961295647915516773907267971265993624118770477281494994164030521647186633406466300477765174730034342217519689499495753987189327439100246975033716479024953602287483097686729<189> (Florian Baur / GMP-ECM 7.0.4+ds-6 B1=43000000, sigma=3611830709 for P51 x P189 /
September 6, 2022 2022 年 9 月 6 日)
3×10262-1 = 2
(9
)262<263> = 3301 × 1285429 × 83177506077359
<14> × 53923144256085589110407627
<26> × 880482910602817002739617065763601
<33> × 1240234201995186467774823670217437
<34> × 484926123512155816956321712789885135319
<39> ×
2976777117384252284440069138530511544288948482411776180555732631854282326207461563193028477806681944513366289<109> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3630484822 for P34 /
September 13, 2015 2015 年 9 月 13 日) (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=2935291095 for P33, B1=3000000, sigma=2402713257 for P39 x P109 /
September 14, 2015 2015 年 9 月 14 日)
3×10263-1 = 2
(9
)263<264> = 7 × 1480495293649441684718533
<25> ×
[28947841334570809944188515128289539305447627701679894424839554229884124348397124283186151627434187834443903570835879470316633372484665834773981258387383682856236196068746928648611377297972877193220221161762503462706761221862290673406363829<239>]
Free to factor
3×10264-1 = 2
(9
)264<265> = 131 × 757 × 1098373 × 71605021 × 12154370646323
<14> × 14512421906794002132541
<23> × 7090403138520872214148127
<25> × 44935842696142638066812646374434954340797517291
<47> ×
6844229497423933032213607160680216426842030864266320538945869390192591476159399320845561656651152532954474787537234405137502958189892474059<139> (Florian Baur / GMP-ECM 7.0.4 B1=11000000, sigma=394084517 for P47 x P139 /
June 21, 2022 2022 年 6 月 21 日)
3×10265-1 = 2
(9
)265<266> = 19 × 431 × 5039 × 31858282185262543
<17> × 31914047027428913
<17> ×
715058856190927926297794100031945235861392108589449597349073685708531516156329989219377167650182482730668151946271171562954805990772321296728952420814103967673578439619508882651391308065818204591884230215445717696746582609691<225>
3×10266-1 = 2
(9
)266<267> = 13 × 23 × 4341866659986390329819
<22> × 29599200727643563736033891
<26> ×
[7807169358757201919417747766736534120388733280054744111302176922943511471319120042245971291792670097356914178811355582411201475093627362705197630522470175093863638503150989249817489893500721113377783177698057719165069<217>]
Free to factor
3×10267-1 = 2
(9
)267<268> = 367 × 5357557 × 435992756237728927873183
<24> ×
[3499525129136309762140291496255745929166445041477767199032025837214534907445599469180360681403064365117283597616833080774078796294569930713461789312161720972268723572760602829105042152448150637086219677766609754836060366453371802162387<235>]
Free to factor
3×10268-1 = 2
(9
)268<269> = 76991 × 194963 × 4124168051
<10> × 89604004706350021
<17> × 36476621181142294259
<20> × 10897768869036654459750187235772507313
<38> ×
13605456742999242476906542548944027844315547594008150218413222010976630012995570716449707863987622574087536615689070173534782027693607986524004601993049789434088019321083578679<176> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1874728461 for P38 x P176 /
September 14, 2015 2015 年 9 月 14 日)
3×10269-1 = 2
(9
)269<270> = 7 × 443 × 1321 × 229903 × 485131 × 3505612159427059113418466173
<28> ×
187304899961664496957660715781706631021471192041867499583804491819398341297793162861232884929112387449078085444426859427535195398281402943922961636586023586123796179091836304583347245818636943254233478201608678231998029735971<225>
3×10270-1 = 2
(9
)270<271> = 73883 × 325751 × 163467210537049
<15> × 296950578209358819584777382159270184236812409336733
<51> ×
[2567888418665877823873329008298114118209388309348789629124549209432482729856160713130613042766745125394409229755916931276173520826342066410759654555281844761522819558262315446059200549707345513359<196>] (Florian Baur / GMP-ECM 7.0.6-dev B1=43000000, sigma=1555168508 for P51 /
September 17, 2022 2022 年 9 月 17 日)
Free to factor
3×10271-1 = 2
(9
)271<272> = 71 × 277 × 30649 × 14750570742387069931488097277147745589193
<41> ×
3374100413134691358447123278700866688221787483792841709503202068999786297462934676975457030379898605444234389425397579727678687403166228771716170472644362943938840093213228406849317274507878471659122590036142466394471710821<223> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2712479544 for P41 x P223 /
February 21, 2017 2017 年 2 月 21 日)
3×10272-1 = 2
(9
)272<273> = 13 ×
[23076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923<272>]
Free to factor
3×10273-1 = 2
(9
)273<274> = 8281454161
<10> × 404959776157
<12> × 543265398769
<12> × 3183054245603646499
<19> ×
517305004103715454478286719795124465811674988156271434140082408879387878823854395107749429286442433830374734727293671542679805497854549737544905531404387884401514837796965474711461144458870356772607090807979006817513203577<222>
3×10274-1 = 2
(9
)274<275> = 1607 × 102957611 ×
[181320505517836357160162547611969315640216780653983680226396255184258407610706906554966241453727528013298758730201544957169951182245681146018961017429078222843255424544226686623485767254114779495777519147464315566303803526125168129972881402933469696189918703388187<264>]
Free to factor
3×10275-1 = 2
(9
)275<276> = 7 × 967 × 116082657840355438543
<21> ×
381794262307023854609443671952237899200757208075923823263709341393668752504010477499661628292298086502190195421951252202154849631782605417020246061771115799547354436894464646385819502627459569494664661947900450057233421482568896927143586423423060608097<252>
3×10276-1 = 2
(9
)276<277> = 41149 × 90998377 ×
801176722398766270909449182853399333710822500740071029196135666675185898247405713888818650273848779654259252110586414821767375536080329127418977171236158371710259945538202976186957003760163095531897583200872462784983801585550312681234882980293862153058091442051763<264>
3×10277-1 = 2
(9
)277<278> = 17 × 347 × 159617 × 89417047 × 402255983069
<12> × 24059267190781606387105992962851
<32> ×
[36817855059728842956489648835118295829539523290243462670764438238669390779341348213689122321454988584037627461796343942496334663616788081950745311008721494625588577912522119090493505470375734224370585853127366634391021<218>] (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=355649155 for P32 /
September 14, 2015 2015 年 9 月 14 日)
Free to factor
3×10278-1 = 2
(9
)278<279> = 13 × 128833 × 2401381 × 24484211 × 129537719 × 5802867349292744413
<19> × 7759093814952037969
<19> × 36510718907360225494603099513007
<32> × 414793047030090727937655318594575732628523814389
<48> ×
34490687826095882852042991459260753867331943552198052585877345799304804663749015120653535671545538734359355772561294058718507528224669<134> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2168117003 for P32 /
September 14, 2015 2015 年 9 月 14 日) (Erik Branger / GMP-ECM B1=43000000, sigma=2701930693 for P48 x P134 /
November 4, 2015 2015 年 11 月 4 日)
3×10279-1 = 2
(9
)279<280> = 107 × 1531 × 6869 × 129504149743
<12> × 2183333953749593339023317375031307053
<37> ×
9428984382447595657235939635641010558397379499756881557614001834224003278685757524914560895963691625574036787087723415835630838196513489549760529705048313894231609462626355973156389646539073179048298902982348334372701095897<223> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2967735357 for P37 x P223 /
September 15, 2015 2015 年 9 月 15 日)
3×10280-1 = 2
(9
)280<281> = 4969 × 19211 × 50691920390500885952031670235569
<32> × 70826888213408535989715027789680943239
<38> ×
[87531703457487725949994801266005358068384775586795162032877987797431212359478145238175325395582320588906475001706530078862969974036012214416606752891186978621861815056396990703732477319186187685742286771<203>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3215036991 for P32 /
September 13, 2015 2015 年 9 月 13 日) (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=1621429921 for P38 /
September 14, 2015 2015 年 9 月 14 日)
Free to factor
3×10281-1 = 2
(9
)281<282> = 7
2 × 29 × 1097 ×
[192451167120102999864642679125527556761867982348378951744152852414973470606612493801468659006682546026300376498633275961502068529294595907076878467729467545355928811030274493099663402908706939853236739954209452303223492898872685213399476661126211399909034748341231315397312227<276>]
Free to factor
3×10282-1 = 2
(9
)282<283> = 48167109226154771
<17> × 10279164266996145047
<20> ×
[6059166206839113917233142979165815607944292614686531067171650026285366327903878933517135239879749942462929047405152337130478267592320689291081474856740091041405072316423591924548697842313221759898719087341343200556649344607527121485319737263193827<247>]
Free to factor
3×10283-1 = 2
(9
)283<284> = 19 × 834825739651
<12> × 15630988526598864961
<20> × 201781068202100853698922810943
<30> × 4620474432330019491083597480544397
<34> ×
[129783173762855209175766742279074614187771261068739847879120474748522082755908758964202337299572311619125746393456135106371531211569451669931835273761734854760004277618293437282864184450541<189>] (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=324818788 for P30, B1=1000000, sigma=987654321 for P34 /
September 14, 2015 2015 年 9 月 14 日)
Free to factor
3×10284-1 = 2
(9
)284<285> = 13
2 × 599 × 4513 × 950459 × 79046252450516653
<17> × 1959412175405071686345785025143
<31> ×
4460688734829337637742714594377010471959773612476103017073703030834258244937859059981088523201881272674826741794638035041216479101421332178900028391237373447287744669876656519134068851507022074900989881641650876550164366953<223> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=1120367998 for P31 x P223 /
September 13, 2015 2015 年 9 月 13 日)
3×10285-1 = 2
(9
)285<286> = 118357885034727703
<18> × 1281873610485759385561
<22> × 112422233103862820222980319
<27> × 136880389899229905837160580703119
<33> ×
1284947578966578175628548427486419443193730997866398993993054678496950345137138914635480377389508471425354669443290047980292800713842199452031657584396449108022851607095641153476662816709873<190> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1732866669 for P33 x P190 /
September 14, 2015 2015 年 9 月 14 日)
3×10286-1 = 2
(9
)286<287> = 97 × 48023 × 14638633 × 425664623 ×
[1033551575065161692772599228849739033103225329661798481298286776509428529340621621170340489447237925603380443466031809094838343034684493706344648408342064775584316537687270869109071248659442713962839467824889942759906617103331059588981061465572807492137299813456831<265>]
Free to factor
3×10287-1 = 2
(9
)287<288> = 7 × 103 × 286879051 × 2258752400414238765259735743461689
<34> × 663819354791150401866569369061347881
<36> × 9079649562854343798202500970257660006847
<40> × 30149367146749551891331686966988768800629
<41> ×
3533632081128482559549190867044706541977488971402868795544572483032266550633803060407988441139591224388590997887097515849946407<127> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3610460432 for P36 /
September 13, 2015 2015 年 9 月 13 日) (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=597366400 for P40 /
September 14, 2015 2015 年 9 月 14 日) (KTakahashi / GMP-ECM 6.4.4 B1=3000000, sigma=3425338188 for P34 /
September 15, 2015 2015 年 9 月 15 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=680710756 for P41 x P127 /
September 16, 2015 2015 年 9 月 16 日)
3×10288-1 = 2
(9
)288<289> = 23 × 12853 ×
10148197510985423805641721269607163274349754244483608969653506709649921013196039496784712755269451557579181311079463769243519530206109891448113957492583358985721486102043508705462098173662721272989895778011562179697516059522561134433172428023909153335881658486091895311194476674368021<284>
3×10289-1 = 2
(9
)289<290> = 15473407 × 162190031767
<12> × 648620617440233
<15> × 40188214538900266543
<20> × 18254665675106241571550859087206555738380907
<44> ×
25121629257527716350155251854299530308694061273986526252845656442360824289261940454616596128775218323013315464391974099993279829751455450523534751276888169081286601813143270957656674008914833187<194> (Florian Baur / GMP-ECM 7.0.4+ds-6 B1=11000000, sigma=4025432993 for P44 x P194 /
August 5, 2022 2022 年 8 月 5 日)
3×10290-1 = 2
(9
)290<291> = 13 × 661 × 39901 × 1180541572869387539
<19> × 3119967510830314574341
<22> × 46908491174594925173187254540327
<32> ×
[5064188256914463733706728788645342241850973708120361793592359294750005243191378757608171214923629299905775985699444763587246204393916921524805853476595263334415464739699771100576399378173059365290982729918655091<211>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3752690032 for P32 /
September 14, 2015 2015 年 9 月 14 日)
Free to factor
3×10291-1 = 2
(9
)291<292> = 757 × 9257 × 10402288791571
<14> ×
[41155341038021548872479711663101089076061285056638618117490880049710234771719225723081957284034129117418889523586955286495465037229189378976716640857466226435394113309271486477877812072971589999189413630654553611096979199630919931148457425895944887859615932037083532391881<272>]
Free to factor
3×10292-1 = 2
(9
)292<293> = 181 × 28749899 ×
[5765093517496919214255134431537361121210407273111767428531416955624956191174466655858743358863770048249868278807015108535805744523625392533423185877350184739606480854398558589488267967336384506643317981551000861656834388390959245760455776486581782599388460133642027981727318560098121<283>]
Free to factor
3×10293-1 = 2
(9
)293<294> = 7 × 17 × 7411 × 45389 × 4725656043701
<13> × 157861526033361859
<18> ×
[10046353610324682659248076016528504470375606586540177428779339568685289494359477675482884666145661544321251706850323096862340478594817322104496971780288014924503214893571307188841485716992785852800424262476182926794879170977597646938580083897653327098161<254>]
Free to factor
3×10294-1 = 2
(9
)294<295> = 101666627 × 13514324659863619539289646433527
<32> × 491860226832047207348930827197685552571
<39> ×
4439221200317092613575120845806108990203165964356643393669617780090480701422968008767626254736275372712237532219115571624604276537611906331189026660357571251754484318366449269032173965634323820144578641219500383183561<217> (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=2886526743 for P32 /
September 14, 2015 2015 年 9 月 14 日) (Florian Baur / GMP-ECM 7.0.4+ds-6 B1=11000000, sigma=1190281723 for P39 x P217 /
August 6, 2022 2022 年 8 月 6 日)
3×10295-1 = 2
(9
)295<296> = 11057 × 162187279428737
<15> × 81324312152902969
<17> ×
[205705904436717939619041352302221263739916844744412586643504933754812568104231429336222214862819674961036611619766472847352072865015835748362026804171507927766941746098200277992560630134709289172322602933884361204145669009596408204108058522663890653833460161319<261>]
Free to factor
3×10296-1 = 2
(9
)296<297> = 13 × 109 × 584336663 ×
[362316630154649705388282696311859636273057120898396664559544058859194988506560644656514222600777107040901351438417086990095609969491560147945854946623390006518671957871553500755756019106746868142863810989857288954843847809170608165626568809409214691817453514729802529383680062430303569<285>]
Free to factor
3×10297-1 = 2
(9
)297<298> = 86957712657619
<14> ×
34499527509560684148292821355325254108943916534170201634508577816722035703343616064816362084958362083535119748639638609849227599612565647660833019053337682610176386650771294294247670839259673142698292332851302416543104953535804432857408031489423131785678186866670277972897429382010021<284>
3×10298-1 = 2
(9
)298<299> = 525348937 × 310834547361024848872269443
<27> × 537852406398139185353428805100536591
<36> × 416019575231946770566704102313780673081132711
<45> ×
821045514121100849016920430250756282665600182262029718447961121045217677841035522832585942062645696504044032765730706341310048416542214722894067438018027733865708890047100821382053189<183> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=759521296 for P45, B1=11000000, sigma=4014515366 for P36 x P183 /
March 6, 2017 2017 年 3 月 6 日)
3×10299-1 = 2
(9
)299<300> = 7 × 719 × 3739 × 155501 × 18590255248396054135119519862636579
<35> ×
[5514680043451945451722659577266014534499613782731427020199543126528843055153003041820782385421251376314589830261452074675316729827943389772405084621134231830243391229918560179885010369147268754986907047166766418542405996783654594184325600079994508505363<253>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1248788013 for P35 /
September 15, 2015 2015 年 9 月 15 日)
Free to factor
3×10300-1 = 2
(9
)300<301> = 158636608584555287822564496483760836474537795744193022267616490070819282284413545159
<84> ×
18911145584664731672161623834145080343808448716496401267776943318321972394867043207863171146420418840120805701950834599928431328193997261491089145805583267931067662501894878002916008487809625902209231182365193202026761<218> (Rainie / for P84 x P218 /
May 28, 2024 2024 年 5 月 28 日)