Table of contents 目次

  1. About 700...003 700...003 について
    1. Classification 分類
    2. Sequence 数列
    3. General term 一般項
  2. Prime numbers of the form 700...003 700...003 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 700...003 700...003 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 700...003 700...003 について

1.1. Classification 分類

Quasi-repdigit of the form ABB...BBC ABB...BBC の形のクワージレプディジット (Quasi-repdigit)

1.2. Sequence 数列

70w3 = { 73, 703, 7003, 70003, 700003, 7000003, 70000003, 700000003, 7000000003, 70000000003, … }

1.3. General term 一般項

7×10n+3 (1≤n)

2. Prime numbers of the form 700...003 700...003 の形の素数

2.1. Last updated 最終更新日

September 9, 2015 2015 年 9 月 9 日

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

  1. 7×101+3 = 73 is prime. は素数です。 (Julien Peter Benney / September 7, 2004 2004 年 9 月 7 日)
  2. 7×104+3 = 70003 is prime. は素数です。 (Julien Peter Benney / September 7, 2004 2004 年 9 月 7 日)
  3. 7×106+3 = 7000003 is prime. は素数です。 (Julien Peter Benney / September 7, 2004 2004 年 9 月 7 日)
  4. 7×1016+3 = 7(0)153<17> is prime. は素数です。 (Julien Peter Benney / September 7, 2004 2004 年 9 月 7 日)
  5. 7×1022+3 = 7(0)213<23> is prime. は素数です。 (Julien Peter Benney / September 7, 2004 2004 年 9 月 7 日)
  6. 7×1039+3 = 7(0)383<40> is prime. は素数です。 (Julien Peter Benney / September 7, 2004 2004 年 9 月 7 日)
  7. 7×10103+3 = 7(0)1023<104> is prime. は素数です。 (Julien Peter Benney / September 7, 2004 2004 年 9 月 7 日)
  8. 7×10163+3 = 7(0)1623<164> is prime. は素数です。 (Julien Peter Benney / September 7, 2004 2004 年 9 月 7 日)
  9. 7×10240+3 = 7(0)2393<241> is prime. は素数です。 (Julien Peter Benney / September 7, 2004 2004 年 9 月 7 日)
  10. 7×101048+3 = 7(0)10473<1049> 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 14, 2006 2006 年 9 月 14 日)
  11. 7×101974+3 = 7(0)19733<1975> 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 / June 17, 2006 2006 年 6 月 17 日)
  12. 7×102559+3 = 7(0)25583<2560> 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: suberi / PRIMO 3.0.4 / September 24, 2007 2007 年 9 月 24 日)
  13. 7×105880+3 = 7(0)58793<5881> is PRP. はおそらく素数です。 (Makoto Kamada / PFGW / December 21, 2004 2004 年 12 月 21 日)
  14. 7×1014436+3 = 7(0)144353<14437> is PRP. はおそらく素数です。 (Erik Branger / PFGW / November 7, 2009 2009 年 11 月 7 日)
  15. 7×1028338+3 = 7(0)283373<28339> is PRP. はおそらく素数です。 (Erik Branger / PFGW / November 7, 2009 2009 年 11 月 7 日)
  16. 7×1032796+3 = 7(0)327953<32797> is PRP. はおそらく素数です。 (Erik Branger / PFGW / November 7, 2009 2009 年 11 月 7 日)
  17. 7×1038079+3 = 7(0)380783<38080> is PRP. はおそらく素数です。 (Erik Branger / PFGW / November 7, 2009 2009 年 11 月 7 日)
  18. 7×1056779+3 = 7(0)567783<56780> is PRP. はおそらく素数です。 (Erik Branger / PFGW / November 7, 2009 2009 年 11 月 7 日)
  19. 7×1091215+3 = 7(0)912143<91216> is PRP. はおそらく素数です。 (Erik Branger / PFGW / November 7, 2009 2009 年 11 月 7 日)
  20. 7×10111325+3 = 7(0)1113243<111326> is PRP. はおそらく素数です。 (Bob Price / September 8, 2015 2015 年 9 月 8 日)
  21. 7×10115863+3 = 7(0)1158623<115864> is PRP. はおそらく素数です。 (Bob Price / September 8, 2015 2015 年 9 月 8 日)
  22. 7×10138604+3 = 7(0)1386033<138605> is PRP. はおそらく素数です。 (Bob Price / September 8, 2015 2015 年 9 月 8 日)

2.3. Range of search 捜索範囲

  1. n≤100000 / Completed 終了 / Erik Branger / November 7, 2009 2009 年 11 月 7 日
  2. n≤200000 / Completed 終了 / Bob Price / September 8, 2015 2015 年 9 月 8 日

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

  1. 7×103k+2+3 = 37×(7×102+337+63×102×103-19×37×k-1Σm=0103m)
  2. 7×108k+1+3 = 73×(7×101+373+63×10×108-19×73×k-1Σm=0108m)
  3. 7×1015k+12+3 = 31×(7×1012+331+63×1012×1015-19×31×k-1Σm=01015m)
  4. 7×1016k+10+3 = 17×(7×1010+317+63×1010×1016-19×17×k-1Σm=01016m)
  5. 7×1018k+2+3 = 19×(7×102+319+63×102×1018-19×19×k-1Σm=01018m)
  6. 7×1022k+10+3 = 23×(7×1010+323+63×1010×1022-19×23×k-1Σm=01022m)
  7. 7×1028k+21+3 = 29×(7×1021+329+63×1021×1028-19×29×k-1Σm=01028m)
  8. 7×1035k+10+3 = 71×(7×1010+371+63×1010×1035-19×71×k-1Σm=01035m)
  9. 7×1042k+29+3 = 127×(7×1029+3127+63×1029×1042-19×127×k-1Σm=01042m)
  10. 7×1044k+18+3 = 89×(7×1018+389+63×1018×1044-19×89×k-1Σm=01044m)

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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 19.75%. 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 19.75% です。

3. Factor table of 700...003 700...003 の素因数分解表

3.1. Last updated 最終更新日

January 18, 2017 2017 年 1 月 18 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=197, 198, 201, 202, 205, 212, 214, 216, 217, 219, 220, 222, 223, 224, 229, 230, 231, 232, 233, 235, 236, 237, 241, 242, 244, 245, 246, 248, 249, 250 (30/250)

3.4. Factor table 素因数分解表

7×101+3 = 73 = definitely prime number 素数
7×102+3 = 703 = 19 × 37
7×103+3 = 7003 = 47 × 149
7×104+3 = 70003 = definitely prime number 素数
7×105+3 = 700003 = 37 × 18919
7×106+3 = 7000003 = definitely prime number 素数
7×107+3 = 70000003 = 431 × 162413
7×108+3 = 700000003 = 37 × 18918919
7×109+3 = 7000000003<10> = 73 × 379 × 5032
7×1010+3 = 70000000003<11> = 17 × 23 × 71 × 827 × 3049
7×1011+3 = 700000000003<12> = 37 × 18918918919<11>
7×1012+3 = 7000000000003<13> = 31 × 199 × 1134705787<10>
7×1013+3 = 70000000000003<14> = 8279539 × 8454577
7×1014+3 = 700000000000003<15> = 37 × 218843 × 86449733
7×1015+3 = 7000000000000003<16> = 2441 × 995023 × 2882021
7×1016+3 = 70000000000000003<17> = definitely prime number 素数
7×1017+3 = 700000000000000003<18> = 37 × 59 × 73 × 1049 × 4187414533<10>
7×1018+3 = 7000000000000000003<19> = 892 × 41443 × 80747 × 264083
7×1019+3 = 70000000000000000003<20> = 2557 × 29804867 × 918502037
7×1020+3 = 700000000000000000003<21> = 19 × 37 × 995732574679943101<18>
7×1021+3 = 7000000000000000000003<22> = 29 × 162859 × 861797 × 1719821209<10>
7×1022+3 = 70000000000000000000003<23> = definitely prime number 素数
7×1023+3 = 700000000000000000000003<24> = 37 × 131 × 144419228388694037549<21>
7×1024+3 = 7000000000000000000000003<25> = 3011 × 21628169 × 107489868122617<15>
7×1025+3 = 70000000000000000000000003<26> = 73 × 443 × 19793 × 108793 × 1005214804873<13>
7×1026+3 = 700000000000000000000000003<27> = 17 × 372 × 5329217 × 5643938410859083<16>
7×1027+3 = 7000000000000000000000000003<28> = 31 × 419 × 538917545615520825313727<24>
7×1028+3 = 70000000000000000000000000003<29> = 269 × 10601 × 45449497 × 540094611485071<15>
7×1029+3 = 700000000000000000000000000003<30> = 37 × 127 × 389 × 3619151 × 105812333075482123<18>
7×1030+3 = 7000000000000000000000000000003<31> = 347 × 5323 × 3789763415897840971781963<25>
7×1031+3 = 70000000000000000000000000000003<32> = 2179 × 41696363 × 19747905371<11> × 39014100409<11>
7×1032+3 = 700000000000000000000000000000003<33> = 23 × 37 × 3041 × 83801567159<11> × 3227750220099287<16>
7×1033+3 = 7000000000000000000000000000000003<34> = 73 × 521 × 170773 × 397807 × 1286953 × 2105150459777<13>
7×1034+3 = 70000000000000000000000000000000003<35> = 139 × 503597122302158273381294964028777<33>
7×1035+3 = 700000000000000000000000000000000003<36> = 37 × 1399 × 8527 × 5001175302709<13> × 317110235848867<15>
7×1036+3 = 7000000000000000000000000000000000003<37> = 3347 × 2091425156856886764266507319988049<34>
7×1037+3 = 70000000000000000000000000000000000003<38> = 107 × 4968727 × 78118217 × 1685453613169208833831<22>
7×1038+3 = 700000000000000000000000000000000000003<39> = 19 × 37 × 4967 × 39821 × 50380721 × 99924507080031586583<20>
7×1039+3 = 7000000000000000000000000000000000000003<40> = definitely prime number 素数
7×1040+3 = 70000000000000000000000000000000000000003<41> = 6073 × 5028431 × 9336371299<10> × 245518458609668754119<21>
7×1041+3 = 700000000000000000000000000000000000000003<42> = 37 × 73 × 381606813145997<15> × 679136912481567898730699<24>
7×1042+3 = 7000000000000000000000000000000000000000003<43> = 17 × 31 × 82942289 × 18989435591311<14> × 8433334983673032691<19>
7×1043+3 = 70000000000000000000000000000000000000000003<44> = 65687 × 2552472279171967709<19> × 417501055941749733241<21>
7×1044+3 = 700000000000000000000000000000000000000000003<45> = 37 × 509 × 37168799447777836775872139329899644241491<41>
7×1045+3 = 7000000000000000000000000000000000000000000003<46> = 71 × 661 × 4451 × 29921131 × 224039852081<12> × 4998933445471474433<19>
7×1046+3 = 70000000000000000000000000000000000000000000003<47> = 302597308627<12> × 231330543941771448107229367806428689<36>
7×1047+3 = 700000000000000000000000000000000000000000000003<48> = 37 × 1123 × 1627 × 1867 × 5546061597838509372089665626454296517<37>
7×1048+3 = 7000000000000000000000000000000000000000000000003<49> = 100237 × 7373711 × 9470738987920673578770364540154004929<37>
7×1049+3 = 70000000000000000000000000000000000000000000000003<50> = 29 × 47 × 61 × 73 × 1453 × 566633 × 9814830305767373<16> × 1427247253083751501<19>
7×1050+3 = 700000000000000000000000000000000000000000000000003<51> = 37 × 749562861861318382769<21> × 25239936343616813435267543351<29>
7×1051+3 = 7(0)503<52> = 24389347 × 287010554239111034830083806671822742937726049<45>
7×1052+3 = 7(0)513<53> = 8431 × 6032898669642243199<19> × 1376236018405101648256080859987<31>
7×1053+3 = 7(0)523<54> = 37 × 72817 × 1937953 × 382113816734066933<18> × 350854904593510277162843<24>
7×1054+3 = 7(0)533<55> = 23 × 12721 × 19910463163<11> × 136572980418849173<18> × 8798381749283302925059<22>
7×1055+3 = 7(0)543<56> = 191 × 102751531 × 2368178554907226877<19> × 1506128155005487912438398659<28>
7×1056+3 = 7(0)553<57> = 19 × 37 × 74869 × 512029021883<12> × 25974434731566763095365871333276915563<38>
7×1057+3 = 7(0)563<58> = 31 × 73 × 4188337 × 5344247 × 102260328393131<15> × 1351382101160513627356664809<28>
7×1058+3 = 7(0)573<59> = 17 × 277 × 461 × 1129 × 2310906293211283<16> × 12359250849266324509191590161390921<35>
7×1059+3 = 7(0)583<60> = 37 × 3593 × 8613868024309203048907<22> × 611280983223493859615227033272269<33>
7×1060+3 = 7(0)593<61> = 27743 × 238538735269<12> × 78240366615452683<17> × 13519319415183249238388577323<29>
7×1061+3 = 7(0)603<62> = 1483 × 7687 × 9511 × 70793 × 183797 × 496221359 × 150668771531483<15> × 663661141811869849<18>
7×1062+3 = 7(0)613<63> = 37 × 89 × 212572122684482235044032796841785605830549650774369875493471<60>
7×1063+3 = 7(0)623<64> = 113 × 61946902654867256637168141592920353982300884955752212389380531<62>
7×1064+3 = 7(0)633<65> = 1973 × 100660729154531977<18> × 352460848829086094947433551001005014854677343<45>
7×1065+3 = 7(0)643<66> = 37 × 73 × 28435201 × 20977753441<11> × 2678034970718467<16> × 162234021139161700314156923749<30>
7×1066+3 = 7(0)653<67> = 1697 × 930656281 × 7728917771701966894842589<25> × 573466691681854868740906615511<30>
7×1067+3 = 7(0)663<68> = 4936777053491<13> × 14179291315272196466393952738015323376126233226178062833<56>
7×1068+3 = 7(0)673<69> = 37 × 193 × 619 × 60601 × 669659 × 18608727887814241<17> × 209699875165920974563419558715441703<36>
7×1069+3 = 7(0)683<70> = 173887737338537586978836129<27> × 40255857642059480549186993689702864815439907<44>
7×1070+3 = 7(0)693<71> = 7823 × 220949251 × 16178994737<11> × 2503114075548444020360998910904996074815776627103<49>
7×1071+3 = 7(0)703<72> = 37 × 127 × 293 × 69067 × 12854759 × 395803621 × 1446807263177265233672652226440282267567072133<46>
7×1072+3 = 7(0)713<73> = 31 × 16356751 × 2340591634189<13> × 5898120693798185395744147552615103390145346469886367<52>
7×1073+3 = 7(0)723<74> = 73 × 4673 × 2857711 × 10209799 × 79187384312853143<17> × 88815323572289303209987619820673754341<38>
7×1074+3 = 7(0)733<75> = 17 × 19 × 37 × 57613818950730495168923<23> × 63389240387291600908937<23> × 16038050719104036452467103<26>
7×1075+3 = 7(0)743<76> = 59 × 881 × 430510464405529097<18> × 312814162764180274673777190185028559555922545807610081<54>
7×1076+3 = 7(0)753<77> = 23 × 857 × 12042608190371153<17> × 219847012337972745665437<24> × 1341368975505329520693615169090193<34>
7×1077+3 = 7(0)763<78> = 29 × 37 × 6827 × 9337 × 10289 × 2756510632466374221777091442819<31> × 360851252603682393164477684328379<33>
7×1078+3 = 7(0)773<79> = 2367284929<10> × 2956974006063973890149325577867521666632466446120816747699575288429507<70>
7×1079+3 = 7(0)783<80> = 2803 × 323699 × 786357080437182868178134838053<30> × 98110114585870646608966603457662892593583<41> (Makoto Kamada / msieve 0.83)
7×1080+3 = 7(0)793<81> = 37 × 71 × 139 × 54609794767226863<17> × 37491349731843928110181543061<29> × 936314063964432494275383997657<30>
7×1081+3 = 7(0)803<82> = 73 × 739 × 65788857698602513<17> × 1972324619173110934014122966523734746806468458217080449948873<61>
7×1082+3 = 7(0)813<83> = 11605960687<11> × 56797820400025342328862697<26> × 106190404414860719984812806891288546309165632677<48>
7×1083+3 = 7(0)823<84> = 37 × 191520055240951<15> × 320947808440067<15> × 307785136491684725872333178444983348123321172322243707<54>
7×1084+3 = 7(0)833<85> = 179354807 × 39028783878650099408821532171144986373295252688711041907006150105583732695829<77>
7×1085+3 = 7(0)843<86> = 521 × 4231 × 22853 × 13220808901<11> × 2211334782726803935956510331<28> × 47529314081865549689931581435110935871<38>
7×1086+3 = 7(0)853<87> = 37 × 2377 × 2599658317<10> × 3061617019600199308342265007622546506178275318776229859681803848981060491<73>
7×1087+3 = 7(0)863<88> = 31 × 5340200312976967<16> × 42284266203307336368434910202178396774739052422268006448720891792319739<71>
7×1088+3 = 7(0)873<89> = 172148841414205902090241764827236561<36> × 406624868485600664233318057044925358316686761169023123<54> (Makoto Kamada / GGNFS-0.70.3 / 0.14 hours)
7×1089+3 = 7(0)883<90> = 37 × 73 × 313 × 67281165463<11> × 12306529935638987421213603187769214793991610830464723197877649828765597137<74>
7×1090+3 = 7(0)893<91> = 17 × 107 × 1063 × 4691 × 1458749 × 50691871 × 23011725523786513222190760199<29> × 453522215822751428959200344094328654609<39>
7×1091+3 = 7(0)903<92> = 787 × 1571 × 8929 × 1236297857903767<16> × 816646943495303646635369<24> × 6280393304778504628636119651022288626892117<43>
7×1092+3 = 7(0)913<93> = 19 × 37 × 359 × 2908271 × 23711881 × 1298922472957<13> × 442355914879419007<18> × 69999077645998966691545482711291387001950511<44>
7×1093+3 = 7(0)923<94> = 97 × 163859 × 432357697033<12> × 3958299705337<13> × 257338127617434101786891673873770926734968627025925126838344241<63>
7×1094+3 = 7(0)933<95> = 42139 × 28072733139049<14> × 422522728446857499995021897<27> × 140048687152761077323790999317989342736433769646409<51>
7×1095+3 = 7(0)943<96> = 37 × 47 × 1087 × 24749 × 1589778503<10> × 88121919273006163<17> × 106804780226580541740150695089251552881834137227623150357111<60>
7×1096+3 = 7(0)953<97> = 1277137 × 758640293 × 7224780343515691901762634225996096609576621025841511346216663678738308316724103383<82>
7×1097+3 = 7(0)963<98> = 73 × 9539 × 1057291 × 10849301 × 1553772995569<13> × 42929366127936416233139<23> × 131381432333586171612770896914372706250669429<45>
7×1098+3 = 7(0)973<99> = 23 × 37 × 314077 × 1824523394303<13> × 13128394015929449<17> × 109338045710575684050814792659497213706098346630468054059129987<63>
7×1099+3 = 7(0)983<100> = 3721631 × 40127119140739769869<20> × 46873431455466153445394850477615578381812674769089931057245821372648612177<74>
7×10100+3 = 7(0)993<101> = 45198479 × 1146794639<10> × 24565244637631441<17> × 72828280143847901461556239<26> × 754861747261501417728155105126304381583837<42>
7×10101+3 = 7(0)1003<102> = 37 × 22709 × 833102246638729971329381254961421415250293668541940152314893606892373901048875728518161033903691<96>
7×10102+3 = 7(0)1013<103> = 31 × 109 × 218458834435204518225157303<27> × 9482879589157446474673484064735583326177687114602581017293041369451847319<73>
7×10103+3 = 7(0)1023<104> = definitely prime number 素数
7×10104+3 = 7(0)1033<105> = 37 × 10871221 × 5169682807715605493<19> × 336630989875194108765240828121579926889120985272434568122702269209669481193023<78>
7×10105+3 = 7(0)1043<106> = 29 × 73 × 24083987 × 137293127385205135204051721013678821053074477905168205332159731648723537539107467545228731251357<96>
7×10106+3 = 7(0)1053<107> = 17 × 89 × 1187 × 5256725437807406804389<22> × 7414691716480231217520181086618968088583107383108395058908222269611234464571717<79>
7×10107+3 = 7(0)1063<108> = 37 × 83635418281<11> × 140299365803<12> × 4117060791541<13> × 826889092214855513<18> × 473604512874832354070314796392028912847740003713816801<54>
7×10108+3 = 7(0)1073<109> = 15932731 × 21135103243411643094225839323775893<35> × 20787556496228678876263628963578198111397575572164064323810422220341<68> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 / 1.97 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / August 3, 2007 2007 年 8 月 3 日)
7×10109+3 = 7(0)1083<110> = 61 × 283 × 6833 × 3752738047<10> × 94998794192060872628935849323365693<35> × 1664577444559100089652031980780871295487207378438987754367<58> (Robert Backstrom / Msieve v. 1.25 for P35 x P58 / 02:06:42 on AMD 64 3400+ / July 31, 2007 2007 年 7 月 31 日)
7×10110+3 = 7(0)1093<111> = 19 × 37 × 62760724109<11> × 84761407142803<14> × 803154437998628211087235799<27> × 233054529447123663329871970637744890768721638386616333837<57>
7×10111+3 = 7(0)1103<112> = 199 × 78101 × 3325898053<10> × 77728044727<11> × 3697427755380236234627<22> × 471196435114465723546238321975910409617411023105411046696555481<63>
7×10112+3 = 7(0)1113<113> = 72077 × 46448851699<11> × 11035256564809<14> × 1894715121853558670446882736556831311166778905145114951475045713704506218685892610829<85>
7×10113+3 = 7(0)1123<114> = 37 × 73 × 127 × 523 × 20143 × 16454791 × 15906103516637<14> × 3406569578578088551<19> × 936855969321695091127<21> × 231898332726876894907707540283208639560439<42>
7×10114+3 = 7(0)1133<115> = 48593 × 4986920837<10> × 1350260504323<13> × 377177032131509861<18> × 1142155916718289309<19> × 49659650238040515294223068397416732858526996543916429<53>
7×10115+3 = 7(0)1143<116> = 71 × 571 × 1753 × 41759 × 101687624751179<15> × 229383234010881253145836095413674027664523319<45> × 1011211039809810274754617373533701326457880829<46> (Sinkiti Sibata / Msieve v. 1.23 for P45 x P46 / 09:45:05 on Celeron 750MHz,Windows 2000 / July 31, 2007 2007 年 7 月 31 日)
7×10116+3 = 7(0)1153<117> = 37 × 223 × 829639 × 679469613595983877<18> × 316259956988478262729<21> × 475869692991096230910420889144359168075567344417898165610155914471419<69>
7×10117+3 = 7(0)1163<118> = 31 × 796610382478821640289686993942482559318724926882166707<54> × 283459086875391589955150402968360965955345854041338678737403759<63> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 1.23 hours on Cygwin on AMD 64 3400+ / July 31, 2007 2007 年 7 月 31 日)
7×10118+3 = 7(0)1173<119> = 179 × 491 × 841873 × 15347665259486976996421<23> × 1139407170046294248864777606642001<34> × 54099801183923492995938105985141721603808960886335319<53> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1580992944 for P34 / July 23, 2007 2007 年 7 月 23 日)
7×10119+3 = 7(0)1183<120> = 37 × 26029 × 591691 × 125313757 × 35091539471<11> × 279346154535902448842097031259446400522154284661319800201432279924844739094548346598832243<90>
7×10120+3 = 7(0)1193<121> = 23 × 366479 × 490913 × 787073943986243214424803305243<30> × 2149319812250807291486495152588101029793779750183550066121886943689304730180801<79> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 1.62 hours on Cygwin on AMD 64 3400+ / August 1, 2007 2007 年 8 月 1 日)
7×10121+3 = 7(0)1203<122> = 73 × 14519 × 12297783804432233<17> × 5370461663804082728489673368790562330545934356189330671883291090032385064275977876996106012255214693<100>
7×10122+3 = 7(0)1213<123> = 173 × 37 × 34057 × 121139 × 447641 × 1966357949<10> × 36803587049889567164794261972333592412847<41> × 28812211472214508546521155757658327809127986705923647<53> (Robert Backstrom / Msieve v. 1.25 for P41 x P53 / 02:18:11 on AMD 64 3400+ / July 31, 2007 2007 年 7 月 31 日)
7×10123+3 = 7(0)1223<124> = 1051 × 6660323501427212178877259752616555661274976213130352045670789724072312083729781160799238820171265461465271170313986679353<121>
7×10124+3 = 7(0)1233<125> = 15204354063320977<17> × 39852682630033327<17> × 16454979289548367744901143<26> × 7020615117095165460306277936299814957685144453038459247590208667499<67>
7×10125+3 = 7(0)1243<126> = 37 × 499 × 13699452564493006814819701274146501315424887911148777<53> × 2767531402418291140749455418859878737861230939330176281407585478703253<70> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 2.02 hours on Cygwin on AMD 64 3200+ / August 2, 2007 2007 年 8 月 2 日)
7×10126+3 = 7(0)1253<127> = 139 × 3467 × 121267 × 43013903 × 486725599 × 22607898319<11> × 4453779204725453740170721<25> × 56820473731842723734333158728988035577213359550080351146041187431<65>
7×10127+3 = 7(0)1263<128> = 277 × 683 × 101758248455110600982078958785140824830321627783059244018899<60> × 3636034073135055601486854090198041730366400527898690994554262567<64> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 2.70 hours on Cygwin on AMD 64 3200+ / August 2, 2007 2007 年 8 月 2 日)
7×10128+3 = 7(0)1273<129> = 19 × 37 × 26282295373764725335115813<26> × 37886058295878306213616108946850864776727658896365098036372977202899697535501526642168774128806363577<101>
7×10129+3 = 7(0)1283<130> = 73 × 520369286050301<15> × 270808955508136127278993<24> × 680456712526241661156953703291776730767927997652114292035446362319384582992378750808175127<90>
7×10130+3 = 7(0)1293<131> = 20346317 × 99919903 × 232724273 × 968648957 × 55425339049583230640793394931<29> × 2755775112490202917983700300340486561295646135907138645419544894886583<70>
7×10131+3 = 7(0)1303<132> = 37 × 167 × 821 × 86381 × 8277265193<10> × 1909043502241<13> × 11221997190059<14> × 245476063044641766698278446037400797293497<42> × 36697498431299323192437388994595232599875443<44> (Robert Backstrom / Msieve v. 1.25 for P42 x P44 / 00:31:35 on AMD 64 3400+ / July 31, 2007 2007 年 7 月 31 日)
7×10132+3 = 7(0)1313<133> = 31 × 1897144835436283709<19> × 1514672391291856973675707124754820474913203927051<49> × 78580927206153670651740539814203277361304443804223185859614493507<65> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 4.29 hours on Cygwin on AMD XP 2700+ / August 2, 2007 2007 年 8 月 2 日)
7×10133+3 = 7(0)1323<134> = 29 × 59 × 1741 × 19286399236854181<17> × 46083256114156603252213<23> × 8783383808652802647890907770843019907393<40> × 3010184316154118713322706068056130317359871964857<49> (Robert Backstrom / Msieve v. 1.25 for P40 x P49 / 00:43:56 on AMD 64 3400+ / July 31, 2007 2007 年 7 月 31 日)
7×10134+3 = 7(0)1333<135> = 37 × 911 × 2477 × 3617 × 49545323 × 32882397982111<14> × 5367062025418043120995211357<28> × 265094467340820790612800457652637262397650002638915153761179523971580034861<75>
7×10135+3 = 7(0)1343<136> = 75019561 × 127203697 × 498282829674007715259141593888416290550964085919<48> × 1472135771787141323267702134218700861789671776680188265909145553844113061<73> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 3.62 hours on Cygwin on AMD 64 3200+ / August 2, 2007 2007 年 8 月 2 日)
7×10136+3 = 7(0)1353<137> = 189532579450789969799143826592293<33> × 2381835865531583487969941738318774107993447<43> × 155060912820934332646084226028944988675098343203271382941181793<63> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 5.52 hours on Cygwin on AMD 64 3400+ / July 31, 2007 2007 年 7 月 31 日)
7×10137+3 = 7(0)1363<138> = 372 × 73 × 373 × 521 × 18719 × 249341 × 960331 × 1467499879<10> × 139631923964055191736784404269<30> × 39243261185324721562992298947369650901900632234898044840233858916987494957<74> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 / 9.59 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / August 2, 2007 2007 年 8 月 2 日)
7×10138+3 = 7(0)1373<139> = 17 × 8243 × 68483 × 259690877 × 416873729 × 472302839 × 39500434691109480414761661938549<32> × 361158125739483496643032610400546386075176007047634753673066706124874797<72> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 / 12.90 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / August 3, 2007 2007 年 8 月 3 日)
7×10139+3 = 7(0)1383<140> = 517222561 × 546738868367<12> × 6655200828291269<16> × 3981759409345941527<19> × 57295780593317396927<20> × 163035360899287075108627762760765546259653073401679508268751156769<66>
7×10140+3 = 7(0)1393<141> = 37 × 8930917 × 113901888018295570523922817<27> × 278323359075849334609317178348129<33> × 66822032691525636457754568132542380413223137289570793768530446299737118299<74> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 / 9.94 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / August 2, 2007 2007 年 8 月 2 日)
7×10141+3 = 7(0)1403<142> = 47 × 1277 × 3825553989407<13> × 541714739387789911<18> × 9465590749942502839939485961<28> × 5945612121765785967914201933760528425476584189513474451167602728122232328084321<79>
7×10142+3 = 7(0)1413<143> = 23 × 3043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478261<142>
7×10143+3 = 7(0)1423<144> = 37 × 107 × 181 × 42929 × 55778925763273769417<20> × 99615388886871440186141889727022388487187792018971<50> × 4095308385474807274359199791739966295408609792078800566560390219<64> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 8.69 hours on Cygwin on AMD 64 3200+ / August 6, 2007 2007 年 8 月 6 日)
7×10144+3 = 7(0)1433<145> = 109883 × 8375489 × 33739941640193<14> × 569413262237671<15> × 395899956791067921005824301163988070692468421748818928744972305528613757396282289391957630313326277780223<105>
7×10145+3 = 7(0)1443<146> = 73 × 28793 × 63545947 × 288853667 × 53326121669<11> × 1531658044549<13> × 54389898345654421049856493544427544048520119<44> × 408415728230237921555405467245794348472339374239159426157<57> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 5.98 hours on Cygwin on AMD 64 3400+ / August 1, 2007 2007 年 8 月 1 日)
7×10146+3 = 7(0)1453<147> = 192 × 37 × 169712311 × 3349398401<10> × 14528779333859387<17> × 40425209585153273<17> × 6931357162131060176383<22> × 22646926584951101608994646259410863938176211823391717360977422701943133<71>
7×10147+3 = 7(0)1463<148> = 31 × 151451 × 7030015143559119037524563<25> × 49184959607580348859573544470471<32> × 4311968914702968224249026994416631354378899830941813009414303440243079537179314918331<85> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 / 22.87 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / August 4, 2007 2007 年 8 月 4 日)
7×10148+3 = 7(0)1473<149> = 541 × 94793 × 1248139200509574640907510234705365019<37> × 668778149760661722591247508440960905084930985277<48> × 1635232116045943944454517876533152037422559560020696414537<58> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 16.09 hours on Cygwin on AMD 64 3200+ / August 3, 2007 2007 年 8 月 3 日)
7×10149+3 = 7(0)1483<150> = 37 × 63947237308808935504223147<26> × 54332487637857980982276524557<29> × 5445213838251929415449467996756948545942266302151184463631784484692515847069284337985563870761<94>
7×10150+3 = 7(0)1493<151> = 71 × 89 × 191 × 5813 × 69387272384806722377<20> × 2860432727051506986615284475786112947115219635815431<52> × 5026948551624322877511681422548970043126094617265313823362275760438297<70> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 14.95 hours on Cygwin on AMD 64 3200+ / August 4, 2007 2007 年 8 月 4 日)
7×10151+3 = 7(0)1503<152> = 149 × 307 × 11981 × 127726298919576192535338258643102254447088972860739726166821388527083366333095265501218077359268550022936632594624208454808418279061720345556641<144>
7×10152+3 = 7(0)1513<153> = 37 × 505533211217<12> × 710664466259752258736962985632455239789<39> × 52660141650353797139373582732951853429418586057828085008415146466989469864283870303119649117935460563<101> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 26.23 hours on Cygwin on AMD XP 2700+ / August 4, 2007 2007 年 8 月 4 日)
7×10153+3 = 7(0)1523<154> = 73 × 131 × 23323831 × 1846251383033<13> × 2379079812909254428043276041211980572721289410506055623377<58> × 7145031581347695270977233930386125972534532154126683920313280001705450711<73> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 20.08 hours on Core 2 Quad Q6600 / September 16, 2007 2007 年 9 月 16 日)
7×10154+3 = 7(0)1533<155> = 17 × 4117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647059<154>
7×10155+3 = 7(0)1543<156> = 37 × 127 × 1395743 × 1451893 × 73511032921154680604594264467842920178089437517714336009825825227286341895956234800313017246479287345052633467857176570653818464129845658603<140>
7×10156+3 = 7(0)1553<157> = 131869366750590330739<21> × 1122763019112328991917896688146547<34> × 47278753694379635584088304024046021007264290269515393607169408994420953596008025338686045504887530367691<104> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 48.61 hours on Cygwin on AMD XP 2700+ / August 19, 2007 2007 年 8 月 19 日)
7×10157+3 = 7(0)1563<158> = 229 × 20670690483852242291<20> × 289487332555897025292304347439098723403965940378647989<54> × 51083189905954193522289990799875185494212136099456609629347350039925026063426710793<83> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs / 31.10 hours on Cygwin on AMD 64 3200+ / August 18, 2007 2007 年 8 月 18 日)
7×10158+3 = 7(0)1573<159> = 37 × 4683555637807654711165402911872475397796795663167619<52> × 4039435074966837668459019948543510692643700803297645131234240674842966427190365006893589626840507633222701<106> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 38.49 hours on Cygwin on AMD 64 3200+ / August 3, 2007 2007 年 8 月 3 日)
7×10159+3 = 7(0)1583<160> = 8783 × 18936371 × 624258449 × 393743988174089796031<21> × 171230071767870652328330714497671132372228899480755443469714202635512070786758135435071643752357635763404000992608964209<120>
7×10160+3 = 7(0)1593<161> = 599 × 3575471 × 32684207402663970868259644290514942764613639197537545293383575416020385297041237051417593707790286764274014796912972315179700744228133911207614045346907<152>
7×10161+3 = 7(0)1603<162> = 29 × 37 × 73 × 1403225401<10> × 3753845625711756879793515975255349607797<40> × 1696569329960212414283207012646965391569808922194244639849139334297461697448507406571284397297756255793527431<109> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 52.92 hours on Cygwin on AMD 64 3400+ / August 12, 2007 2007 年 8 月 12 日)
7×10162+3 = 7(0)1613<163> = 31 × 593 × 5407 × 11863 × 760434737 × 152542129822030128211<21> × 442825008495119170811915908973911<33> × 115570464819492499800637613712265721541579149801960067104596793688468703483720951765048513<90> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1888950106 for P33 / July 26, 2007 2007 年 7 月 26 日)
7×10163+3 = 7(0)1623<164> = definitely prime number 素数
7×10164+3 = 7(0)1633<165> = 19 × 23 × 37 × 337 × 929 × 269413 × 347533 × 3469921837<10> × 10858699084919331104580583379<29> × 329805675824054241199035943707983<33> × 118849963103897079083614037915925391439183742364207872856583449031842800979<75> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs for P33 x P75 / 19.99 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / August 5, 2007 2007 年 8 月 5 日)
7×10165+3 = 7(0)1643<166> = 152833588533830632515504625196129899<36> × 2783607568442084600657258901797095301845534239737<49> × 16453989692271955709439095429034688807841041398306296314589415102129894839413356881<83> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 52.97 hours on Cygwin on AMD 64 3400+ / August 3, 2007 2007 年 8 月 3 日)
7×10166+3 = 7(0)1653<167> = 193428159165995799552166817<27> × 361891465554027926328212109315492958100997206097379289106276719937497238193433484091111073933052484219352678045229183201550946673080791943459<141>
7×10167+3 = 7(0)1663<168> = 37 × 2003 × 1538111 × 6140838679507652677023566807863570764672268917609820631428822778337092182987741633764651826741137994401508805797026063220904931764487509670939380900542930243<157>
7×10168+3 = 7(0)1673<169> = 341870677521159820404771314461<30> × 5749965473293729696597801765242916256625281553550128309455278186337<67> × 3560991610105122471722990488660298925687905168583791168409158735294004479<73> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=576124639 for P30 / July 26, 2007 2007 年 7 月 26 日) (Serge Batalov / Msieve-1.38 snfs / 36.00 hours on Opteron-2.6GHz; Linux x86_64 / November 24, 2008 2008 年 11 月 24 日)
7×10169+3 = 7(0)1683<170> = 61 × 73 × 1670391467493499<16> × 32397946134897073854757<23> × 5175216009374760485968852867656086119<37> × 56128200837449627643617345573916608964872045642509134587009683630669439311948801876882681303<92> (Robert Backstrom / GMP-ECM 6.1.3 B1=928000, sigma=3134470293 for P37 / February 13, 2008 2008 年 2 月 13 日)
7×10170+3 = 7(0)1693<171> = 17 × 37 × 1112877583465818759936406995230524642289348171701112877583465818759936406995230524642289348171701112877583465818759936406995230524642289348171701112877583465818759936407<169>
7×10171+3 = 7(0)1703<172> = 193663 × 1870021 × 5209480256572103393851<22> × 2894880042580604713105118836471073339<37> × 80382204556821276120047494428888590479349<41> × 15944834639689281626909755621895853382079436807483057371958301<62> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=799800686 for P37 / November 5, 2008 2008 年 11 月 5 日) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P41 x P62 / 4.35 hours on Core 2 Quad Q6700 / November 7, 2008 2008 年 11 月 7 日)
7×10172+3 = 7(0)1713<173> = 139 × 263 × 459678549047<12> × 4165558648519257075398117430852608235410611617423563142333471512657588671663996081120942357921298500901612797688759830352823967751034362974023084396051713257<157>
7×10173+3 = 7(0)1723<174> = 37 × 4830247 × 253488539 × 22348446469487<14> × 4395944156853610582716741443564661893213<40> × 290110443363764923642894085090214904885689697<45> × 542132919827093529306769989453942968418390454867117966238849<60> (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=1786388023 for P40 / December 12, 2009 2009 年 12 月 12 日) (Dmitry Domanov / GGNFS/msieve gnfs for P45 x P60 / 6.56 hours / December 13, 2009 2009 年 12 月 13 日)
7×10174+3 = 7(0)1733<175> = 16017107 × 2323972359634351<16> × 188054185866772671191665178569550149161634714942182327136840192042382849382646036456931740746618529402699948626694851557946812398235380579618455184534079<153>
7×10175+3 = 7(0)1743<176> = 113 × 487 × 8389 × 15382421157285425929466447017738051797673565880227<50> × 9857249360937578381060501178705637693417639727420036892990380567114305681621039301876173072701917734426786021572283771<118> (matsui / GGNFS-0.77.1-20060513-prescott snfs / April 5, 2008 2008 年 4 月 5 日)
7×10176+3 = 7(0)1753<177> = 37 × 2207 × 1053449 × 8137302623761235010855796584072911389981801056482462568600813832297176194646605842923648629769815943571734807927098580864348762769799419000175401545881957225189263633<166>
7×10177+3 = 7(0)1763<178> = 31 × 73 × 10141 × 13509889 × 363118907 × 62177328753972491311278652488762682241014806732595811306775457447049246828632191347968703892951988821296429153836011601282263722375529794517406379941778267<155>
7×10178+3 = 7(0)1773<179> = 2141 × 158029 × 7746367 × 213244001 × 137059505906208078071<21> × 913819724245006394544594778433113056501017933605219958402243098887544337692518145201410568436095032975372322460006341093414531578797411<135>
7×10179+3 = 7(0)1783<180> = 37 × 104947 × 224351 × 117100092960585003361<21> × 7377639422767413795152038802532449<34> × 8924589012579945383764872567099224584777759201<46> × 104216236811622888894520864063301304707400428779271994024902963412643<69> (Ignacio Santos / GMP-ECM 6.3 B1=1000000, sigma=1484558775 for P34 / November 21, 2010 2010 年 11 月 21 日) (Dmitry Domanov / Msieve 1.40 gnfs for P46 x P69 / November 24, 2010 2010 年 11 月 24 日)
7×10180+3 = 7(0)1793<181> = 1661635052382325894228860798388965059<37> × 131913960468256481049783481878995394120408634187<48> × 31935346709903794461672028654050306602845641564412306934217578538639453607167090484368169049565091<98> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, sigma=1692799595 for P37 / August 3, 2007 2007 年 8 月 3 日) (Kenji Ibusuki / Msieve v. 1.49 (SVN unknown) + GGNFS-0.77.1-VC8 with factMsieve.pl (decomposed + modified) snfs / October 8, 2013 2013 年 10 月 8 日)
7×10181+3 = 7(0)1803<182> = 1307951 × 163667033636679029<18> × 141841795076420712913980812493112825124222601248955632166449031731<66> × 2305372645795761082391178326649414245146333413240828452602567296737367149385317590295058383747<94> (Youcef Lemsafer / GGNFS (SVN430), msieve 1.50 (SVN708) snfs / November 12, 2013 2013 年 11 月 12 日)
7×10182+3 = 7(0)1813<183> = 19 × 37 × 5796213552807101290302139288236547086048674920761890437988566399723613188147<76> × 171790180884158531835765998721853676674416631560705620499042258287282118632167531441001689658431400392783<105> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 549.90 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / June 24, 2008 2008 年 6 月 24 日)
7×10183+3 = 7(0)1823<184> = 2521 × 40903 × 31573785372835301<17> × 6532146026519860457157147209255179524173<40> × 329145176340330144366067696273650835525363281649760739050879404222106372606647737182646483636713315293456550191850515597<120> (Ignacio Santos / GMP-ECM 7.0 B1=11000000, sigma=1:3277507288 for P40 / October 20, 2013 2013 年 10 月 20 日)
7×10184+3 = 7(0)1833<185> = 3163 × 409753 × 852368918477<12> × 477967106515971827982803<24> × 10353940181472354735743878357133906382757885744626795077825537<62> × 12803993354478757798948858513755811035616773207420548027821509860182615116604391<80> (Dmitry Domanov / Msieve 1.50 snfs / January 28, 2014 2014 年 1 月 28 日)
7×10185+3 = 7(0)1843<186> = 37 × 71 × 732 × 1213 × 1744828062310637<16> × 23625380330382524612684685202352518907464561821199107262513207110669840793252362550376852716738561590930610276053909409965948177519959225214760946180826955554361<161>
7×10186+3 = 7(0)1853<187> = 17 × 23 × 6217 × 85947685102648127667543837824599<32> × 2935025821474710522373226657650253973539388376844261729<55> × 11415483348167852008275676098662676700917828937365724798901968306864980550722949713100200107819<95> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=4149229516 for P32 / July 28, 2007 2007 年 7 月 28 日) (Erik Branger / GGNFS, Msieve snfs for P55 x P95 / January 17, 2017 2017 年 1 月 17 日)
7×10187+3 = 7(0)1863<188> = 47 × 1489361702127659574468085106382978723404255319148936170212765957446808510638297872340425531914893617021276595744680851063829787234042553191489361702127659574468085106382978723404255319149<187>
7×10188+3 = 7(0)1873<189> = 37 × 600857 × 1633493778036774146509<22> × 19275591161847456977382152268219000035295474874561534384065003675184236533160199164688668964937134309986923842085310707943683849107032856099959039706464533265563<161>
7×10189+3 = 7(0)1883<190> = 29 × 97 × 521 × 2150831 × 381070380281561<15> × 5827457351737515133463848205355341524045172428171606098486674404198650493744698885448251395120248677164107420640249760839439762664576620002182162626895515787579921<163>
7×10190+3 = 7(0)1893<191> = 1801 × 264487 × 146953521143558208322264671659532909450660089710044264982751739826298040924611653329833376309190813094819175235244823632020640705301997180016511991542732487403506303037008436771695069<183>
7×10191+3 = 7(0)1903<192> = 37 × 59 × 363924621565554504860719<24> × 881115548912592343224292572074541633209126916238065998273586054071179410214022514269555239761075788512145136165749616828837042321163829129116899178942091854903314539<165>
7×10192+3 = 7(0)1913<193> = 31 × 1105109 × 1243211 × 4470822866051487481<19> × 5290673163123042490177645270463<31> × 360922089125386739265100361213804922199<39> × 19251941213231301805507821363673906075280686340797762406923312617295075302212157369103874171<92> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2554121386 for P31 / July 28, 2007 2007 年 7 月 28 日) (Robert Backstrom / GMP-ECM 6.1.3 B1=2148000, sigma=1344192446 for P39 / February 1, 2008 2008 年 2 月 1 日)
7×10193+3 = 7(0)1923<194> = 73 × 958904109589041095890410958904109589041095890410958904109589041095890410958904109589041095890410958904109589041095890410958904109589041095890410958904109589041095890410958904109589041095890411<192>
7×10194+3 = 7(0)1933<195> = 37 × 89 × 711549423651204178804703845878926067199337895119<48> × 298745407724036587596846553046331517575087722040410770709987309288456174674024401314163963624147750872498764458224098031975479126729720370314609<144> (Wataru Sakai / Msieve / 644.03 hours / July 12, 2009 2009 年 7 月 12 日)
7×10195+3 = 7(0)1943<196> = 10853 × 1155441953<10> × 82157819227893172508801401<26> × 3264429666208402941646844264448525016971036119<46> × 2081344097739694518485623114863207666580074112266611692519396401802216778880649252109357498189265361435766375993<112> (Serge Batalov / GMP-ECM B1=110000000, sigma=3341907957 for P46 / October 30, 2013 2013 年 10 月 30 日)
7×10196+3 = 7(0)1953<197> = 107 × 277 × 2713 × 6209295025861248104401498918612644843252814534446112342360551710652554123<73> × 140198189187298177033134475194820344937688280235805400687901079429074440127140284360976916800670096474701071003670823<117> (Wataru Sakai / August 16, 2010 2010 年 8 月 16 日)
7×10197+3 = 7(0)1963<198> = 37 × 127 × 255202990243<12> × [583723040868188398708597090156241795531993542291926409332571092713616810806791118215733781720504096037754967368622540416612763148781932602531673090118185678243217961071094830531676979<183>] Free to factor
7×10198+3 = 7(0)1973<199> = 4151954057<10> × 117871039717<12> × [14303370437529736035776509021020367994977563743718072242830294592017946229786059564291921595196918594785013092205330293250436877969336545570611980419433044939382199912869165524687<179>] Free to factor
7×10199+3 = 7(0)1983<200> = 3047419399<10> × 9072288419<10> × 544255039845653<15> × 4652072821357268342311218558927049396924163868683228412322637831718777440707373836111117710106437614781578074110125746615301630792884176539792449566529213758644818171<166>
7×10200+3 = 7(0)1993<201> = 19 × 37 × 7501217 × 20402275557381199<17> × 116942959866455304271567<24> × 30140964087251698621351505100337<32> × 1845870187280936627842607751822820884327424820308665648049783479624333044500932291554887245148311810314856011773399314893<121> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=721870745 for P32 / July 30, 2007 2007 年 7 月 30 日)
7×10201+3 = 7(0)2003<202> = 73 × 2549 × 21739 × 847003063883<12> × [2043058492307067550223787256705332909947066274414760791548170707723398336498263778729521492707748176450075551852219460025505931254136390203052158453596295307634918824329063029075447<181>] Free to factor
7×10202+3 = 7(0)2013<203> = 17 × 6673 × 4353653 × 1793258149946950549505155314272581687<37> × [79037167731619367064646295811996973912509341300003788988243863560636996657843086441558616189531026784673009053593529999453293710597199270027151583251649153<155>] (Serge Batalov / GMP-ECM B1=11000000, sigma=2119995705 for P37 / November 19, 2013 2013 年 11 月 19 日) Free to factor
7×10203+3 = 7(0)2023<204> = 37 × 347 × 2158841 × 10963871 × 18434111300263091<17> × 39421058788435533306235532145937<32> × 11161082229868366178586047078195906213830944275401463<53> × 284004661875520229748354481165373733772213270925504868400991084706402200408864083124567<87> (Serge Batalov / GMP-ECM B1=2000000, sigma=3839599914 for P32 / November 18, 2013 2013 年 11 月 18 日) (Youcef Lemsafer / GGNFS (SVN 440), msieve 1.51 (SVN 845) for P53 x P87 / December 4, 2013 2013 年 12 月 4 日)
7×10204+3 = 7(0)2033<205> = 4877 × 53611 × 308291 × 641372298928399<15> × 5396904049036253429396109729240338143<37> × 25088554182525885596739966302426014545032142855717083058096800211032876592311215655652188376631954202866760200561135138478555417285172588127<140> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=2483173277 for P37 / November 26, 2013 2013 年 11 月 26 日)
7×10205+3 = 7(0)2043<206> = 19327737301<11> × 8762137733341<13> × 70062851575176993405893<23> × [5899553461139675179912882213016471722934865502498794687623580161308214078279299524547466036204550618860402930369201325049526621661496510062595118968133176263431<160>] Free to factor
7×10206+3 = 7(0)2053<207> = 37 × 1117 × 10939 × 41081 × 5314086901<10> × 403794741613<12> × 1959119440307<13> × 436509026704285907<18> × 185837350131898929749363764227586673830577636841094338108364844767441<69> × 110521826926414827248016437625056657689818035352943332588844089689442988169<75> (Youcef Lemsafer / msieve 1.52 GPU for polynomial selection, GGNFS (SVN 440), msieve 1.51 (SVN 845) gnfs / December 11, 2013 2013 年 12 月 11 日)
7×10207+3 = 7(0)2063<208> = 31 × 55621 × 146464379 × 1188028131071590758930498763379193055166617<43> × 23331293370909830112753518691795680285842593525007177818993216446285282195177465806442743444736734832170691967844901567091171572559767268061281827244371<152> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3662884385 for P43 / May 5, 2014 2014 年 5 月 5 日)
7×10208+3 = 7(0)2073<209> = 23 × 102672526173105876700515068182897<33> × 29642576980508504694993798852590656516820034394346110328727438300207926928579716222939595958107388618768416681332961461614278066011078076173633167038867156128217165559327439813<176> (Serge Batalov / GMP-ECM B1=11000000, sigma=3717163228 for P33 / November 19, 2013 2013 年 11 月 19 日)
7×10209+3 = 7(0)2083<210> = 37 × 73 × 13439934931113904319881321945371697<35> × 19283074969502363385339409984983143972856363139426105368328720637251979578799804945134645882721133469401878150604925523181900247815845928251368791831964839378900776860908799<173> (Serge Batalov / GMP-ECM B1=2000000, sigma=1716420890 for P35 / November 18, 2013 2013 年 11 月 18 日)
7×10210+3 = 7(0)2093<211> = 109 × 199 × 439 × 28547 × 8343781456013<13> × 3086246070963832364695824557698265620409862802972656701032796707351567969654957775431601553717951601556987863145863228481751405967537056163991071864028025740671218227998382858463694841977<187>
7×10211+3 = 7(0)2103<212> = 233 × 885213946551580702999<21> × 339385959427888946845331996259129808521751292906869816423020706316715544443564861810826698014573766456918871248643139366979655299647525122512100295694212502600498663993171598772895457643309<189>
7×10212+3 = 7(0)2113<213> = 37 × 290473 × [65131419852856957166135643997613956956133337414902310779035982411167023850474635917689144667211475486254897766466827963077184175186399145252463805306926698587885686170208311681013102487731799234073111507503<206>] Free to factor
7×10213+3 = 7(0)2123<214> = 701 × 3706860927323951327696943477366192243798867586538315006021070431813569<70> × 2693851984345552719374647011864777375768535211135930458196417662532168996562661466414894102908412028132596341826873565044421826630562900834687<142> (Serge Batalov / Msieve v. 1.52 (SVN 923M) for P70 x P142 / November 22, 2014 2014 年 11 月 22 日)
7×10214+3 = 7(0)2133<215> = 34980221 × [2001130867640887689074348615464722192578485996414945463037526263770603393271872124535748359051247846604514019508338726619251490720999161211703036410204498136246766422659250780605416986930985942027067238940543<208>] Free to factor
7×10215+3 = 7(0)2143<216> = 37 × 255847 × 996866328370908883<18> × 74178673051665200016025424159564064101211379535222085715768976435283967117356179327226920527827894172192783367095060247132868694954147004354861727579655709690739038835315391176126463642909819<191>
7×10216+3 = 7(0)2153<217> = 2059469 × 2690604244960557033247<22> × 121641118324834361763118796233<30> × [10385144735345945569510941953764410444310283430640328102009745468340937242017104098480777003320481139551424294273876827762558612082203263347631493968371600438537<161>] (Makoto Kamada / GMP-ECM 6.4.4 B1=1e6, sigma=474211932 for P30 / October 30, 2013 2013 年 10 月 30 日) Free to factor
7×10217+3 = 7(0)2163<218> = 29 × 73 × 293 × 12073 × 2180501 × 838812801318421<15> × [5110613303174167333511062067656329548529943484140767046670953352619757687727246878758603511441195985911673739151006024845903689308018432670207981397063085063753049028924256253688075231611<187>] Free to factor
7×10218+3 = 7(0)2173<219> = 17 × 19 × 37 × 139 × 41874767197<11> × 3624419988793<13> × 1957941643207614562193<22> × 1177199853976900283599763<25> × 6260912466135837184555391199525986430130346123065958687500997130124261<70> × 192397974640196617059291295389129996678764450645044076196121227785839943813<75> (Youcef Lemsafer / msieve 1.52 (SVN 942) CUDA for polynomial selection, GGNFS (SVN 440), msieve 1.51 (SVN 845) gnfs / December 16, 2013 2013 年 12 月 16 日)
7×10219+3 = 7(0)2183<220> = 61082965717313<14> × [114598234021501689699158488079737573971060533850913348456477076360636045164524618850760634790801932687869576368242939198621948928296030626496100561199061279108140161485328296432150988436210947386987791064131<207>] Free to factor
7×10220+3 = 7(0)2193<221> = 71 × 1433 × 4957 × 1060723 × [130849659272491633204254777792809866019412918502345453367160021166487459483630388063705179605572508019032437866241391059787220872772259894466047979532988239155310555022650899448534300474428546069577604792811<207>] Free to factor
7×10221+3 = 7(0)2203<222> = 37 × 18918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918918919<221>
7×10222+3 = 7(0)2213<223> = 31 × 431 × 19016695740841<14> × [27550153187087148338772321956561896463860501740748310378698551757534754205402004020770525801534209151640567972418300259892431330226075674577320017731844340337770656008752089470476809063262159005556414550203<206>] Free to factor
7×10223+3 = 7(0)2223<224> = 70202191 × [997119876215829218207733715889294680275719599691696232101929696182844207811120880828349075315897191869695348967099901483131772910050627907040679114986596358509665317995559426343260426159633678669658615070860110334733<216>] Free to factor
7×10224+3 = 7(0)2233<225> = 37 × 22637 × 6388823297<10> × 1888616195713014199936279<25> × [69264843763964617568208124355189268233190081372218877027832367639316366799426128506729557857315217903095531234956374871974606279943333107875424338515654457474184084762076305129157252149<185>] Free to factor
7×10225+3 = 7(0)2243<226> = 73 × 1523 × 27253 × 50392306231003517204360326654783240793<38> × 11490186445963043272757708162816409649508168469737<50> × 27274110549533639162128771337949537322724747518364736341662065053<65> × 146291486698253608805179035063607291595329945292541200561222261353<66> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4193646824 for P38 / November 22, 2013 2013 年 11 月 22 日) (Dmitry Domanov / GMP-ECM B1=11000000, sigma=1034487263 for P50 / May 13, 2014 2014 年 5 月 13 日) (Cyp / yafu v1.34.3 / May 14, 2014 2014 年 5 月 14 日)
7×10226+3 = 7(0)2253<227> = 89515807 × 338495831 × 2310175557685584259816705829406160322602754916167649333313473907843513795778395508145303321788350365350644785310969825740246742106403944258116136915166018399579981883849127464265455558971909996398764460446210859<211>
7×10227+3 = 7(0)2263<228> = 37 × 136376513248181991989<21> × 138725638809152669413954612687207143272338088923859873791596050638239128638634551083286447469646848509865884614488473950507461087535219710504871120814213040243435810738783135834471163884648507574376658919371<207>
7×10228+3 = 7(0)2273<229> = 4470421 × 1302233897<10> × 26030729623<11> × 46192798977987385169123166698458912870039062214903081267965621283080515871320925669497199849476634190796132643140299202906847688037719453710373383852323374671633673034078554527930033148826170297159992953<203>
7×10229+3 = 7(0)2283<230> = 61 × 3579487 × 158399777 × 119877546293599123685450881<27> × [16883209308648344188049015856737761723715320612731070151412307318545017238272983742978694415192605274450278379433661040010544246693740036008573023116543400707152241924050632479921676985217<188>] Free to factor
7×10230+3 = 7(0)2293<231> = 23 × 37 × 29663 × 2672852879268961<16> × [10374767035400774674438602966950190856739905409661460661002465864572427591595823157481249302254910920749324109231176075969234080264006392450326135125522576442964698937300263248827942505602903337088658016178671<209>] Free to factor
7×10231+3 = 7(0)2303<232> = 10499 × 87982113884134640398342003644621056125511209<44> × [7578019387618122109207134371339204628849506926817597094340240451410616495519221913900230897842215835319837708389541004900129127169426582620793163042616938534598770972125643313423985433<184>] (Serge Batalov / GMP-ECM B1=11000000, sigma=202485836 for P44 / November 19, 2013 2013 年 11 月 19 日) Free to factor
7×10232+3 = 7(0)2313<233> = 743 × 7134514243<10> × 25675997687<11> × 351761499459651679<18> × 3056919077486918816940875845578571<34> × [478283328448247624358799510465754225428844210588495270471120561287363267402694523465521726923614929111962729918063236590979902770881076830446875109991305967709<159>] (Serge Batalov / GMP-ECM B1=1000000, sigma=1984847614 for P34 / November 18, 2013 2013 年 11 月 18 日) Free to factor
7×10233+3 = 7(0)2323<234> = 37 × 47 × 73 × 2341 × 2335357067<10> × 9058627147<10> × [111341869167160693449109782019255242310697005612465071326684607529631860198801091679657178419708920258881002127189498627649269700225270296543559408120746219450572900407210972261216332763447856256083997510261<207>] Free to factor
7×10234+3 = 7(0)2333<235> = 17 × 102497 × 15374075981084878216668043<26> × 30533855655490826866446675252201001359632354423<47> × 8557901690791309231657096285124708665799310293909095913778419888502919416932255556291122672579094866542390110225523082607118296443729755855591135960821454223<157> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3134900388 for P47 / May 12, 2014 2014 年 5 月 12 日)
7×10235+3 = 7(0)2343<236> = 3607 × 7159 × 8929 × 96979 × 1321997120762420412838677730813<31> × [2368037096036225950198477496528971175674799694298148786305321528191796590130171779136666176699361020725438310944703039872583156424853658244032598777959929738683125784873369371762967734435157<190>] (Serge Batalov / GMP-ECM B1=11000000, sigma=231417044 for P31 / November 19, 2013 2013 年 11 月 19 日) Free to factor
7×10236+3 = 7(0)2353<237> = 19 × 37 × [995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943100995732574679943101<234>] Free to factor
7×10237+3 = 7(0)2363<238> = 31 × 950203543 × 2504979269199138128401<22> × [94867086867966779896710937358605216453156602133589882818349223622976322051975529817346064056796527581790341008140185091921470672304877384827426108649345034151909059758328014114565037565319383423625822700091<206>] Free to factor
7×10238+3 = 7(0)2373<239> = 89 × 9925931694500868884933083164403<31> × 79238592218837016342518986892279546910420072993760711534572986796217368513239646144648994069502905104455312336307705859863607066675319408088490842504647231550737511481825618727298322927878798015348306179609<206> (Serge Batalov / GMP-ECM B1=1000000, sigma=4042820070 for P31 / November 18, 2013 2013 年 11 月 18 日)
7×10239+3 = 7(0)2383<240> = 37 × 127 × 474512359 × 4892298713<10> × 609950995403<12> × 692456220695383<15> × 619406699046924853756071225212316403<36> × 170611387456251992881757564074844934024228427370889419<54> × 1437675666143983925089195484064912061373931891245112796796396803106628975879700112112335353063759559987<103> (Serge Batalov / GMP-ECM B1=11000000, sigma=850474681 for P36 / November 19, 2013 2013 年 11 月 19 日) (Serge Batalov / GMP-ECM B1=11000000, sigma=431402397 for P54 / November 19, 2013 2013 年 11 月 19 日)
7×10240+3 = 7(0)2393<241> = definitely prime number 素数
7×10241+3 = 7(0)2403<242> = 73 × 521 × 5741 × 80084748671<11> × [4003133676727429509010087563532162318830828981469922235613700260743218895813653882894952265354610134570156186316117135063726401268153796126526486520015743857677387115112132895791426342093632056816176073419172032942102886081<223>] Free to factor
7×10242+3 = 7(0)2413<243> = 37 × 1699 × 76367 × 177027491 × [823676153522482049388171145287506843918766054951321124495591981140292164684555541124760845567393417911347316258009816052791674421630530573101473960712341450246612377442990342959985630939832029127489611038245605000786390870273<225>] Free to factor
7×10243+3 = 7(0)2423<244> = 887017 × 3220126537391<13> × 172434818223266338699<21> × 590321684428680379356721<24> × 1311820135242860956879961665353966762366406453<46> × 18352919765008207633933452583058018127658293993518222363659269160996943999379586853531818421062861096833717152719623619862766358974739427<137> (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3543840413 for P46 / May 14, 2014 2014 年 5 月 14 日)
7×10244+3 = 7(0)2433<245> = 257 × 8609 × 185812769849731<15> × [170269418015375401808237178167594361950570816029235132473926193430243069525816392491105957008886063392459061459499827132167387864367124839266806160144534103839617557186260851592425183350591363454196108652272037820694871372001<225>] Free to factor
7×10245+3 = 7(0)2443<246> = 29 × 37 × 191 × 2735151574922376664866913524272831<34> × [1248773149020535337312221356974049911598442132918644419640194245335921110721385311041740876285126160147650365342967311083914658356692263355504730160514266597435291240120160982778889190962918289020118026011891<208>] (Serge Batalov / GMP-ECM B1=11000000, sigma=2732035713 for P34 / November 19, 2013 2013 年 11 月 19 日) Free to factor
7×10246+3 = 7(0)2453<247> = 443 × 7669 × 1112034756365909<16> × 6373530591310074481<19> × 12639341241249741348353147872030007878097009477<47> × [23000257643567801121660005940641007421587802985093997308298989101195962860938534722685986154482434113914216321748741213870915514365273147699134792247530461271773<161>] (Dmitry Domanov / GMP-ECM B1=11000000, sigma=3082790376 for P47 / May 12, 2014 2014 年 5 月 12 日) Free to factor
7×10247+3 = 7(0)2463<248> = 4302152983<10> × 2882854444829<13> × 5644032097297895821917641637934764534556545451079268316192674528475670164627816815465161083279875326672540823881504832275849216777786764522767804401690651832516713490347227604715468065589963553899146480562421646398645387091129<226>
7×10248+3 = 7(0)2473<249> = 372 × 11399161 × [44856119932313840060350669475465732104411181022312457478749245452217857083585501810459035084744083996013293408217615501083259949164345252936476590710584038831760012434767499778128334179224382601773413397323404526708491063553828403067888467<239>] Free to factor
7×10249+3 = 7(0)2483<250> = 59 × 73 × 107 × 1163 × 388373 × [33628743914678721915365542216492209428894673435401839760086346085668431515773770178242850945904131973522364461961066976205008299416409260802893004437640503151830736384459903968169652657739199145668420976121594144578846475456683113618453<236>] Free to factor
7×10250+3 = 7(0)2493<251> = 17 × 283 × 5553497 × 5267732803828851698125415773<28> × [497361774057902575795257859575238416899066324604015674931212793330879513655108479450797048891106412916768556135083041144728889345327142257141926310258378099443082338639551148618026285253146675282747092128796828933<213>] Free to factor
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