Table of contents 目次

  1. About 44...447 44...447 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 44...447 44...447 の形の素数
    1. Last updated 最終更新日
    2. Known (probable) prime numbers 既知の (おそらく) 素数
    3. Range of search 捜索範囲
    4. Prime factors that appear periodically 周期的に現れる素因数
    5. Difficulty of search 捜索難易度
  3. Factor table of 44...447 44...447 の素因数分解表
    1. Last updated 最終更新日
    2. Range of factorization 分解範囲
    3. Terms that have not been factored yet まだ分解されていない項
    4. Factor table 素因数分解表
  4. Related links 関連リンク

1. About 44...447 44...447 について

1.1. Classification 分類

Near-repdigit of the form AA...AAB AA...AAB の形のニアレプディジット (Near-repdigit)

1.2. Sequence 数列

4w7 = { 7, 47, 447, 4447, 44447, 444447, 4444447, 44444447, 444444447, 4444444447, … }

1.3. General term 一般項

4×10n+239 (1≤n)

2. Prime numbers of the form 44...447 44...447 の形の素数

2.1. Last updated 最終更新日

December 11, 2018 2018 年 12 月 11 日

2.2. Known (probable) prime numbers 既知の (おそらく) 素数

  1. 4×101+239 = 7 is prime. は素数です。 (Makoto Kamada / May 21, 2003 2003 年 5 月 21 日)
  2. 4×102+239 = 47 is prime. は素数です。 (Makoto Kamada / May 21, 2003 2003 年 5 月 21 日)
  3. 4×104+239 = 4447 is prime. は素数です。 (Makoto Kamada / May 21, 2003 2003 年 5 月 21 日)
  4. 4×1010+239 = 4444444447<10> is prime. は素数です。 (Makoto Kamada / May 21, 2003 2003 年 5 月 21 日)
  5. 4×1020+239 = (4)197<20> is prime. は素数です。 (Makoto Kamada / PPSIQS / May 21, 2003 2003 年 5 月 21 日)
  6. 4×1026+239 = (4)257<26> is prime. は素数です。 (Makoto Kamada / PPSIQS / May 21, 2003 2003 年 5 月 21 日)
  7. 4×10722+239 = (4)7217<722> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 29, 2006 2006 年 5 月 29 日)
  8. 4×101310+239 = (4)13097<1310> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 17, 2004 2004 年 12 月 17 日) (certified by: (証明: Tyler Cadigan / PRIMO 2.2.0 beta 6 / September 10, 2006 2006 年 9 月 10 日)
  9. 4×103170+239 = (4)31697<3170> is prime. は素数です。 (discovered by: (発見: Makoto Kamada / PFGW / December 18, 2004 2004 年 12 月 18 日) (certified by: (証明: Ray Chandler / Primo 4.0.1 - LX64 / February 7, 2013 2013 年 2 月 7 日)
  10. 4×1028934+239 = (4)289337<28934> is PRP. はおそらく素数です。 (Erik Branger / PFGW / January 31, 2010 2010 年 1 月 31 日)
  11. 4×1066284+239 = (4)662837<66284> is PRP. はおそらく素数です。 (Bob Price / December 5, 2014 2014 年 12 月 5 日)
  12. 4×1067796+239 = (4)677957<67796> is PRP. はおそらく素数です。 (Bob Price / December 5, 2014 2014 年 12 月 5 日)

2.3. Range of search 捜索範囲

  1. n≤30000 / Completed 終了
  2. n≤50000 / Completed 終了 / Erik Branger / March 5, 2013 2013 年 3 月 5 日
  3. n≤100000 / Completed 終了 / Bob Price / December 5, 2014 2014 年 12 月 5 日

2.4. Prime factors that appear periodically 周期的に現れる素因数

Cofactors are written verbosely to clarify that they are integers. 補因子はそれらが整数であることを明確にするために冗長に書かれています。

  1. 4×103k+239 = 3×(4×100+239×3+4×103-19×3×k-1Σm=0103m)
  2. 4×106k+1+239 = 7×(4×101+239×7+4×10×106-19×7×k-1Σm=0106m)
  3. 4×106k+5+239 = 13×(4×105+239×13+4×105×106-19×13×k-1Σm=0106m)
  4. 4×1015k+6+239 = 31×(4×106+239×31+4×106×1015-19×31×k-1Σm=01015m)
  5. 4×1016k+9+239 = 17×(4×109+239×17+4×109×1016-19×17×k-1Σm=01016m)
  6. 4×1018k+9+239 = 19×(4×109+239×19+4×109×1018-19×19×k-1Σm=01018m)
  7. 4×1028k+16+239 = 29×(4×1016+239×29+4×1016×1028-19×29×k-1Σm=01028m)
  8. 4×1035k+32+239 = 71×(4×1032+239×71+4×1032×1035-19×71×k-1Σm=01035m)
  9. 4×1041k+35+239 = 1231×(4×1035+239×1231+4×1035×1041-19×1231×k-1Σm=01041m)
  10. 4×1043k+37+239 = 173×(4×1037+239×173+4×1037×1043-19×173×k-1Σm=01043m)

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2.5. Difficulty of search 捜索難易度

The difficulty of search, percentage of terms that are not divisible by prime factors that appear periodically, is 14.05%. 捜索難易度 (周期的に現れる素因数で割り切れない項の割合) は 14.05% です。

3. Factor table of 44...447 44...447 の素因数分解表

3.1. Last updated 最終更新日

October 10, 2019 2019 年 10 月 10 日

3.2. Range of factorization 分解範囲

3.3. Terms that have not been factored yet まだ分解されていない項

n=203, 204, 210, 213, 225, 227, 231, 232, 238, 239, 242, 244, 245, 249, 250, 252, 253, 254, 257, 258, 259, 260, 263, 264, 265, 267, 268, 270, 271, 272, 273, 275, 276, 279, 280, 281, 282, 283, 284, 285, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300 (50/300)

3.4. Factor table 素因数分解表

4×101+239 = 7 = definitely prime number 素数
4×102+239 = 47 = definitely prime number 素数
4×103+239 = 447 = 3 × 149
4×104+239 = 4447 = definitely prime number 素数
4×105+239 = 44447 = 132 × 263
4×106+239 = 444447 = 35 × 31 × 59
4×107+239 = 4444447 = 72 × 90703
4×108+239 = 44444447 = 179 × 248293
4×109+239 = 444444447 = 3 × 17 × 19 × 458663
4×1010+239 = 4444444447<10> = definitely prime number 素数
4×1011+239 = 44444444447<11> = 13 × 1361 × 2511979
4×1012+239 = 444444444447<12> = 3 × 148148148149<12>
4×1013+239 = 4444444444447<13> = 7 × 24481 × 25935241
4×1014+239 = 44444444444447<14> = 3571 × 12445937957<11>
4×1015+239 = 444444444444447<15> = 32 × 49382716049383<14>
4×1016+239 = 4444444444444447<16> = 29 × 153256704980843<15>
4×1017+239 = 44444444444444447<17> = 13 × 3418803418803419<16>
4×1018+239 = 444444444444444447<18> = 3 × 2371 × 62483402846119<14>
4×1019+239 = 4444444444444444447<19> = 7 × 277 × 2292132256031173<16>
4×1020+239 = 44444444444444444447<20> = definitely prime number 素数
4×1021+239 = 444444444444444444447<21> = 3 × 31 × 8243 × 10208507 × 56791979
4×1022+239 = 4444444444444444444447<22> = 197 × 58727 × 4685641 × 81986893
4×1023+239 = 44444444444444444444447<23> = 13 × 571 × 1948005967<10> × 3073602767<10>
4×1024+239 = 444444444444444444444447<24> = 32 × 2699 × 57601 × 317645030087317<15>
4×1025+239 = 4444444444444444444444447<25> = 7 × 17 × 151 × 9629 × 12379 × 165719 × 12521447
4×1026+239 = 44444444444444444444444447<26> = definitely prime number 素数
4×1027+239 = 444444444444444444444444447<27> = 3 × 19 × 14333463167<11> × 543990720478313<15>
4×1028+239 = 4444444444444444444444444447<28> = 1000651 × 4441552993445711286397<22>
4×1029+239 = 44444444444444444444444444447<29> = 13 × 409 × 1193 × 639533 × 10955883836480039<17>
4×1030+239 = 444444444444444444444444444447<30> = 3 × 853189 × 173640480770553943086641<24>
4×1031+239 = 4444444444444444444444444444447<31> = 7 × 217411 × 2920370335082562154789411<25>
4×1032+239 = 44444444444444444444444444444447<32> = 71 × 2706727 × 231267538531526511978991<24>
4×1033+239 = 444444444444444444444444444444447<33> = 33 × 181 × 90944228451901871177500397881<29>
4×1034+239 = 4444444444444444444444444444444447<34> = 2056829 × 133955472943<12> × 16130908691736101<17>
4×1035+239 = 44444444444444444444444444444444447<35> = 13 × 61 × 1231 × 15483703 × 24284681 × 121081838404663<15>
4×1036+239 = 444444444444444444444444444444444447<36> = 3 × 31 × 114849004427<12> × 41610918133344393095777<23>
4×1037+239 = 4444444444444444444444444444444444447<37> = 7 × 173 × 419 × 23795045783<11> × 368105893782059170601<21>
4×1038+239 = 44444444444444444444444444444444444447<38> = 11141111 × 640877509513<12> × 6224635850142835729<19>
4×1039+239 = 444444444444444444444444444444444444447<39> = 3 × 148148148148148148148148148148148148149<39>
4×1040+239 = 4444444444444444444444444444444444444447<40> = 19853 × 60457 × 3702923556340005839856671700707<31>
4×1041+239 = 44444444444444444444444444444444444444447<41> = 13 × 17 × 3720867961981<13> × 3836357491079<13> × 14088406662593<14>
4×1042+239 = 444444444444444444444444444444444444444447<42> = 32 × 1093 × 1493293 × 11183027 × 259877243 × 10410753341591047<17>
4×1043+239 = 4444444444444444444444444444444444444444447<43> = 7 × 587 × 1709 × 23399 × 29637109 × 142520034127<12> × 6403688903891<13>
4×1044+239 = 44444444444444444444444444444444444444444447<44> = 29 × 4733 × 2446337247509861609<19> × 132363015179088663919<21>
4×1045+239 = 444444444444444444444444444444444444444444447<45> = 3 × 19 × 619439984952770023309<21> × 12587613238690435341619<23>
4×1046+239 = 4444444444444444444444444444444444444444444447<46> = 163 × 264535967 × 7439869347569<13> × 13854148561456451020603<23>
4×1047+239 = 44444444444444444444444444444444444444444444447<47> = 13 × 3418803418803418803418803418803418803418803419<46>
4×1048+239 = 444444444444444444444444444444444444444444444447<48> = 3 × 47 × 4444487 × 5185554234656393947<19> × 136767071627764320503<21>
4×1049+239 = 4444444444444444444444444444444444444444444444447<49> = 72 × 94261899883<11> × 962244002702974764760519008754938541<36>
4×1050+239 = 44444444444444444444444444444444444444444444444447<50> = 6793 × 806783 × 8109594311101311736852594241250274015513<40>
4×1051+239 = (4)507<51> = 32 × 31 × 97 × 3185611348889<13> × 408330867672643<15> × 12625149890234651947<20>
4×1052+239 = (4)517<52> = 2099 × 12689 × 1898977151449927481<19> × 87873496340086076453933117<26>
4×1053+239 = (4)527<53> = 13 × 311 × 1423 × 94731008387<11> × 312368627090203<15> × 261065372630767451843<21>
4×1054+239 = (4)537<54> = 3 × 148148148148148148148148148148148148148148148148148149<54>
4×1055+239 = (4)547<55> = 7 × 113 × 38047 × 495383414337337<15> × 298111766400268658337015105201503<33>
4×1056+239 = (4)557<56> = 1082195590634897<16> × 31097624895757928411<20> × 1320640163838102417341<22>
4×1057+239 = (4)567<57> = 3 × 17 × 37705743122771<14> × 147550182425909<15> × 1566390536072851380675511723<28>
4×1058+239 = (4)577<58> = 55051 × 181926883438207<15> × 443767394736083803464910330185710296771<39>
4×1059+239 = (4)587<59> = 13 × 229 × 13841 × 7440659 × 102836957 × 1409647611606720258870809359921603417<37>
4×1060+239 = (4)597<60> = 33 × 10473284509<11> × 308779322069<12> × 5090056545693452733064325159614122541<37>
4×1061+239 = (4)607<61> = 7 × 317 × 77617 × 1220766047<10> × 612924789601<12> × 34487657633694537670282436602387<32>
4×1062+239 = (4)617<62> = 439 × 2239 × 28815742362400197896957<23> × 1569166600087413001300819789945651<34>
4×1063+239 = (4)627<63> = 3 × 192 × 1753 × 6331859 × 11756051 × 3144954831749268666509036019217232060380717<43>
4×1064+239 = (4)637<64> = 59 × 3187 × 23636512976150167494240077244124406058747371176572433798559<59>
4×1065+239 = (4)647<65> = 13 × 3257 × 3212129903383424909<19> × 19989480983695899517<20> × 16347891719476362306539<23>
4×1066+239 = (4)657<66> = 3 × 31 × 5039 × 14387 × 574491527225213614441127<24> × 114745669277609956730432560802689<33>
4×1067+239 = (4)667<67> = 7 × 71 × 5881 × 1784828569<10> × 93719273776643<14> × 9090431325161866944782368455014125813<37>
4×1068+239 = (4)677<68> = 1066909 × 1183607 × 163010492870627461<18> × 215907146524388774522290134897829064329<39>
4×1069+239 = (4)687<69> = 32 × 681884461 × 23865060060479977<17> × 396495750402225933427<21> × 7653553283872205657257<22>
4×1070+239 = (4)697<70> = 4926730643<10> × 902108267428665359744215357633556027236710542538268911090629<60>
4×1071+239 = (4)707<71> = 13 × 5337078668734634329<19> × 4710080431566072716387783<25> × 136001031347830981641911317<27>
4×1072+239 = (4)717<72> = 3 × 29 × 269 × 829 × 6105737023657<13> × 1734206622527139517<19> × 2163477999590275945648022334157549<34>
4×1073+239 = (4)727<73> = 7 × 17 × 503 × 95539 × 452953 × 56255990558387109151<20> × 30500006198335864399113763127933532163<38>
4×1074+239 = (4)737<74> = 318474122034643817267<21> × 16087673009815644698771<23> × 8674612874124734959085719480871<31>
4×1075+239 = (4)747<75> = 3 × 167462593 × 14792818727<11> × 63293417498652485122037<23> × 944863199392672797363393142349207<33>
4×1076+239 = (4)757<76> = 1231 × 224551273442508179<18> × 16078439900860692816061570559343532433703540534708770603<56>
4×1077+239 = (4)767<77> = 13 × 17140103 × 199462244701996178402125320880709923587903959433815467936149708015373<69>
4×1078+239 = (4)777<78> = 32 × 155461857903211<15> × 317651652408064631739489976318282593581590733333132436497467253<63>
4×1079+239 = (4)787<79> = 7 × 330557 × 695689 × 154284761 × 17895132357943216541482616007860575697275504203197549306557<59>
4×1080+239 = (4)797<80> = 173 × 2099117569<10> × 190062505378411<15> × 643929268352891011215802668067059466153870540627971121<54>
4×1081+239 = (4)807<81> = 3 × 19 × 31 × 109 × 367 × 499325131 × 10750559819<11> × 294490812461<12> × 14937159044237<14> × 266277278835205394274536351939<30>
4×1082+239 = (4)817<82> = 547 × 5175587 × 484358761 × 245440774827035107109<21> × 13205555334095977971866208531949114747333027<44>
4×1083+239 = (4)827<83> = 132 × 14149010261972083<17> × 1254197084055743132395106407843<31> × 14819683511755477450861580673140927<35>
4×1084+239 = (4)837<84> = 3 × 2797797591456876011424246142956417673613<40> × 52951703368578597476886647257050159171868873<44> (Makoto Kamada / SNFS for P40 x P44 / 0:24:34:10)
4×1085+239 = (4)847<85> = 7 × 3821153003<10> × 1444031129012855087<19> × 18663964228422159602479<23> × 6165163028988938972498489953959259<34>
4×1086+239 = (4)857<86> = 602489 × 525886213170863<15> × 140273803963828098092636622534268860118461490590448726434981800921<66>
4×1087+239 = (4)867<87> = 34 × 5486968449931412894375857338820301783264746227709190672153635116598079561042524005487<85>
4×1088+239 = (4)877<88> = 277 × 45852097667<11> × 190785878783222223847496556743<30> × 1834139133830248212705352073127614049703846231<46>
4×1089+239 = (4)887<89> = 13 × 17 × 683 × 2783041530127529778887003102701359211<37> × 105799792843783900881761366943351483484952985539<48>
4×1090+239 = (4)897<90> = 3 × 6469 × 16567740544429535339<20> × 36061466782505860845207791684893<32> × 38331198965195778059780642194143023<35>
4×1091+239 = (4)907<91> = 72 × 14113013 × 12502906914271062102469<23> × 514032599527744847385763696679272227973664754181406151173399<60> (Tetsuya Kobayashi / GMP-ECM 5.0.1 for P60 / May 1, 2003 2003 年 5 月 1 日)
4×1092+239 = (4)917<92> = 17456737 × 2545976630365940922661803545785472075591471902477790920745637884356305788673132008831<85>
4×1093+239 = (4)927<93> = 3 × 1367 × 803939 × 134804569960023769821559956770885333722273096236833434307735979328172948812840337873<84>
4×1094+239 = (4)937<94> = 47 × 2111 × 12323977 × 112398584633430683847566012263<30> × 32338484919758118612634834563608123684567825913264241<53>
4×1095+239 = (4)947<95> = 13 × 61 × 2577071006954495230832347<25> × 21747929154476565842284721824811136517272254888659733817783734548757<68>
4×1096+239 = (4)957<96> = 32 × 31 × 36556087 × 43576623512868547983746372234394953819144702265124569823424160787709772365267823226639<86>
4×1097+239 = (4)967<97> = 7 × 5689 × 1952169295457<13> × 4237190980009327<16> × 1311271598249807231<19> × 7252225042611394529<19> × 1418809424101885110912482849<28>
4×1098+239 = (4)977<98> = 84406720890721<14> × 95349967662273439<17> × 34189091575566325291424434411<29> × 161522244753246536081771987325408277283<39>
4×1099+239 = (4)987<99> = 3 × 19 × 7797270955165692007797270955165692007797270955165692007797270955165692007797270955165692007797271<97>
4×10100+239 = (4)997<100> = 29 × 151 × 257 × 16193 × 1560539 × 10578977 × 51129877067<11> × 290964809501288602763843<24> × 992998477224347848591617000816255844847351<42>
4×10101+239 = (4)1007<101> = 13 × 56467 × 68521 × 91529 × 49249848475427698337035978544737817<35> × 196016263333277923782134808765090643470976204849169<51>
4×10102+239 = (4)1017<102> = 3 × 71 × 4261 × 61549368528389241655159601<26> × 7956145973581354359778211118940338653949842089405723066608494362193879<70>
4×10103+239 = (4)1027<103> = 7 × 347 × 761 × 26625626800093<14> × 1702148423277574750578383<25> × 53052767409263789538840947670137340708606391718655564514577<59>
4×10104+239 = (4)1037<104> = 21597929 × 2057810470830070996364718322967190254419506816808428458323223696329608475166505290597281083961543<97>
4×10105+239 = (4)1047<105> = 32 × 17 × 30529 × 31351877 × 75819607 × 1230566645521<13> × 32528441595064707323258880024420846823380621192006495073226087906685149<71>
4×10106+239 = (4)1057<106> = 1051 × 4228776826302991859604609366740670261126969024209747330584628396236388624590337244951897663600803467597<103>
4×10107+239 = (4)1067<107> = 13 × 166887000701<12> × 351935082798001<15> × 4503507955644804203<19> × 12925225355676706832622079004565652768463034003221482150077173<62>
4×10108+239 = (4)1077<108> = 3 × 19283061813447239<17> × 111717295700712189283<21> × 68770125896209646369547265617454114877414976537620334392129585010765377<71>
4×10109+239 = (4)1087<109> = 7 × 10067 × 14543 × 4336759805846485704788578935493978972083633446191988753635184147396756662868719993567917346919561341<100>
4×10110+239 = (4)1097<110> = 3722048751013<13> × 50791985284199161397<20> × 426759831185079278484473800971407<33> × 550879614963323686411142900571230721730621961<45>
4×10111+239 = (4)1107<111> = 3 × 31 × 883 × 521161 × 10384890485719559756802765299073275364423055083979255804272865657280047744617918010800595943548428833<101>
4×10112+239 = (4)1117<112> = 366055379 × 343327993629629733089<21> × 35364007447671204288186064113527962117839959034532106284391741606719756019147030437<83>
4×10113+239 = (4)1127<113> = 13 × 24371 × 69466139 × 5454700829<10> × 70519868594158526969<20> × 5249829373183696131039648147508188044668268419283972688317362286978351<70>
4×10114+239 = (4)1137<114> = 33 × 35221427093<11> × 425390831411115278470313909736884176526672760838939<51> × 1098648188409286404055623855085835499684366825065243<52> (Robert Backstrom / NFSX v1.8 for P51 x P52 / October 1, 2003 2003 年 10 月 1 日)
4×10115+239 = (4)1147<115> = 7 × 31151 × 100604239397<12> × 21487165381601663<17> × 9428704838900802812077866710290422811426466342702862969302209554864150990654519461<82>
4×10116+239 = (4)1157<116> = 5503 × 189959999507<12> × 1099341692243<13> × 38674357771147440682520549259017704887982852351552412057787673026844211953309998887945849<89>
4×10117+239 = (4)1167<117> = 3 × 19 × 1231 × 66204757 × 1777581307<10> × 78685752353822148653<20> × 684021576519014507980855063976030811688491196318623286843444658933330702603<75>
4×10118+239 = (4)1177<118> = 131 × 24135829793<11> × 461327723010277<15> × 260320995139728525049660224279457187<36> × 11704832469823086637691345357336293323133053204008723291<56> (Robert Backstrom / GMP-ECM 5.0c for P36 x P56 / October 1, 2003 2003 年 10 月 1 日)
4×10119+239 = (4)1187<119> = 13 × 2904851 × 59471628752438670616249619<26> × 19789755840881663560317915115131648968223237798624342756089837574082088850255609042851<86>
4×10120+239 = (4)1197<120> = 3 × 197 × 165872452147028862235165595802809771100097<42> × 4533730868842496022424949057614008960220900910675713645935490384248932392561<76> (Robert Backstrom / NFSX v1.8 for P42 x P76 / October 3, 2003 2003 年 10 月 3 日)
4×10121+239 = (4)1207<121> = 7 × 17 × 6639593 × 438401876693435490907<21> × 96613292057610951858769<23> × 132806636187796977045445504794121128570911675366249477468192890010227<69>
4×10122+239 = (4)1217<122> = 59 × 307 × 443 × 38724067 × 65951181323624640961136714741<29> × 2168801608193138504453789233281218794333838743555722604933261077238570632769939<79>
4×10123+239 = (4)1227<123> = 32 × 173 × 8291 × 1332186658024507<16> × 25843829924594617084028835632197305791328725888731645724113149662031870596344130420227342317654365683<101>
4×10124+239 = (4)1237<124> = 47497 × 108769211 × 22388822797986383630299651141233757<35> × 77469452047874751157203011774981771<35> × 496002174955248190550584653054871856985403<42> (Robert Backstrom / NFSX v1.8 for P35(2238...) x P35(7746...) x P42 / October 4, 2003 2003 年 10 月 4 日)
4×10125+239 = (4)1247<125> = 13 × 337 × 138547 × 2886467073471779573<19> × 232915315929691318717<21> × 108913683686293971721473348342451916126763830365921587219513092763635314492681<78>
4×10126+239 = (4)1257<126> = 3 × 31 × 41999 × 150120037922403471536713775953886401041222117107<48> × 757978553889234672313937006633068559688306485645501161474076605128093703<72> (Robert Backstrom / NFSX v1.8 for P48 x P72 / October 6, 2003 2003 年 10 月 6 日)
4×10127+239 = (4)1267<127> = 7 × 163 × 2027 × 169399 × 99018853 × 5342546041337<13> × 1025135020107889<16> × 310540751992355666872792283560039<33> × 67359896535372727109158917536024002030634592109<47>
4×10128+239 = (4)1277<128> = 29 × 167 × 1089380311<10> × 6088023311<10> × 33554080415264464984837<23> × 41238403471049583271943186638411506254058959759349275806565578879067235202235666977<83>
4×10129+239 = (4)1287<129> = 3 × 148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148149<129>
4×10130+239 = (4)1297<130> = 8883006716943893644475417909344907<34> × 500331091269680979408317529035351352539747941022332894120443084124503050410247994884350346460221<96> (Robert Backstrom / GMP-ECM 5.0c for P34 x P96 / October 11, 2003 2003 年 10 月 11 日)
4×10131+239 = (4)1307<131> = 13 × 18553 × 20426924713689289932026769612825914663<38> × 9021048064362124993117342832940372935363592523525275595090424528258172760800647732872021<88> (Robert Backstrom / NFSX v1.8 for P38 x P88 / October 11, 2003 2003 年 10 月 11 日)
4×10132+239 = (4)1317<132> = 32 × 49382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049383<131>
4×10133+239 = (4)1327<133> = 72 × 6764350390863059925436511862677086220783892751<46> × 13408966508938081048570095474838694956550003507051030785291357085932413838671890549953<86> (Robert Backstrom / NFSX v1.8 for P46 x P86 / October 27, 2003 2003 年 10 月 27 日)
4×10134+239 = (4)1337<134> = 18133 × 236781359 × 10351429091053200221705555764803834428401825544357852283307718954932679951263239873497206647126319506904540696628204321101<122>
4×10135+239 = (4)1347<135> = 3 × 19 × 216472609621<12> × 36019665346193891107077037066019063824372497493345086742267572929827483246965457226970194043574263264439495532574951454651<122>
4×10136+239 = (4)1357<136> = 9871 × 58193 × 65313991739<11> × 3724084852015254931<19> × 498353078230155580753<21> × 63829676506205038399646660958722143763609548182701970334002054946727524836337<77>
4×10137+239 = (4)1367<137> = 13 × 17 × 71 × 48353 × 3873427810897206492826803544173207904097049309161228410649094089<64> × 15123348794966710220577957154576315517166316170179252829192622901<65> (Robert Backstrom / NFSX v1.8 for P64 x P65 / November 17, 2003 2003 年 11 月 17 日)
4×10138+239 = (4)1377<138> = 3 × 44403503 × 404075450621<12> × 9497885900756293280043187<25> × 869339834576011508691804586491725914322812628006295953294618776243409310347119094332455915629<93>
4×10139+239 = (4)1387<139> = 7 × 4288073 × 3675504634224769<16> × 9549855650125183090843901183<28> × 4218358540552039784453286049782528036435823588944633362225167141617658090477015279048351<88>
4×10140+239 = (4)1397<140> = 47 × 317 × 1734431 × 512469907150373<15> × 952940642357627103757683958791274463<36> × 3521835903730148463940397457798746847161872306085763962734545904806276307580737<79> (Robert Backstrom / GMP-ECM 5.0c for P36 x P79 / October 6, 2003 2003 年 10 月 6 日)
4×10141+239 = (4)1407<141> = 33 × 31 × 2273 × 736429 × 317220836364304402303411400548603021723077816096607228812647436643233749219614348041473498172791968163166649916594698858533424543<129>
4×10142+239 = (4)1417<142> = 18661 × 2912371954729247<16> × 81777857587362906276861166088055666369194547205574293387852677598223695905930362236560266131930943509244397718091062306541<122>
4×10143+239 = (4)1427<143> = 13 × 180844134716075035203997990871394431806442451443269<51> × 18904696158218976770356643450736744237863202773063745264948680236412794860271753591597064351<92> (Greg Childers / GGNFS 0.53.3 for P51 x P92 / September 4, 2004 2004 年 9 月 4 日)
4×10144+239 = (4)1437<144> = 3 × 1709453 × 153264557 × 3836919551<10> × 147371883734310683228617177624247030399877848384704634855888077658235804527222065269860359536291224561801489202152581619<120>
4×10145+239 = (4)1447<145> = 7 × 57582146900107672708051209481<29> × 212094783166834350629892681988789255277<39> × 51987819487280784914261973215411773441379456453962632550440615658756439459333<77> (Robert Backstrom / GMP-ECM 5.0c for P29 x P39 x P77 / October 7, 2003 2003 年 10 月 7 日)
4×10146+239 = (4)1457<146> = 7907 × 98563 × 731403688389372487999<21> × 563101656997933224378611<24> × 138467508506526175010355833277948916308587427142343818456186115998496518521311334152285789603<93>
4×10147+239 = (4)1467<147> = 3 × 97 × 5953 × 256559801171285288277327290836896147222223825720979542755273955517789952823142361121132978344364442684444208409427366861979229303336874499989<141>
4×10148+239 = (4)1477<148> = 3093043 × 2409926839<10> × 596249002957830755855305952975225403291609473392347440034675707611483004472158842519369854883101774044766040801774976024468729583811<132>
4×10149+239 = (4)1487<149> = 13 × 1019 × 119221957896880184054806821523081<33> × 28141270188198395074351233769235813820403745564661352369324584369745461439974404727949685505887823518125498072921<113> (Robert Backstrom / GMP-ECM 5.0c for P33 x P113 / October 31, 2003 2003 年 10 月 31 日)
4×10150+239 = (4)1497<150> = 32 × 14797 × 158129 × 2334639100316582423542633998614479963495682843452583<52> × 9040033073803432887815150453074684725159462725714073113819607020985016556962672188533077<88> (Greg Childers / GGNFS for P52 x P88 / September 8, 2004 2004 年 9 月 8 日)
4×10151+239 = (4)1507<151> = 7 × 149 × 1310797 × 16076983247191394230946741155197657291883<41> × 202205598358382954832611424841846506881013779686739839063387159950853143131222498975167645613503455179<102> (Sinkiti Sibata / GMP-ECM 6.0 B1=10000000, sigma=1770116776 for P41 x P102 / April 24, 2005 2005 年 4 月 24 日)
4×10152+239 = (4)1517<152> = 594453599347<12> × 18888841427341<14> × 192426221843740554519959<24> × 6545315710328438844985500344313439462073<40> × 3142674111334242877001354822741675047074385195768806298906117223<64> (Anton Korobeynikov / GGNFS-0.73.3 gnfs for P40 x P64 / 17.56 hours / March 5, 2005 2005 年 3 月 5 日)
4×10153+239 = (4)1527<153> = 3 × 17 × 19 × 81017 × 241784369429<12> × 1470703507530817065767950099767404004845089349<46> × 15920774731201487385655812078291835754560386012725533646207019291393849532640008894695559<89> (Sinkiti Sibata / GGNFS-0.77.1 for P46 x P89 / 41.25 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / January 29, 2006 2006 年 1 月 29 日)
4×10154+239 = (4)1537<154> = 821 × 129641 × 2910860153<10> × 56086150620462803846741<23> × 10809513037137616553126857<26> × 23661858219233639076934261018125730594588648150819233863665210259805080376176062985347807<89>
4×10155+239 = (4)1547<155> = 13 × 61 × 148385991234646868255677763169400682719601527549176821<54> × 377703833218830785744902903453732714767953802089122910383042080301772785279239335742045411173229499<99> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P54 x P99 / 30.59 hours on Cygwin on AMD XP 2700+ / April 2, 2007 2007 年 4 月 2 日)
4×10156+239 = (4)1557<156> = 3 × 29 × 31 × 233 × 1162061 × 658237800790060433128895853813992111237171477712259462648973<60> × 924631893046383441534389809744737352040680519541286830846552261752181915098853210999<84> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp for P60 x P84 / 33.77 hours on Cygwin on AMD 64 3200+ / April 14, 2007 2007 年 4 月 14 日)
4×10157+239 = (4)1567<157> = 7 × 277 × 18803 × 435855073937907821<18> × 279685802182260358285757119531485029810472497860437611759585231096621727719597481374048348871839694348141448184730804992176829601571<132>
4×10158+239 = (4)1577<158> = 1231 × 5101 × 10222013 × 16128867583691<14> × 93923274949627<14> × 457078267711613687290902161752004578947907557707533984495461912962907327680014611510461137955675060732870251195599857<117>
4×10159+239 = (4)1587<159> = 32 × 73331 × 12788459 × 52658580714651112983750010114176991824709437971657614122684533749267300837506463646656371945363227444962880283488182312421321238636780773108788727<146>
4×10160+239 = (4)1597<160> = 55871 × 16258533507335326759<20> × 4892712161091195907091326332880287117441296662273458879526092857616124318973224487841137569322861317203435390789429320335579109733237623<136>
4×10161+239 = (4)1607<161> = 133 × 132253376785665958621<21> × 208122669820059734018270507907490349851<39> × 734955876882058340201805409936009321630527412736093444708338848258488834565508219522142315629339181<99> (Robert Backstrom / GMP-ECM 6.0.1 B1=2936000, sigma=2115102082 for P39 x P99 / December 14, 2007 2007 年 12 月 14 日)
4×10162+239 = (4)1617<162> = 3 × 191537 × 36201871247<11> × 14267717847005813507700165288034158445726684150241889062913896709923<68> × 1497469599792136047698907928447361359099204601762726546842329109356470216353817<79> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.26 for P68 x P79 / October 11, 2007 2007 年 10 月 11 日)
4×10163+239 = (4)1627<163> = 7 × 14653 × 24469 × 64811 × 81929 × 2036542457<10> × 1630218827711<13> × 1296468959746039<16> × 177398463287035313968056151<27> × 436756065516448467442281333737017520714758168538104180331337529631398901862774229<81> (Kenichiro Yamaguchi / GMP-ECM 6.0 B1=3000000, sigma=3826037145 for P27 x P81 / May 4, 2005 2005 年 5 月 4 日)
4×10164+239 = (4)1637<164> = 12479 × 58510372933963<14> × 178177201699221593983<21> × 18554403610873627860756559<26> × 78023895748638867893972217224252601733553999<44> × 235981559314942106709930447382847896871156692971850502237<57> (Kenichiro Yamaguchi / msieve 0.88 for P44 x P57 / 50:01:02 on Pentium M 1.3GHz / May 17, 2005 2005 年 5 月 17 日)
4×10165+239 = (4)1647<165> = 3 × 22861 × 13947484289<11> × 15206050833373<14> × 30555450039070478417476472385777004282428762464629524972192676696532306208041823380752855784763448905352000279576437347767225919970090397<137>
4×10166+239 = (4)1657<166> = 173 × 4549 × 15643 × 227729 × 970259 × 23118371 × 258609421979814579149841551730853<33> × 273292557681194023226924285723337331180267943187476708699991416925411391320101221509571772342056887933889<105> (Robert Backstrom / GMP-ECM 6.0.1 B1=584000, sigma=3688070583 for P33 x P105 / February 8, 2008 2008 年 2 月 8 日)
4×10167+239 = (4)1667<167> = 13 × 113 × 2137 × 1096957 × 214937561 × 98086756633<11> × 1250598496272460297895511064721<31> × 489509322601012063383111734967112161453194018253930855634754706926333655720002913346029020711375571104959<105> (Makoto Kamada / GMP-ECM 5.0.3 B1=58570, sigma=1400938555 for P31 x P105)
4×10168+239 = (4)1677<168> = 34 × 1265197 × 1058672780199082273664589389440212686058586452944274704237975222290582762325807<79> × 4096496258940085111741497387505341221216333433858971073571460415594977424825412453<82> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.36 for P79 x P82 / 70.39 hours on Cygwin on AMD 64 3400+ / June 13, 2008 2008 年 6 月 13 日)
4×10169+239 = (4)1687<169> = 7 × 17 × 57349 × 503852761342782171346683824703620971518120723133<48> × 1292531178579433361975754521183369234349970232633887731714815503149502104258374903219488361379931169871046875018089<115> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.36 for P48 x P115 / 68.29 hours on Cygwin on AMD 64 X2 6000+ / June 23, 2008 2008 年 6 月 23 日)
4×10170+239 = (4)1697<170> = 193 × 549040020458710771002201900655139572384963724205511693<54> × 419426794015259711436313029497443646256396503285623169529962875069579148740583046787001583894004049064540008475803<114> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P54 x P114 / 100.59 hours on Cygwin on AMD 64 3200+ / May 31, 2007 2007 年 5 月 31 日)
4×10171+239 = (4)1707<171> = 3 × 19 × 31 × 251524869521473935735395837263409419606363579198893290574105514682764258316040998553732000251524869521473935735395837263409419606363579198893290574105514682764258316041<168>
4×10172+239 = (4)1717<172> = 71 × 55733 × 100733 × 423599224073048071<18> × 5580494907322836989<19> × 4716795766194983922712252054449769582991918726709747088403781844297337457386268629115997839053233024126545332837857916209627<124>
4×10173+239 = (4)1727<173> = 13 × 547 × 3457 × 7742677 × 92344480022803<14> × 17066676439984957<17> × 11547865405892626687884211439681<32> × 12830236827967471491637490179825912863260274126012053520529623406724702467484496830797955662017043<98> (Robert Backstrom / GMP-ECM 6.0.1 B1=882000, sigma=1495608592 for P32 x P98 / February 14, 2008 2008 年 2 月 14 日)
4×10174+239 = (4)1737<174> = 3 × 431698729585373966167026238230882951903861668583514905584774408843<66> × 343174853190875443246946483687163515522963880644358945766137050568648583698244978599326968646362907761905343<108> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon for P66 x P108 / 219.68 hours on Cygwin on AMD 64 3200+ / July 9, 2007 2007 年 7 月 9 日)
4×10175+239 = (4)1747<175> = 74 × 151 × 4077068417<10> × 912028673482967<15> × 18287204296526384115739261382729<32> × 1474496589385636624872422204643590358428021<43> × 122264617559167997611060160283499497988751361155452737911400912906085147<72> (Makoto Kamada / GMP-ECM 6.0.1 B1=11000000, sigma=2183042982 for P32 / June 1, 2005 2005 年 6 月 1 日) (Sinkiti Sibata / GGNFS-0.77.1 gnfs for P43 x P72 / 66.44 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / April 27, 2006 2006 年 4 月 27 日)
4×10176+239 = (4)1757<176> = 190797617 × 232940249166971747055124092270211343595787385774553171932144437864988871661035705935700677249257491745530786395746464928041760838367517160575671364094890369854275718991<168>
4×10177+239 = (4)1767<177> = 32 × 88771 × 34257828589<11> × 382118227297<12> × 185328018246049181<18> × 74350271904345532210869653201<29> × 3084058668005186409866574388041834948237746363854798987149474877501583105706865140518254798826491068901<103> (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=645271091 for P29 / February 21, 2005 2005 年 2 月 21 日)
4×10178+239 = (4)1777<178> = 3739 × 31239146595462079<17> × 21547953973449457285963310887<29> × 1548065010359119640600075273692710581629117<43> × 1140689966840456065098945861599843349913983470693969623741142865996909234661412137064953<88> (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=4075950993 for P29 / February 19, 2005 2005 年 2 月 19 日) (Dmitry Domanov / Msieve 1.40 snfs for P43 x P88 / January 31, 2011 2011 年 1 月 31 日)
4×10179+239 = (4)1787<179> = 13 × 1129 × 1068209353<10> × 4580453449268690402279557<25> × 4350096229342528260116893990630301077<37> × 142271029265416575875338086225461356162340830827056279182201282910066824179702907590984231521837085273683<105> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=454280835 for P37 x P105 / August 6, 2008 2008 年 8 月 6 日)
4×10180+239 = (4)1797<180> = 3 × 59 × 317128349 × 971654996231<12> × 66018002849107<14> × 178139006085760561<18> × 11757062412922805745713059<26> × 977491832312192896389896625176726445871<39> × 60292555656044812428976587194559990987738290050680487578282923<62> (Anton Korobeynikov / GGNFS-0.73.3 gnfs for P39 x P62 / 12.38 hours / March 3, 2005 2005 年 3 月 3 日)
4×10181+239 = (4)1807<181> = 7 × 18047 × 19717 × 547499 × 5285119826498519321<19> × 276312463679449103362613629120034638570861539160906344109227556153<66> × 2231695529175186567760002631248211138386955421489181601690387183086228510522146417<82> (Dmitry Domanov / Msieve 1.48 for P66 x P82 / January 28, 2011 2011 年 1 月 28 日)
4×10182+239 = (4)1817<182> = 87251 × 125276343956978792639<21> × 43061226561173338228741117<26> × 81708507919317964448492982739<29> × 1155644673982122686010447962349542259496922676903598271093231559319744504340389927728020934002786216621<103>
4×10183+239 = (4)1827<183> = 3 × 659 × 43171433 × 167699656420725837272625731399311336199588874148496993519579<60> × 31051470741734126361167084603612732961197648742830591970432979567919377947554573102634749940250284671722830406573<113> (Ignacio Santos / GGNFS, Msieve snfs for P60 x P113 / May 10, 2010 2010 年 5 月 10 日)
4×10184+239 = (4)1837<184> = 29 × 178817719547<12> × 27141025341743284700368084141669831618003158364834023279064772256248327491639501<80> × 31577859013909240200754952411524587838249400419038875187037160175417454226331402675555518869<92> (Ignacio Santos / GGNFS, Msieve snfs for P80 x P92 / May 19, 2010 2010 年 5 月 19 日)
4×10185+239 = (4)1847<185> = 13 × 17 × 389 × 478739 × 1620692449<10> × 5977201780407416716628944479077932997<37> × 111475203220689472471259054366200185313680037945724181981551672761488789114394997997266280462007290648882851087167834564033140689<129> (matsui / Msieve 1.48 snfs for P37 x P129 / January 17, 2011 2011 年 1 月 17 日)
4×10186+239 = (4)1857<186> = 32 × 31 × 47 × 179 × 12743 × 18541 × 1519769856019001<16> × 2375090177092212015679433<25> × 118270750950320247085810333307<30> × 1877250672708337815991348552500624443658145975176294067599617799874145110659688921540769920338722450837<103> (Robert Backstrom / GMP-ECM 6.1.3 B1=980000, sigma=3394528185 for P30 x P103 / February 16, 2008 2008 年 2 月 16 日)
4×10187+239 = (4)1867<187> = 7 × 2121683 × 6310304191949<13> × 4705808395185739<16> × 10077537198693264100583536999965332835841240324372155232849987407466008105300655648886729584761990298830931951574244484972674086541201481094432981216317<152>
4×10188+239 = (4)1877<188> = 425731706854363127<18> × 294759853636511703499898037163218403742081692616212262909<57> × 354171127250494697180898759196346128541697002970842984056448602744138266645495679130811180273572985212316324433229<114> (Ignacio Santos / GGNFS, Msieve snfs for P57 x P114 / June 8, 2010 2010 年 6 月 8 日)
4×10189+239 = (4)1887<189> = 3 × 19 × 109 × 8867 × 8067508280021574695368013296560581816918593067135530885881648536182186716230855936469614691105222596479981963633088521365885059640033145438443551439851666436309052116000628208802257<181>
4×10190+239 = (4)1897<190> = 9569335559270336914133<22> × 2204456588025119545885777787<28> × 914614705542996095283314411688089<33> × 230354111071823462818299073248460216708575614431593821351666507826249002338559777821243718681313328757074913<108> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=2831025570 for P33 x P108 / August 3, 2008 2008 年 8 月 3 日)
4×10191+239 = (4)1907<191> = 13 × 32321 × 87433 × 476401 × 1103936514897427727<19> × 2300367361569504102365661382162448012461744443490581252084282995237886251820056817725274489529242717173287873328688818398293734888359282093279419678716870429<157>
4×10192+239 = (4)1917<192> = 3 × 48611 × 6531632829179<13> × 547212943771526343714089726405265284554468421<45> × 34282718668213406423247137977911535706601495681608641369<56> × 24871861593812651693792165120591109219085526282995068841143556459801995529<74> (Ignacio Santos / GMP-ECM 6.2.3 B1=11000000, sigma=1413471672 for P45 / April 15, 2010 2010 年 4 月 15 日) (Sinkiti Sibata / Msieve 1.44 gnfs for P56 x P74 / May 5, 2010 2010 年 5 月 5 日)
4×10193+239 = (4)1927<193> = 7 × 1481 × 346417 × 3232050862911078001246259267<28> × 51583019853496735903645964800750877<35> × 7423013265080590008491647917250829488752628024056283837902479298974147109134922114321978937756025932141670360318023197047<121> (Ignacio Santos / GMP-ECM 6.2.3 B1=1000000, sigma=3159666292 for P28 / March 25, 2010 2010 年 3 月 25 日) (Ignacio Santos / GMP-ECM 6.2.3 B1=1000000, sigma=3645311426 for P35 x P121 / March 25, 2010 2010 年 3 月 25 日)
4×10194+239 = (4)1937<194> = 485088184103<12> × 2668267451458286527361<22> × 14364084537772869990106871<26> × 2390504000325057694634663290628184041748315175435858572277651544406623017158195735845546076333911264032742518627980711497761106733826879<136>
4×10195+239 = (4)1947<195> = 33 × 34219021093<11> × 1171609496720681<16> × 1598056968854189900114035543585395251489097872706741191576600318177<67> × 256927739335154901832251372331137801300180294966756495116326824661909049156739369236063369560073118721<102> (Dmitry Domanov / Msieve 1.48 for P67 x P102 / February 3, 2011 2011 年 2 月 3 日)
4×10196+239 = (4)1957<196> = 719 × 101869 × 12859331 × 11131671840872570374351<23> × 1273179380551084940837663668915711<34> × 628871623561285719056205219077612865623326549296386361857419<60> × 529439309389438291105821852449436076666688296428276456606245431813<66> (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=1725878624 for P34 / September 2, 2010 2010 年 9 月 2 日) (Erik Branger / GGNFS, Msieve gnfs for P60 x P66 / September 8, 2010 2010 年 9 月 8 日)
4×10197+239 = (4)1967<197> = 13 × 67061420451949139<17> × 3875850410397358728150007205989<31> × 65992559819048532891678510313063436073632082918437309<53> × 199314731864314201471143591230909055055381840222515134345894141184208753717635646229442594062921<96> (Shusuke Kubota / GMP-ECM 5.0.3 P-1 B1=50000000, B2=7260750615 for P31 / January 31, 2005 2005 年 1 月 31 日) (Dmitry Domanov / Msieve 1.48 for P53 x P96 / January 28, 2011 2011 年 1 月 28 日)
4×10198+239 = (4)1977<198> = 3 × 113759 × 8313869 × 2347393571<10> × 6070281604678056040776619<25> × 10992906515795380369777467280822803904102960984601290096706822630336813741743675723736680123183567651282275041284891925969761126596643078481188633480631<152>
4×10199+239 = (4)1987<199> = 7 × 1231 × 14225762137075170435338246532576567317<38> × 36256497391523557391150836153499812526265014545716861850062848979279699883581750510325625228713377300801607790879317559258903710821964811855003806638790958123<158> (Andreas Tete / Msieve-1.39 ECM for P38 x P158 / 73.27 hours on Core 2 Duo T8100 2,1GHz Windows Vista 32bit / February 17, 2009 2009 年 2 月 17 日)
4×10200+239 = (4)1997<200> = 978085421263<12> × 773916339569145261630900729032811297529<39> × 58714677570858605919926571866071578635546143881947982772187870528788269392408355299585771649185909401322611507057744072403383339520391069969811575161<149> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3585100652 for P39 x P149 / December 24, 2010 2010 年 12 月 24 日)
4×10201+239 = (4)2007<201> = 3 × 17 × 31 × 68351 × 4112829814364783835489752211555731765636122200354203278499307449327322469575107531040819579883914535359442031462615468429636101989908495489951539852684954884709211195136327039329003989762636037<193>
4×10202+239 = (4)2017<202> = 2266683581<10> × 173595061619414122619<21> × 1076829812955082372842703<25> × 10489194677772547236193734750652976855737620704199863888200683065894065918237719093961907590080804936252235054009129530606116801292871591694077016191<149>
4×10203+239 = (4)2027<203> = 13 × 75185831359395097657<20> × 49415469640025457256097<23> × [920185098717476251604089085442383322329545393071445159461833707071912726781201867385134983446499269032297214068023398477286191209314674546094358572838752326611<159>] Free to factor
4×10204+239 = (4)2037<204> = 32 × 10891 × 1069007974652412661299794973020534361341196419<46> × [4241566393301224975038566101599958910858708750140079140521569653189506373484339336959930183368340312007560970239656876199020907453379954811478404563307527<154>] (Wataru Sakai / GMP-ECM 6.3 B1=11000000, sigma=3369821387 for P46 / October 26, 2011 2011 年 10 月 26 日) Free to factor
4×10205+239 = (4)2047<205> = 7 × 619 × 1439 × 184117 × 966203467 × 9352762191292205437<19> × 625963683978802302865967<24> × 6946646549460017847658117759<28> × 55784705997064293764813222535375430864564821029<47> × 1766144108932196328359872046907674356690185136145307685998420979091<67> (Serge Batalov / Msieve 1.49 gnfs for P47 x P67 / February 24, 2011 2011 年 2 月 24 日)
4×10206+239 = (4)2057<206> = 223 × 487 × 23929 × 150039865610231<15> × 1801899989149276324439698657<28> × 63258917918591008621359493549540521596875377218247205666988730277148548669304033199680917983893833168997494604759048734722374163543780978364757857919139529<155>
4×10207+239 = (4)2067<207> = 3 × 19 × 71 × 953 × 977 × 585997 × 82812409 × 204037331 × 74241282671<11> × 230845921348955352373<21> × 474961849519586529799<21> × 13984315016010330049679737289903699<35> × 104647478956087602086035195485638974148991524746397206006802424441701236085405766534319249<90> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4151556755 for P35 x P90 / February 24, 2011 2011 年 2 月 24 日)
4×10208+239 = (4)2077<208> = 163 × 311 × 1106265019134941<16> × 2838275732100041685523<22> × 114056539552972142738855725701084193039<39> × 244813596224120437885472364977073275085478086778546600818314498530838859475036905754668167098693128019916838714974306757042911227<129> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=375628957 for P39 x P129 / March 24, 2011 2011 年 3 月 24 日)
4×10209+239 = (4)2087<209> = 13 × 173 × 4524673 × 4367579595885079830447279598706731698575957026498086835102547830021666348297247714883783085506637645452891411156802567983255752154004436481199477986104903067595235651492299523258881227571096640918311<199>
4×10210+239 = (4)2097<210> = 3 × 11075203 × 8286823840601<13> × [1614196588444929356801645132399344912516702609625959924604451885650674209380823354398441759214487071874217663697208992638457774970542216121856267191193168534209832063863420000682354661512383<190>] Free to factor
4×10211+239 = (4)2107<211> = 7 × 661 × 1423 × 106341661 × 478940327053<12> × 4573364032430662575962677<25> × 2897960519179552751614032250235723402099885805240464671695617137120098729819750370143321372475183105613497950125183848137560942866667040615394640198131861488727<160>
4×10212+239 = (4)2117<212> = 29 × 1021 × 2879 × 25672051 × 151410771348589<15> × 8698765315341859<16> × 3713882271410118625130233<25> × 663732894024001657294746468900476869602909499739<48> × 6255408127036446203433644487083682283504911241156789958388764068313871840570376983759432340471<94> (Robert Backstrom / GGNFS-0.77.1-20060513-nocona, Msieve 1.44 gnfs for P48 x P94 / November 1, 2013 2013 年 11 月 1 日)
4×10213+239 = (4)2127<213> = 32 × 181 × 6703 × 15739 × 58937783808744683<17> × [43878951498823684378213624026801025558370670593080761911548909480016312060953237082863403819096883703430621552495743356743396956479707657967525895526850425458363101175144999147884265213<185>] Free to factor
4×10214+239 = (4)2137<214> = 3413 × 4027 × 38860099919<11> × 123454449179181713178647<24> × 67404502089728919737414094226207121873817618792904970744187272154352172073675350280074888375220345538278601105411986101642327864606094877205535328852789760108579642934000929<173>
4×10215+239 = (4)2147<215> = 13 × 61 × 131013149 × 298290193 × 6169862874559<13> × 58319742784669367951<20> × 3985651503308104945782789928998432373752343267235282651064340868944285192816954085048294058836525940292933340208977910360532576191104691348330067758318567770413283<163>
4×10216+239 = (4)2157<216> = 3 × 31 × 491966411956969<15> × 12687916334779319951<20> × 7532639335812268243840961431106514043531609<43> × 101639284732750733986790765444213327908768199121766646306911302198304348197719903006359767802768264202522145096994922166610453736641837349<138> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=321247498 for P43 x P138 / October 8, 2011 2011 年 10 月 8 日)
4×10217+239 = (4)2167<217> = 72 × 17 × 19581275047<11> × 4838097973245591194740579312665593379006956863354556859303189403<64> × 15249414487256004731065018989859567159901284302564364353809464295017<68> × 3693207297823602920188301246066868078511803647466619723887206768840808947<73> (Bob Backstrom / Msieve 1.54 snfs for P64 x P68 x P73 / October 10, 2019 2019 年 10 月 10 日)
4×10218+239 = (4)2177<218> = 197 × 864047 × 5819081 × 391510372937<12> × 114608337714893327796577566716543299300117223404580061971519020221470903668809598746166502935038887114371546693687757557928389154806391506746472153489256296935412807781924028950924204127222989<192>
4×10219+239 = (4)2187<219> = 3 × 317 × 1527485556422368332133947853921066807702943461603827574501803569<64> × 305956618679496815090742951129307655706694034370313913039610622835124868357627791678927643579924581900447038610697929382553410443531271160973090863811113<153> (RSALS + Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve SVN r719 for P64 x P153 / June 19, 2012 2012 年 6 月 19 日)
4×10220+239 = (4)2197<220> = 857 × 77863 × 1378057 × 175631568817444068699547<24> × 10861175156820815722739331304591338258018176031648871302376614058671313477024443207503243<89> × 25337219134574972631643338438745786615745781842059307766505823174684994369678943803717550479361<95> (Erik Branger / GGNFS, NFS_factory, Msieve snfs for P89 x P95 / August 23, 2017 2017 年 8 月 23 日)
4×10221+239 = (4)2207<221> = 13 × 2765094465406799<16> × 2021312762955519366784463<25> × 321742359232991679639643557799<30> × 2260336005204290414287240769099791204949<40> × 841103409372334465601487624407001699472676072319376985706549258850832507968986833784868697221761957650739232537<111> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=3039844809 for P30 / February 20, 2011 2011 年 2 月 20 日) (Serge Batalov / GMP-ECM B1=1000000, sigma=1401678322 for P40 x P111 / February 24, 2011 2011 年 2 月 24 日)
4×10222+239 = (4)2217<222> = 33 × 16460905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683127572016460905349794238683127572016461<221>
4×10223+239 = (4)2227<223> = 7 × 547902661 × 1158820133784009712329031077512205987688971335221594991733249922873864123530731738717791919311230786157169111896174263918449778499835821970273147906687452501047299412405363223149085298785644920667615875880250416661<214>
4×10224+239 = (4)2237<224> = 1327 × 5855537 × 7060073 × 2427864713050147807<19> × 333692276530323689267758889974789351678877707698992075553365324828548271014926714629159730369079480952076984831964160931830253191127655762664110548421371697036804904622214088671528737656423<189>
4×10225+239 = (4)2247<225> = 3 × 19 × 49564553321825714955173<23> × 7674823575551346333098301014633<31> × [20497600697051715789508467687921628652946920938521166984785579053965902230536723574258710285316899974897619856269415734290871911180647922337879420868897373756005280590419<170>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1496564407 for P31 / February 24, 2011 2011 年 2 月 24 日) Free to factor
4×10226+239 = (4)2257<226> = 277 × 1009321 × 956083212198043<15> × 28206638591597324139379237<26> × 320454872323902551228487881<27> × 430666821932885567814288683969<30> × 2030109547272273805364900012054941349925949926460730017<55> × 2103941250956739424450896329118475264934284756895827227823786901077<67> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=3617263802 for P30 / February 20, 2011 2011 年 2 月 20 日) (Serge Batalov / Msieve 1.49 gnfs for P55 x P67 / March 6, 2011 2011 年 3 月 6 日)
4×10227+239 = (4)2267<227> = 13 × 886690507453782393199<21> × 3316978961655854534153195003688101181773<40> × [1162410042951082853969973586800067402242363622954077562914528831740710242343444344922415802345636535570579323655356701330810668456729435505409801965507095820389830697<166>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2512348465 for P40 / September 11, 2011 2011 年 9 月 11 日) Free to factor
4×10228+239 = (4)2277<228> = 3 × 541 × 641909044541<12> × 185259698487964361753<21> × 2302737927931321136504411952112325251101298707986021081235159793537357254856582460132959677622223017400623538821448426420843211706631940015911472084767443614978278870308760419004545495043739893<193>
4×10229+239 = (4)2287<229> = 7 × 107753432782479605029873<24> × 3549520132436187635195981874091<31> × 40652763128185333162077869162640072762599738915124517<53> × 229646796052161277890120344282396129558668168803225205547<57> × 177814930030672949096761202351679581437822710278504747331923508653<66> (Makoto Kamada / GMP-ECM 6.0.1 B1=11000, sigma=649166371 for P31 / February 3, 2006 2006 年 2 月 3 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=468313029 for P53, nfs for P57 x P66 / September 27, 2011 2011 年 9 月 27 日)
4×10230+239 = (4)2297<230> = 117531373 × 378149623457937860084766000686850177819708142475664301517556886231937786044960475739906862522949037993833735307801130209245870414909935957648043849912690498769587626994236206569665823987646638352845962621779671070842033339<222>
4×10231+239 = (4)2307<231> = 32 × 31 × 1787 × 28323549773<11> × 584391928849316960834373755456346674707696331<45> × [53856339826156721666139855385587817561889491774255084117034926169035095214711042042596492977986843128651914250465680682331155712556309125854563650767218456925077181144053<170>] (Dmitry Domanov / GMP-ECM B1=43000000, sigma=3323301268 for P45 / September 26, 2011 2011 年 9 月 26 日) Free to factor
4×10232+239 = (4)2317<232> = 47 × 45496937 × 3974414403153952122433<22> × [522954996042221170716811804581868211546585032094747560935615525915614243342805629956805524040191054519455386114928971209394591989983275138528273288262782360963354483718862816093640318292778717122563881<201>] Free to factor
4×10233+239 = (4)2327<233> = 13 × 172 × 409 × 5381 × 178001 × 149917447 × 2931443527319<13> × 37657261523551<14> × 1520579486729087<16> × 1199985429503128425311624783155823403613450210877575890803862549365082181371581973261353707186009092824811081446708291133460605918890131805962944605350955848128060920039<169>
4×10234+239 = (4)2337<234> = 3 × 7197593714499944415400713296228423797337881577928619705636601224591934481780615391723734416573528050145659630547797<115> × 20583010659478547348971480934725675800429106951065856524841478987937960007840545342132531205923310072349652696111534817<119> (NFS@Home + Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve for P115 x P119 / January 6, 2015 2015 年 1 月 6 日)
4×10235+239 = (4)2347<235> = 7 × 481181 × 1516357 × 11319293 × 111116733519527<15> × 427621083909751<15> × 11225330813651593<17> × 278803581453707408060017845286669<33> × 6848417295296577992049315970855790729<37> × 467651787396932012324144965925280579047<39> × 161414045489448785645140306134984506155356577844905764766138823<63> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=4027528892 for P33 / February 20, 2011 2011 年 2 月 20 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2766205295 for P39, B1=11000000, sigma=372211901 for P37 x P63 / February 27, 2011 2011 年 2 月 27 日)
4×10236+239 = (4)2357<236> = 3709 × 2893609113801317<16> × 12821732971550728178314180605937<32> × 322978830042188966775485192748422633915889120372414718057125216653483550203821097546034700115896488154362501023810971635987378345774560113692463261844341705317702837155267681683038655327<186> (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=1249349021 for P32 x P186 / February 21, 2011 2011 年 2 月 21 日)
4×10237+239 = (4)2367<237> = 3 × 13428135418373402886630148134834896621<38> × 18832847128620735848271547853592995086588206581<47> × 585820457589565142038573829209962111465174246685987311601262566825765932331251897260439095640368828573827522287947809895634544625575779498648402575350949<153> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4020258548 for P38 / February 24, 2011 2011 年 2 月 24 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1352069305 for P47 x P153 / February 25, 2011 2011 年 2 月 25 日)
4×10238+239 = (4)2377<238> = 59 × 169761829 × 133254919138951<15> × [3329984212583301292619667689074149455447423599592890703211233128105319651651767927667606413363526162595617001967745950764011708139827801717991006614040102372701687506778466008146474684024093807501186747907966395727<214>] Free to factor
4×10239+239 = (4)2387<239> = 132 × 1931 × 42767 × 5000709258003094026079929815167<31> × 723223372071441657148035048929900783840993<42> × [880512770116115583149165117519001863170434943978664810758938630680185702933098260274495026241193970130653962303883143179084647146499185466744860290384971749<156>] (Makoto Kamada / GMP-ECM 6.3 B1=1e6, sigma=3592730819 for P31 / February 21, 2011 2011 年 2 月 21 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=1209544664 for P42 / September 25, 2011 2011 年 9 月 25 日) Free to factor
4×10240+239 = (4)2397<240> = 32 × 29 × 1231 × 1721353573<10> × 528145550809<12> × 1349436015749<13> × 100943775150353<15> × 579750300729407<15> × 406761978052799346188165823062399<33> × 47367671670158789233008224875504601203605298693367012704366265330088806297986181613392322192779311184174918905859993832571779294651598260061<140> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=3658169993 for P33 x P140 / February 24, 2011 2011 年 2 月 24 日)
4×10241+239 = (4)2407<241> = 7 × 653 × 2969 × 3187 × 102757611161087813492294625400511768067750544691246843365176833787106989337137555348084614412598198923846231140790589271070214093807416965880664668813531172769774907857208519243544376574828456721951241701874178732446031503647349719<231>
4×10242+239 = (4)2417<242> = 71 × 60917149 × 11503948319<11> × 44342439897253<14> × 519133397546636945223252728933<30> × [38803784690845529774385236984764275884514422206223819921080410523884935395227743725622205330638965767510273540181571876668179658310331062138236921991254876511838776348588996584603<179>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2537341986 for P30 / February 24, 2011 2011 年 2 月 24 日) Free to factor
4×10243+239 = (4)2427<243> = 3 × 19 × 97 × 5569771 × 42117295107110698772197<23> × 342667629761110701145425450349425390776001330053934745787278431227391958894412984998218078904314266254792261092877430235907999171754567149715401637809381854451855806955075266300658605768536418688458319156356289<210>
4×10244+239 = (4)2437<244> = 2844641 × 8700456466859<13> × 11685566679439<14> × [15367322318418399365966257917770510258594713596834777241245455310722174384385753247255479916792229962766175495461577804329268044547583649881440108632025098451626074765444029977265811790148413724518737553783122867<212>] Free to factor
4×10245+239 = (4)2447<245> = 13 × 21752586227<11> × [157167675747902176258262323761316071091504029959104816443525844978755720963073298971707544879546309167397688827412430640697020941812604028411044506133492170131683690339678284518072142466235621989188652202436747220108073579798103122297<234>] Free to factor
4×10246+239 = (4)2457<246> = 3 × 31 × 1777 × 11621 × 36449591599<11> × 168072966781631<15> × 7506674135277540221490673949839600389032807<43> × 5032288231478366797095006830990261706053673453078640729705206817127370360142023437886861178489622878603747685378742235924271765710016209159915456069105300603578180320089<169> (Dmitry Domanov / GMP-ECM B1=43000000, sigma=4132933709 for P43 x P169 / September 26, 2011 2011 年 9 月 26 日)
4×10247+239 = (4)2467<247> = 7 × 289075387 × 14357064865301<14> × 185375314904118877407925408084912241<36> × 5312776168868277648748467284434704073171185463844543722957373<61> × 155334971713713440535637019984833551443750453456680918701697948680589441624798553252044109534763220320707973133051554950610514331<129> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=2682574846 for P36 / September 10, 2011 2011 年 9 月 10 日) (Dmitry Domanov / GMP-ECM B1=43000000, sigma=1091070925 for P61 x P129 / September 26, 2011 2011 年 9 月 26 日)
4×10248+239 = (4)2477<248> = 131 × 160709 × 39831079 × 54214476133006481<17> × 426620999585417232389113025081944102669<39> × 37440268844725210877019172474261381567673<41> × 210702158445950282588592615413383479875818485532709839<54> × 290481499946065669090870884743268835723706379935715106564790670858985084984149570149<84> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=557723112 for P39 / February 24, 2011 2011 年 2 月 24 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3328405264 for P41 / September 11, 2011 2011 年 9 月 11 日) (Erik Branger / GGNFS, Msieve gnfs for P54 x P84 / September 10, 2012 2012 年 9 月 10 日)
4×10249+239 = (4)2487<249> = 36 × 17 × [35862538888440607152783381299479096622645400181105821386625066121556075562369437944359270914584398002456583913858181589965661619014318118651209912405748764983817029326591176022306499188610057649031263168275998099285438912647820902480791127607879<245>] Free to factor
4×10250+239 = (4)2497<250> = 151 × 596224709443492459613333<24> × [49366298394984908890616595815235204520807676693902607989273203779056213866780215119344726436151132588219787510286461075591212006532094867096853293625605902108853295771439620784009495278899342773887585768022413308549385180309<224>] Free to factor
4×10251+239 = (4)2507<251> = 13 × 3418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803418803419<250>
4×10252+239 = (4)2517<252> = 3 × 173 × 1867 × 17159 × 199321 × [134109880175405108095993045300124293948112832167423721847821598133519818559467514724999765475610194505384148131549914561085395253046571392750538495388321095959875053659877810725486097737135255693135386201564366453779004157525241423732501<237>] Free to factor
4×10253+239 = (4)2527<253> = 7 × 1741677943<10> × 423216128340500452518958361<27> × [861369282327510112440565980827667461750218532418069785494079712863926136407035100242574515136138018040707355397292986442778872241925660598619191591082038117808541185636960132506423309680795040274014505966881583625527<216>] Free to factor
4×10254+239 = (4)2537<254> = 8688587919233<13> × 1075107964002118860631<22> × [4757909782327308527783745924558753538296656470228591248121004273976508210851126720341232871229885377371893328274817472569628986731273189644855350887166278119268494462194000526121107183041582554297392553613794811917200889<220>] Free to factor
4×10255+239 = (4)2547<255> = 3 × 11136871886447<14> × 199017829593152777<18> × 66840704348134032010563774728532845962517791319775402172233019712367276774637377585530761863997342415117412894628350323920734510492478298631532563221891589597403797404620583445324849372369916563005560837052349431377349197571<224>
4×10256+239 = (4)2557<256> = 1277 × 52669065824942451818821273<26> × 10731856173709325599288664294921<32> × 6157382392218127274428048318038970435371667918645130822273153189611255384792499197888822184753539821135051733756654237553871802876540098368293798857759542879845489790391686117598259301087914535467<196> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=972562391 for P32 x P196 / August 13, 2015 2015 年 8 月 13 日)
4×10257+239 = (4)2567<257> = 13 × 388211 × 1398399568961<13> × [6297599111610379584847855681392861331716368657530531938407322343217280274081009736103645702924573635157890161788237304609915192292542849946202915218329411197285683634480123798021823889220516115183110456771479807212349747616275136565096889<238>] Free to factor
4×10258+239 = (4)2577<258> = 32 × 577 × 110977 × 627119329 × [1229747623693000526820113354134080481366306570410115568343146052237151935695161069695082956772087660355010552200101047401433402725979726801548380852343009538949295596903142762717652091073652867791860923231715557210829596151466150204300739463<241>] Free to factor
4×10259+239 = (4)2587<259> = 72 × 313 × 601 × 11173 × 3749058392279183623149728959533810887592761<43> × [11510934663515051706097811041303245192390282370648777200212827343665194238082721135889434361993117203731274040108770693845571920370020343275769320229698320200475321136267926283400243615729852902039660111627<206>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3:35648371 for P43 / February 3, 2018 2018 年 2 月 3 日) Free to factor
4×10260+239 = (4)2597<260> = 222267155000543797637<21> × 12776158092928163064918867083582740229<38> × [15650993610145202300258808234442781448603109572685452391042556372551993166058405401122467202759270476079041475438026414900788661369465988227621689672939961946772717871841996970318673849702574173199710839<203>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3:3859864259 for P38 / January 30, 2018 2018 年 1 月 30 日) Free to factor
4×10261+239 = (4)2607<261> = 3 × 19 × 31 × 599 × 16979 × 109680853013<12> × 1036517653405777<16> × 117545063617094173<18> × 520231133634746492394327349860841<33> × 149767615810315382672800068522602237<36> × 23752855581063137390497936188920547870799065912945170892892598634541782336993789469230245186085127537727273591137583060000489238975385432081<140> (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=1797259939 for P33, B1=3000000, sigma=766053541 for P36 x P140 / August 20, 2015 2015 年 8 月 20 日)
4×10262+239 = (4)2617<262> = 15231319 × 29397978929305616962837<23> × 9925730830113273313492855980929453464927415626599060762548499580239427442444538767455826280590149248011869563932307148428130388082572624816648057970821384963252276039263752993919184213195245024641507266241366601028644419471232712149<232>
4×10263+239 = (4)2627<263> = 13 × 66683 × 873437 × 2933118553388144225321743923321233677<37> × [20012336519502720076761795125741574476639253101799071543837539199703051924237051872975559630561460550165185215439885707878733301064617849015448396806607266603363903253273613325628129706439819445298089939727954998057<215>] (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=784047577 for P37 / August 20, 2015 2015 年 8 月 20 日) Free to factor
4×10264+239 = (4)2637<264> = 3 × 547 × 991 × 375546284987<12> × 70162317951211<14> × 72116426430291600314010594633499314505681<41> × [143824757261657101060814464467829305151569107889756732648809343678143838218378940618273425042332935194926774968281044876190889274571344630622698033127180173450744556345559756333563116631705761<192>] (Dmitry Domanov / GMP-ECM B1=3000000, sigma=1763530650 for P41 / August 21, 2015 2015 年 8 月 21 日) Free to factor
4×10265+239 = (4)2647<265> = 7 × 17 × 5509973162813715793<19> × [6778303911614347806233236166426239031373300124726791088973244361900562717622552342244804805622082012917009389026430356830554280558758580126155851541943262483579918119416992941029166935692201331296087542028401236894067685432002741565547774551241<244>] Free to factor
4×10266+239 = (4)2657<266> = 1987 × 9883 × 2263241090585947403668948053292696386903644530510976637246852311167201015059102645616238650715864005667744133510764645111999851938767853867320851977418353591802368763574813971908391310921803441709594833504923785667470168176749216178785725776916772969686165807<259>
4×10267+239 = (4)2667<267> = 32 × 263 × 87864373 × 51692144264371427967116713<26> × 168073303078517176435456369<27> × [245970558267758900713468977827777764064638585523905219042716425009655749380500361673912474235568728555710032900964211406663545868712488454071977222462533271960782906115105242043470623177576070615575576261<204>] Free to factor
4×10268+239 = (4)2677<268> = 29 × [153256704980842911877394636015325670498084291187739463601532567049808429118773946360153256704980842911877394636015325670498084291187739463601532567049808429118773946360153256704980842911877394636015325670498084291187739463601532567049808429118773946360153256704980843<267>] Free to factor
4×10269+239 = (4)2687<269> = 13 × 315123405192510240521233<24> × 1764422236237939307242111377693244889143<40> × 6148808202214092475504233615104414811195051220296319924382143838055271238860496604761301857191175025901611277027202300066517956076914611422726887182457831696161638566724419270638878337534985805359017897901<205> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3:3308040420 for P40 x P205 / February 6, 2018 2018 年 2 月 6 日)
4×10270+239 = (4)2697<270> = 3 × 1783 × 27616681 × 29997917 × 25492808291033<14> × [3934274168104150512042562850674303903515657865265595846850723111036707140164238861869478881572638941146256343848188464913830966540667000074680295672045938482665526179968045269333661340381413505867384956265698919421302385068589802880983183<238>] Free to factor
4×10271+239 = (4)2707<271> = 7 × 50833433851<11> × 1392816691251929<16> × [8967595936186827434478597755530195571287347147388287766016987254034377644895716053145341195232732773655215109918200015846660058188642393714600565576304281851789809637355124093947152490230424199049694410303039159447068891483706403667849407886499<244>] Free to factor
4×10272+239 = (4)2717<272> = 1511 × 94727 × 1558321 × [199261002442074040402026699874461866121778662199610891671190438461090476892244046385870031014153965329675927158780943633291105421385529241198212055833919169144949797518079502211964226525103927480490986614808894588585308349587680491395897731555962258607158431<258>] Free to factor
4×10273+239 = (4)2727<273> = 3 × 9239 × [16035084765466841449090610255238461754318448765899788737758214974363908231209887233266386854437509270283380035517712755509053809735701715353192785815364016468032054134446168216056732129900221685046882579083033677686778671733753452554188564579299507322020581031296476691<269>] Free to factor
4×10274+239 = (4)2737<274> = 9967 × 26951 × 1733917 × 396246469 × 176825389191095017426703467<27> × 2255250259912290502671653609257<31> × 60387224005861526825413195164945406602405240034909175339036217350334284050789621465308459487381747371423110381279455268471397182257301514063660477699723016634126650136573583336651727189214936093<194> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=4243753058 for P31 for P194 / August 15, 2015 2015 年 8 月 15 日)
4×10275+239 = (4)2747<275> = 13 × 61 × 307 × 122090335940392693<18> × 6969893498151763367400437194031098848523934496296730781019<58> × [214535164848481174589915072673710917034419955973135741344538965121525280102003398540113063655700760097868890900431422158796675128249125309402899381486596517577822561833510457227578265480865836891<195>] (Erik Branger / GMP-ECM GPU B1=110000000, sigma=3:4207257921 for P58 / September 6, 2019 2019 年 9 月 6 日) Free to factor
4×10276+239 = (4)2757<276> = 33 × 31 × 347 × 191935457534058643<18> × 87697713376365334661282831011211<32> × [90911550984415515637204764409352764822097782538534711747778062956910400542571799571506340657387786611971492508342558068501172990554015196481586434781604770341021682568317454682301891536065581034002587040853348199370855001<221>] (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=2089608970 for P32 / August 20, 2015 2015 年 8 月 20 日) Free to factor
4×10277+239 = (4)2767<277> = 7 × 71 × 6047 × 165030413 × 232213259 × 38589586448204660623659975270797172753137153632523077843212045849254294772644201026558950009746853152007606158660463909311639741667389897759876295843006573955381744508024327619197323610930375283725851359533995312211453999850312223749664269722875447167199<254>
4×10278+239 = (4)2777<278> = 47 × 8124501220789985434646376663788021<34> × 116391942328912988856981506435773396376019997404599172114476373791604533094866398918134555295067062160249490595272867730221284547488913438230952093553381792517857185649811476556168854840364686842567717893964263492179773426599718572406678465581<243> (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=1353731310 for P34 x P243 / August 20, 2015 2015 年 8 月 20 日)
4×10279+239 = (4)2787<279> = 3 × 19 × 113 × 1571 × 1306014647521<13> × 7129696925443<13> × 461419231829144293<18> × [10222878263941501213394099980438136988258151110139580569148598379957978332002487534794311430934858980665129160842702253497713692038895245387381973555525917569659183093787088631391355117446702397348795622553225980121764494508006563<230>] Free to factor
4×10280+239 = (4)2797<280> = 593 × 4363 × 5087 × 210311019128062063953708847416822229159<39> × [1605660819258316773253791441462687954324933884720798152278580595303336564225764630694147281039535745843613700784786874636948128719258916346914689076227706708721620505311655216290667639672896268838632316481950036807427348849625382101<232>] (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=1393401583 for P39 / August 20, 2015 2015 年 8 月 20 日) Free to factor
4×10281+239 = (4)2807<281> = 13 × 17 × 439 × 1231 × 658806707682800244559<21> × 577493811593742612340208689481<30> × [978131596275673160142800726288559512006110752420808062545527750245571329363702794782058687790478695827101754555936488710221424637486021042136434122036401126874037253705386947465546483599399359825089495582022963412850664037<222>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=551888127 for P30 / August 15, 2015 2015 年 8 月 15 日) Free to factor
4×10282+239 = (4)2817<282> = 3 × 269902886278043741<18> × 85312529582496972797<20> × [6433923296130575171984052937268927582170936803436036342829460157423869612679264701502921016684190871984116674124348962814939752528216491023802560552713002570488372780277987720463378364228693081231651289914151180918727658332710270358018670195437<244>] Free to factor
4×10283+239 = (4)2827<283> = 7 × 379 × 41189 × 1083922573<10> × 2976024327904685413<19> × [12608523899654496638478524275651550527005902175633452026049222957671271934481865568107009901422198546034814602680229649596058227019530115724423698387987512698283844614314794578134491408436473196440517323231263211212213695692996351120977441229643759<248>] Free to factor
4×10284+239 = (4)2837<284> = 48338514678490297<17> × 2857552896147728789<19> × 52547909616688209312163599601363<32> × [6123143785413916578980302377743710875645266475054140630948700569566123159393591586850986398323667092447555240095174799922745954928024519605153931340112326010873854107472613168533065195094540751126847438356853965470393<217>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=3183573333 for P32 / August 15, 2015 2015 年 8 月 15 日) Free to factor
4×10285+239 = (4)2847<285> = 32 × 1117 × 1125990685412145036941<22> × [39263318359760245842673709437606508410456551281462612394915327918630970183933206044507400144433787779507317977529749544161285845506117941995519767615303856290734387668231074082717947296078207453816759443817009396088946187561813049087006726552508881191124663839<260>] Free to factor
4×10286+239 = (4)2857<286> = 225781 × 14982629741660862728899<23> × 1313838676883978834082516600219411269280246254270166242260697961221901589553765285400595261594414493682613695487558971501365301307258891049017649936908493343919767051782467379563964341570929318674290446683723708713512450522526469455608836171760176301464234113<259>
4×10287+239 = (4)2867<287> = 13 × 229 × 1579 × 462239095481183<15> × 32463220079702096327<20> × 630083702639870394791462816390340806266538049517522718359644298698051258690635856006668993376798445110287459912285604767081130247409979938508818876879235778408829445953656424814666608030271351056788623192228934223529862655815761296997267997666949<246>
4×10288+239 = (4)2877<288> = 3 × 7829 × 74873 × 2436538087<10> × 19184118776618200353674521<26> × 5406916219858338898176048509703617832526406398029494316120036524953836100139576926503930875437302042562389827317442562702027487424801370190913336599056495385835582823900734484110274964864810090070879914122656310668234521712290530698643074411911<244>
4×10289+239 = (4)2887<289> = 7 × 163 × 107227 × 7661119 × 184829753 × 1123134500666390756997488303<28> × 24138042068601166359138886344095827<35> × 3923112760985889382053890064991938959<37> × 69261086144392765400067734105779284203<38> × 3482648899451812967796732429279498670570344735851264336546336682000822217337116323605591048222323739970745791476751639721690412719<130> (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=556106747 for P38 / August 16, 2015 2015 年 8 月 16 日) (Dmitry Domanov / GMP-ECM B1=3000000, sigma=777081531 for P35 / August 20, 2015 2015 年 8 月 20 日) (Serge Batalov / GMP-ECM B1=11000000, sigma=1775858310 for P37 x P130 / August 22, 2015 2015 年 8 月 22 日)
4×10290+239 = (4)2897<290> = 70679642851691<14> × 522646243759101389<18> × 167281671723231602345723917<27> × 7192285891193597875416256531864264303745443971735637840615016906182864109577184804728129495282413139861243978742951509542221971767540151632718768529134907743948274232046652793362324440665778042884104319823666406848155024684825065109<232>
4×10291+239 = (4)2907<291> = 3 × 31 × 97569214888127<14> × [48980331822774032167643454020774432839159422670298768041767465855999483194704489074367189599666791651357733700992312486432241433074378538571848417081690950744053026739719252444130217791079909405300244318047062665942854644623611624122405937469363589359800810239392793637997077<275>] Free to factor
4×10292+239 = (4)2917<292> = 1087 × 170873 × 3290107 × 4330306460951<13> × 1723737512072123<16> × [974349362631834467699813998664825450962456907004586894760269933840598291838145758208317842253928160072205920860352867845384449035765995836653261223707503290185759664842317525453904492141851942091860799905411776017717040469437903787772795861105090327<249>] Free to factor
4×10293+239 = (4)2927<293> = 13 × 11443 × 182287486610083<15> × 6431005972849929253553<22> × [254858112171969582657659819064995926986833476523165021523851895366254578356704375018302633588957319743922504829677401843811652008426247008531828864408170178011117242268307313343200550778108647199303386600622176287571951529263736406711561408865243437667<252>] Free to factor
4×10294+239 = (4)2937<294> = 32 × 167 × 1429 × 70439 × 717505184593614523<18> × 30966839839643863820221<23> × 1703917085045993812288223<25> × [77596601634043941702856809162790971330058150166802900296407507006308178863690448102672502104138200295147073932324232361523661698823877235862255081188949050299813157540778404094390470243559965809088998788054583146078731<218>] Free to factor
4×10295+239 = (4)2947<295> = 7 × 173 × 277 × 973028981 × 2712003611<10> × 452258781239<12> × 147751356309409<15> × 1035363545024875425391<22> × [72571512882754523197709702718158197429155169946819589820630530413361297882107463745971664539001251979607049890708851233819395866514609664775965417364715825915051430713196883501610955242678726963999781143812441018362085671271<224>] Free to factor
4×10296+239 = (4)2957<296> = 29 × 59 × 18919 × 139239059 × 12525201763<11> × [787269606132354181178675241586072500027225226134006006499985579148580395907201629520389069635711438157038568085860302318293027588862269089969913029762601869745171983265589185820101325074397659948179785069470237222319818267481154001893875501594390660678529158157844176799<270>] Free to factor
4×10297+239 = (4)2967<297> = 3 × 17 × 19 × 109 × 730451 × 609575221 × 13863879442507<14> × [681654083853694867799812462941333723199604038689653407109930633332955782261534106867337906141613537243860599102022178807662471843901447346532119200429525558658912511380662050029166510004906999131300356964172638386711262351367554566078266599151636946108332556241031<264>] Free to factor
4×10298+239 = (4)2977<298> = 317 × 33459520692444319307181451061847417490952611<44> × [419023619812603461117016207852171634277776505298290695057773051994308253696968973235028536357662936865041323077685025560134803695493449427928157960221844262128114942797410756891605321504542643259797280107567895590896713857963438809589212656477730271481<252>] (KTakahashi / GMP-ECM 6.4.4 B1=1000000, sigma=2271986940 for P44 / August 20, 2015 2015 年 8 月 20 日) Free to factor
4×10299+239 = (4)2987<299> = 13 × 149 × 11833 × 12907 × 325541 × 20641764287<11> × 247013384015242182257<21> × [90509609991708104502056154625754522561201317505616117483143265400068842156257515056432480328624157816420695186775455232968740260467099338042364793555536882212079829494965719069999703147037229976822980884565327705320587268665882838691793015773975901279<251>] Free to factor
4×10300+239 = (4)2997<300> = 3 × 3229 × 27073 × [1694695978529954267667279401368337951564173015123845253278518696953058097937403361206366688590821438710295280908185236213752120706005650347718419936867160246107800325508645341342039464479307653853443629790953671261820831208814791323786508421853733544821392747598299208030565675633836494627897<292>] Free to factor
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