[PR]ŠΕŒμŽt‚̍DπŒ‚Θ‹lξ•ρ–žΪ:”NŠΤ30,000l‚Μ“]EŠΕŒμŽt‚ͺ—˜—p’†

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counterSince June 16, 2000STUDIO KAMADAEnglish text only.
Factorizations
Factorizations of 700...0012008-09-24(Wed) 22:05

Last update

Sep 24, 2008 22:05 JST

Sequence

71, 701, 7001, 70001, 700001, ...

General term

7·10n+1

Room for prime numbers

upper limit of periods: 10000
upper limit of periodical factors: 4294967296
checked terms: 100000000
terms divided by periodical factors: 70767251
room for prime numbers: 29.23%

Prime numbers

  1. 7·101+1 = 71 is prime.
  2. 7·102+1 = 701 is prime.
  3. 7·103+1 = 7001 is prime.
  4. 7·104+1 = 70001 is prime.
  5. 7·105+1 = 700001 is prime.
  6. 7·108+1 = 700000001 is prime.
  7. 7·109+1 = 7000000001<10> is prime.
  8. 7·1045+1 = 7(0)441<46> is prime.
  9. 7·10136+1 = 7(0)1351<137> is prime.
  10. 7·10142+1 = 7(0)1411<143> is prime.
  11. 7·10158+1 = 7(0)1571<159> is prime.
  12. 7·10243+1 = 7(0)2421<244> is prime.
  13. 7·10923+1 = 7(0)9221<924> is prime.
  14. 7·101235+1 = 7(0)12341<1236> is prime.
  15. 7·102196+1 = 7(0)21951<2197> is prime.
  16. 7·104650+1 = 7(0)46491<4651> is prime. (Makoto Kamada / Jul 29, 2004)
  17. 7·106119+1 = 7(0)61181<6120> is prime. (Makoto Kamada / Jul 29, 2004)
  18. 7·107324+1 = 7(0)73231<7325> is prime. (Makoto Kamada / Jul 29, 2004)
  19. 7·109543+1 = 7(0)95421<9544> is prime. (Makoto Kamada / Jul 29, 2004)
  20. 7·1013494+1 = 7(0)134931<13495> is prime. (Yves Gallot / Yves Gallot's Proth.exe / Jan 20, 1999)
Searched:
References:

Condition

n≤200

Status

Completed up to n=100. (Jul 29, 2004)
Completed up to n=150. (Apr 10, 2007)
The following numbers are not factored yet. (n≤200)
n= 172, 175, 177, 180, 181, 184, 185, 186, 191, 193, 195, 196, 197, 199 (14/200)

Factorization results

7·101+1 =
71
= definitely prime number
7·102+1 =
701
= definitely prime number
7·103+1 =
7001
= definitely prime number
7·104+1 =
70001
= definitely prime number
7·105+1 =
700001
= definitely prime number
7·106+1 =
7000001
= 197 · 35533
7·107+1 =
70000001
= 43 · 61 · 26687
7·108+1 =
700000001
= definitely prime number
7·109+1 =
7000000001<10>
= definitely prime number
7·1010+1 =
70000000001<11>
= 53 · 1320754717<10>
7·1011+1 =
700000000001<12>
= 41149 · 17011349
7·1012+1 =
7000000000001<13>
= 23 · 304347826087<12>
7·1013+1 =
70000000000001<14>
= 67 · 1044776119403<13>
7·1014+1 =
700000000000001<15>
= 964517 · 725751853
7·1015+1 =
7000000000000001<16>
= 17 · 19 · 4397 · 4928775671<10>
7·1016+1 =
70000000000000001<17>
= 421 · 7057 · 23561114333<11>
7·1017+1 =
700000000000000001<18>
= 7993 · 87576629550857<14>
7·1018+1 =
7000000000000000001<19>
= 883 · 11897 · 666346122451<12>
7·1019+1 =
70000000000000000001<20>
= 151 · 463576158940397351<18>
7·1020+1 =
700000000000000000001<21>
= 1709 · 409596255119953189<18>
7·1021+1 =
7000000000000000000001<22>
= 353 · 6909827 · 2869829928971<13>
7·1022+1 =
70000000000000000000001<23>
= 29 · 2546657 · 947828114837717<15>
7·1023+1 =
700000000000000000000001<24>
= 53 · 13207547169811320754717<23>
7·1024+1 =
7000000000000000000000001<25>
= 373 · 366097 · 12904369 · 3972430109<10>
7·1025+1 =
70000000000000000000000001<26>
= 1201 · 4091 · 14247069835676331811<20>
7·1026+1 =
700000000000000000000000001<27>
= 103723 · 6748744251516057190787<22>
7·1027+1 =
7000000000000000000000000001<28>
= 131 · 1165583 · 3256553 · 14077495236829<14>
7·1028+1 =
70000000000000000000000000001<29>
= 43 · 8597482263017<13> · 189346942156171<15>
7·1029+1 =
700000000000000000000000000001<30>
= 38557 · 1527616714369<13> · 11884485990197<14>
7·1030+1 =
7000000000000000000000000000001<31>
= 22751 · 311728909 · 987007539137739739<18>
7·1031+1 =
70000000000000000000000000000001<32>
= 17 · 47 · 7620101 · 11497158881471824049299<23>
7·1032+1 =
700000000000000000000000000000001<33>
= 8933779 · 318157145149<12> · 246275468603831<15>
7·1033+1 =
7000000000000000000000000000000001<34>
= 19 · 313 · 86837 · 13554867923990783781946759<26>
7·1034+1 =
70000000000000000000000000000000001<35>
= 23 · 2039 · 2683 · 556329776746211678345922851<27>
7·1035+1 =
700000000000000000000000000000000001<36>
= 971 · 138064909 · 3116790401<10> · 1675281919706159<16>
7·1036+1 =
7000000000000000000000000000000000001<37>
= 53 · 71 · 149 · 12484683968060611357138653116623<32>
7·1037+1 =
70000000000000000000000000000000000001<38>
= 6994839869<10> · 57678426193<11> · 173502949270994053<18>
7·1038+1 =
700000000000000000000000000000000000001<39>
= 317 · 1829879 · 1206747491361166227530967239507<31>
7·1039+1 =
7000000000000000000000000000000000000001<40>
= 2887 · 357974663581<12> · 388814273833<12> · 17420345593451<14>
7·1040+1 =
70000000000000000000000000000000000000001<41>
= 2219623680068849293<19> · 31536877457456530777157<23>
7·1041+1 =
700000000000000000000000000000000000000001<42>
= 163 · 1667 · 2576171882187979581997710887270398681<37>
7·1042+1 =
7000000000000000000000000000000000000000001<43>
= 9913661 · 13905242467<11> · 50779148014500236425667623<26>
7·1043+1 =
70000000000000000000000000000000000000000001<44>
= 59 · 22787 · 5115254569928473549<19> · 10178683817570268053<20>
7·1044+1 =
700000000000000000000000000000000000000000001<45>
= 631 · 5273 · 283802089 · 1184863787<10> · 625643439962731117589<21>
7·1045+1 =
7000000000000000000000000000000000000000000001<46>
= definitely prime number
7·1046+1 =
70000000000000000000000000000000000000000000001<47>
= 67 · 1723 · 167483 · 192326681 · 2965271891<10> · 6348383739954260377<19>
7·1047+1 =
700000000000000000000000000000000000000000000001<48>
= 17 · 809 · 624595408303267<15> · 81489529409530467454585396451<29>
7·1048+1 =
7000000000000000000000000000000000000000000000001<49>
= 335774807663894173723<21> · 20847305516162787430315360787<29>
7·1049+1 =
70000000000000000000000000000000000000000000000001<50>
= 43 · 53 · 15749 · 20707 · 10102501 · 9322977717564135646809458279333<31>
7·1050+1 =
700000000000000000000000000000000000000000000000001<51>
= 29 · 24137931034482758620689655172413793103448275862069<50>
7·1051+1 =
7000000000000000000000000000000000000000000000000001<52>
= 19 · 107 · 36571 · 8844086717<10> · 10645616898971703821463777637649471<35>
7·1052+1 =
70000000000000000000000000000000000000000000000000001<53>
= 331 · 5066744745133<13> · 510879105643829609<18> · 81700154832720689143<20>
7·1053+1 =
700000000000000000000000000000000000000000000000000001<54>
= 277 · 353 · 28969223382025922341<20> · 247119327220915612206258469081<30>
7·1054+1 =
7000000000000000000000000000000000000000000000000000001<55>
= 2076617 · 609738900073<12> · 5528378025258263660015531789025244561<37>
7·1055+1 =
70000000000000000000000000000000000000000000000000000001<56>
= 1733 · 746807 · 8300940757<10> · 6515740551155259920298211947108344303<37>
7·1056+1 =
700000000000000000000000000000000000000000000000000000001<57>
= 232 · 65171 · 3663073 · 80356697 · 68979546095780249020263358014353219<35>
7·1057+1 =
7000000000000000000000000000000000000000000000000000000001<58>
= 431 · 872008382213547623659<21> · 18625164201652084566455624905345069<35>
7·1058+1 =
70000000000000000000000000000000000000000000000000000000001<59>
= 23627 · 131910613 · 22459998357768729911032893796446983194067544151<47>
7·1059+1 =
700000000000000000000000000000000000000000000000000000000001<60>
= 1063 · 222317 · 4530622027<10> · 5040195171932521817<19> · 129714019157402149748609<24>
7·1060+1 =
7000000000000000000000000000000000000000000000000000000000001<61>
= 6260983 · 1128365662841<13> · 128449842236097864451<21> · 7713865790225245405717<22>
7·1061+1 =
70000000000000000000000000000000000000000000000000000000000001<62>
= 31379 · 33840991 · 1053222795517808050831153<25> · 62588654898405631375738453<26>
7·1062+1 =
700000000000000000000000000000000000000000000000000000000000001<63>
= 53 · 263 · 30606318229<11> · 1640798810097282938237794899318827947449057529871<49>
7·1063+1 =
7000000000000000000000000000000000000000000000000000000000000001<64>
= 17 · 411764705882352941176470588235294117647058823529411764705882353<63>
7·1064+1 =
70000000000000000000000000000000000000000000000000000000000000001<65>
= 155747 · 177830773 · 2527385174946935080064493411253552809147917330305471<52>
7·1065+1 =
700000000000000000000000000000000000000000000000000000000000000001<66>
= 911 · 4111 · 8725373753730989<16> · 21421414613986237422732343423725139036463429<44>
7·1066+1 =
7000000000000000000000000000000000000000000000000000000000000000001<67>
= 179 · 3413 · 11457997436682287736505343518947435618330831670559657700510863<62>
7·1067+1 =
70000000000000000000000000000000000000000000000000000000000000000001<68>
= 61 · 877 · 1041340910419<13> · 1256538156552716729623377520533044743728407425653107<52>
7·1068+1 =
700000000000000000000000000000000000000000000000000000000000000000001<69>
= 18777609181<11> · 37278441214352803927387266884878937133950993374868450991221<59>
7·1069+1 =
7000000000000000000000000000000000000000000000000000000000000000000001<70>
= 19 · 1371427934093335549122631<25> · 268640475720764515979633440698742187063360909<45>
7·1070+1 =
70000000000000000000000000000000000000000000000000000000000000000000001<71>
= 43 · 8704354929404289446554626939267521<34> · 187022127423243424834177726936224067<36>
7·1071+1 =
700000000000000000000000000000000000000000000000000000000000000000000001<72>
= 71 · 144169 · 23996248319<11> · 3102680142255775117<19> · 918517534965761229165416642252824613<36>
7·1072+1 =
7000000000000000000000000000000000000000000000000000000000000000000000001<73>
= 2843 · 5021 · 438439 · 21337290059<11> · 52418250189967080049323234426128298639333271509067<50>
7·1073+1 =
70000000000000000000000000000000000000000000000000000000000000000000000001<74>
= 443 · 96130808681091469<17> · 9742871641117961701<19> · 168711519586986544202026669610698003<36>
7·1074+1 =
700000000000000000000000000000000000000000000000000000000000000000000000001<75>
= 109 · 2857 · 38873 · 247607413 · 233533721798448810420708866439356342455756308842550402673<57>
7·1075+1 =
7000000000000000000000000000000000000000000000000000000000000000000000000001<76>
= 53 · 181 · 503 · 1163 · 6197 · 42073 · 2038369 · 530935502475713<15> · 4420652191725997735888870130542131409<37>
7·1076+1 =
70000000000000000000000000000000000000000000000000000000000000000000000000001<77>
= 191 · 130916809033144889755051<24> · 16904389146780147811198177<26> · 165603602344810655649299293<27>
7·1077+1 =
700000000000000000000000000000000000000000000000000000000000000000000000000001<78>
= 47 · 2953 · 37507 · 224629 · 96912111559<11> · 6177041607312669385954348727264644004250809539685743<52>
7·1078+1 =
7000000000000000000000000000000000000000000000000000000000000000000000000000001<79>
= 23 · 29 · 9052035909381906005231<22> · 1159380356943895725035755204692052417643220887504346013<55>
7·1079+1 =
70000000000000000000000000000000000000000000000000000000000000000000000000000001<80>
= 17 · 67 · 7433 · 64957250287<11> · 2104847299828787515681<22> · 60473061555825894732690012430445685827309<41>
7·1080+1 =
700000000000000000000000000000000000000000000000000000000000000000000000000000001<81>
= 1709686599653<13> · 29046208851986050526491<23> · 14095876190325431000221984046542857295930081687<47>
7·1081+1 =
7000000000000000000000000000000000000000000000000000000000000000000000000000000001<82>
= 1917887 · 80978482637540183<17> · 45071850576775516869573739586045324426052488100321878261081<59>
7·1082+1 =
70000000000000000000000000000000000000000000000000000000000000000000000000000000001<83>
= 15889141 · 14747139615121<14> · 298737559793260759146850073050986309527116916277283924218166541<63>
7·1083+1 =
700000000000000000000000000000000000000000000000000000000000000000000000000000000001<84>
= 252960538573<12> · 2767230034964493908395091215727935925673484749582139323602459161340773637<73>
7·1084+1 =
7000000000000000000000000000000000000000000000000000000000000000000000000000000000001<85>
= 10784957 · 372912963901<12> · 1740492438042218441600795654554179784546137928409913148690052494393<67>
7·1085+1 =
70000000000000000000000000000000000000000000000000000000000000000000000000000000000001<86>
= 353 · 8457781026839364786981083<25> · 23445899421709539751838042733667823710889768177163251387699<59>
7·1086+1 =
700000000000000000000000000000000000000000000000000000000000000000000000000000000000001<87>
= 1577653981<10> · 5021705514998995631491<22> · 88355795491020302517303932518723295632640532937242680231<56>
7·1087+1 =
7000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<88>
= 19 · 593 · 607 · 751 · 4051 · 336433221704369803061231886913782658143785716072528301445460952243148626329<75>
7·1088+1 =
70000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<89>
= 53 · 1789 · 47133224833<11> · 123493451992541<15> · 6005920050222233<16> · 21118409050452993269124024319544304371346397<44>
7·1089+1 =
700000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<90>
= 16529 · 6243817 · 397081413119922646343245506851472307<36> · 17081332072428353100585483934303689653375251<44>
7·1090+1 =
7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<91>
= 1499 · 4669779853235490326884589726484322881921280853902601734489659773182121414276184122748499<88>
7·1091+1 =
70000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<92>
= 43 · 97 · 19559 · 8920251484891621327<19> · 138822435642830570322917<24> · 692906196600348666579091765215947239101551<42>
7·1092+1 =
700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<93>
= 3819198191<10> · 2448841163382511<16> · 74845419553176991590681628881541137812735208625185046937629625522401<68>
7·1093+1 =
7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<94>
= 1657 · 687312877619899348261627<24> · 6146403260884787336746557339603038490831997243563850080314216456459<67>
7·1094+1 =
70000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<95>
= 151 · 4135397809<10> · 34135832070661090930273<23> · 59299334117980730945669<23> · 55378793445353177835710883773416871947<38>
7·1095+1 =
700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<96>
= 17 · 287191 · 142648321 · 1005105451437390945022542405895081794619391226822138248536885606765570286907375223<82>
7·1096+1 =
7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<97>
= 113 · 8646955367<10> · 22159917465967<14> · 323286999680819274641136173183578158286785122252061218497706849870919593<72>
7·1097+1 =
70000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<98>
= 19035585744111823<17> · 52639681454775704063<20> · 69858385186026643924161034207590802616119188445855778196765649<62>
7·1098+1 =
700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<99>
= 1031 · 3502244828934538713156144576629<31> · 193862081747557226714681138891356596234903148078641452959796245499<66>
7·1099+1 =
7000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<100>
= 22501 · 2136181 · 450480450735019<15> · 320186759530822356575497238971417<33> · 1009668610319485011591771706987015657322627<43>
7·10100+1 =
70000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<101>
= 23 · 86614592761<11> · 35138169722365234470784794732495630356286437616663986391742843166619544065547252492235167<89>
7·10101+1 =
7(0)1001<102>
= 53 · 59 · 8263 · 27091459723068776585671845560412194237561372315570146929757766357136418774520915593809384721601<95>
7·10102+1 =
7(0)1011<103>
= 673 · 11813 · 494459880209<12> · 6789844280473557307399700579<28> · 262259904248636684132091769713556091513551905597773425759<57>
7·10103+1 =
7(0)1021<104>
= 1259 · 2189639 · 1084487141<10> · 5118387310405609<16> · 54119446405814219<17> · 84525722518020314554799292267603061355961625076981291<53>
7·10104+1 =
7(0)1031<105>
= 107 · 193 · 197 · 359 · 4951 · 373276191289916587<18> · 259342123229793379601513864522935022071345647264756418005901008032940784501<75>
7·10105+1 =
7(0)1041<106>
= 19 · 6793 · 10059622147<11> · 4868902060907309917<19> · 1107312283062255288305948744024504672397484495735935683620222498413006197<73>
7·10106+1 =
7(0)1051<107>
= 29 · 71 · 38677 · 2297189887169<13> · 25483902450521<14> · 15015025815375250460003131008522648759390248687445270890050110546562303343<74>
7·10107+1 =
7(0)1061<108>
= 1009 · 3614887589<10> · 718466531357219922722261<24> · 107332746631731595459206997027<30> · 2488704264616083541639494383491405517168483<43> (Makoto Kamada / Msieve 1.17 for P30 x P43 / 2.6 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Apr 1, 2007)
7·10108+1 =
7(0)1071<109>
= 463 · 21211 · 41941 · 676363 · 184385670043<12> · 195710949330785987011597433<27> · 696297751445264707829860395468478578666765855808932841<54>
7·10109+1 =
7(0)1081<110>
= 829 · 954067 · 24398641671217086891103<23> · 3627429547287681541354288847808015802890765120425766657908550155246373222376169<79>
7·10110+1 =
7(0)1091<111>
= 4139 · 169122976564387533220584682290408311186276878473061125875815414351292582749456390432471611500362406378352259<108>
7·10111+1 =
7(0)1101<112>
= 17 · 411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882353<111>
7·10112+1 =
7(0)1111<113>
= 43 · 67 · 63421 · 602579979031719044717<21> · 635780199408547170771151786827616042986701340502855247631626697770161565979510377353<84>
7·10113+1 =
7(0)1121<114>
= 3779 · 58211 · 958787 · 9300697050713007875573999<25> · 2683449002182317784858528004222630179<37> · 132979625824198218520351735945182440927<39> (Makoto Kamada / Msieve 1.17 for P37 x P39 / 5.4 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Apr 1, 2007)
7·10114+1 =
7(0)1131<115>
= 53 · 55127 · 2395840000328572342902204207026588005535074926473381704202063776576283032216175958703932702907967913541664171<109>
7·10115+1 =
7(0)1141<116>
= 661 · 2879 · 8447 · 297546427300992344521<21> · 19564766569232601804888102765823<32> · 748036881256401812942007445925303222764775511468137579<54> (Makoto Kamada / Msieve 1.17 for P32 x P54 / 47 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Apr 1, 2007)
7·10116+1 =
7(0)1151<117>
= 2699 · 19134803 · 259968494214599<15> · 30811056406169099<17> · 1692169458708502808995926188152381385415283020990663737179982049144249631733<76>
7·10117+1 =
7(0)1161<118>
= 317 · 353 · 83014772529111787429408381<26> · 119793224689648388450802900474095381<36> · 6290373519699002449341406920469699944412118490423541<52> (Makoto Kamada / Msieve 1.17 for P36 x P52 / 53 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Apr 1, 2007)
7·10118+1 =
7(0)1171<119>
= 233 · 2053 · 3761 · 68777 · 573478493821804383126117265442725302450908591<45> · 986482696674090871440722049772557294942194567424256350401987<60> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 1.23 hours on Core 2 Duo E6300@2.33GHz / Apr 1, 2007)
7·10119+1 =
7(0)1181<120>
= 228281899010583296767945037279<30> · 3066384163763888902949592988428636997602230211082647655130845684522014813451773825877452319<91> (Makoto Kamada / GMP-ECM 6.1.2 B1=50000, sigma=2781698972 for P30 / Mar 24, 2007)
7·10120+1 =
7(0)1191<121>
= 38528183 · 104817829 · 2761462141<10> · 58058856079593791465851800829<29> · 10811271738685902783389387496655065729541894101615562151663724263587<68>
7·10121+1 =
7(0)1201<122>
= 2702603 · 14226607 · 24654257 · 4813855525596240239<19> · 11411793943210051785369918203<29> · 1344236113850473402608905646586208972724256388984102249<55>
7·10122+1 =
7(0)1211<123>
= 23 · 163 · 277 · 46559 · 13868681 · 179176771 · 695948269 · 2888354505059136268957<22> · 2898376950410756486631189477453625810045121535972483258696394672621<67>
7·10123+1 =
7(0)1221<124>
= 19 · 47 · 2029 · 1130793109766280907<19> · 111126294019581567532427817147389<33> · 1299891867398249140896400816452691<34> · 23651425575341536609870582458796781<35> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1122879459 for P34 / Mar 29, 2007) (Makoto Kamada / Msieve 1.17 for P33 x P35 / 35 seconds on Pentium 4 3.06GHz, Windows XP and Cygwin / Apr 1, 2007)
7·10124+1 =
7(0)1231<125>
= 78294553894460255262812761337<29> · 894059631457365799463320070816535742477048704910755885627890918729562543989238260932341535315273<96>
7·10125+1 =
7(0)1241<126>
= 894964537 · 4541136451<10> · 5846891135784131<16> · 29457959035603347204270465483050784873777468902669317754729056254546383817531217101681848833<92>
7·10126+1 =
7(0)1251<127>
= 75679 · 630273181421687406409<21> · 146755311049399059157331290833994884894158824078691244501068729135129736367738511280481415418414796391<102>
7·10127+1 =
7(0)1261<128>
= 17 · 53 · 61 · 96640340758217911<17> · 32026256230584280039<20> · 42343594919387034629<20> · 9718316999838019926867981506356760002003495074574166243273092803901<67>
7·10128+1 =
7(0)1271<129>
= 463752403 · 23173252175870603<17> · 769395054618273598877816227<27> · 77869118298827494691063374224943<32> · 1087201972155263714852297993406422614113372949<46> (Makoto Kamada / Msieve 1.17 for P32 x P46 / 9.4 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Apr 1, 2007)
7·10129+1 =
7(0)1281<130>
= 20339094283792370330464042356579607994600801891<47> · 344164784445593301152541755553359867327580661913692995263470054136783938426510011211<84> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 3.36 hours on Core 2 Duo E6300@2.33GHz / Apr 1, 2007)
7·10130+1 =
7(0)1291<131>
= 5703267238439297<16> · 365538164758125101<18> · 27761662426981271125283255479<29> · 7215493164143024352001386544961<31> · 167621646582705309569926513219943139907<39> (Makoto Kamada / Msieve 1.17 for P31 x P39 / 2 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Apr 1, 2007)
7·10131+1 =
7(0)1301<132>
= 16573 · 827182080526619<15> · 60570823643539584765292420545299<32> · 843009197215127294834358695906019746493107625259983272341093175391722476971875477<81> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 6.67 hours on Athlon XP 3000+ / Apr 2, 2007)
7·10132+1 =
7(0)1311<133>
= 3917 · 8731 · 14638283495713663736241157708855869290229636409<47> · 13982677029538623333501754987296211103374639783010627959614701454655065820539607<80> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 5.29 hours on Cygwin on AMD XP 2700+ / Apr 2, 2007)
7·10133+1 =
7(0)1321<134>
= 43 · 31938787737893<14> · 2453625078680201566748816367059723<34> · 20773178568202312946561506523760891062078565941949791090519972188145838947872363815413<86> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 5.53 hours on Core 2 Duo E6300@2.33GHz / Apr 3, 2007)
7·10134+1 =
7(0)1331<135>
= 29 · 347 · 23753 · 1619918959<10> · 2906434717<10> · 7704541993<10> · 48751543478733853<17> · 236142858679332973<18> · 7012747867264861258628432471574510309408105143540607498174295309<64>
7·10135+1 =
7(0)1341<136>
= 425027 · 16469541934982954024097292642585059302114924463622311053180150908059958543810157942907156486529091093036442390718707282125606137963<131>
7·10136+1 =
7(0)1351<137>
= definitely prime number
7·10137+1 =
7(0)1361<138>
= 401 · 819319 · 94462361101393<14> · 15300445053292681<17> · 78763062104760693596513<23> · 258787878652319024306477498105531<33> · 72322138322265272755297913721084726006639421<44> (Makoto Kamada / Msieve 1.17 for P33 x P44 / 7.2 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Apr 1, 2007)
7·10138+1 =
7(0)1371<139>
= 683 · 323565643 · 5455759339741710826253913205440113<34> · 5805768712228287085116276448327387554343755401317995474938232335903884659779580329249392645433<94> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 10.45 hours on Core 2 Duo E6300@2.33GHz / Apr 2, 2007)
7·10139+1 =
7(0)1381<140>
= 868451 · 4230765977679406827389503051<28> · 19051699252422062688206066138557556924036559617662919866782206797311788639804341499722390566839227421856001<107>
7·10140+1 =
7(0)1391<141>
= 53 · 19597 · 61541309707039<14> · 52143054355223185883<20> · 10854524950314912484667997912049<32> · 19349001352421860990031887892254003455517463005159744816652778091636397<71> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P32 x P71 / 7.73 hours on Athlon XP 3000+ / Apr 3, 2007)
7·10141+1 =
7(0)1401<142>
= 192 · 71 · 288313621751<12> · 3053463834919049029013<22> · 3345092274004510611419<22> · 92148925276609062141707715311<29> · 1006412843425557458231103085699176491026342350208974913<55>
7·10142+1 =
7(0)1411<143>
= definitely prime number
7·10143+1 =
7(0)1421<144>
= 17 · 419 · 22881959 · 1082531743<10> · 474685933669<12> · 255559769903549<15> · 39487949562433818587<20> · 828204943303538804294799840975534200719003469254996500030706812644159131312633<78>
7·10144+1 =
7(0)1431<145>
= 23 · 809940785427965343526229739355042505157936405047381591533420897433<66> · 375765527014597615163944861799356289186159071363960150031523628164542872741439<78> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 14.94 hours on Core 2 Duo E6300@2.33GHz / Apr 3, 2007)
7·10145+1 =
7(0)1441<146>
= 67 · 599 · 412457 · 466747 · 1141698744217337<16> · 2434518084465653<16> · 1795008466954729168800209414936453<34> · 1815955371841082430332694563327821684185611841419005671789292422271<67> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 4.36 hours on Core 2 Duo E6300@2.33GHz / Apr 2, 2007)
7·10146+1 =
7(0)1451<147>
= 1611773 · 184985242269227057794527421<27> · 2347778282697900525301150769488586939894677015640579123650376087635529935797615271526247988318046013093790614783097<115>
7·10147+1 =
7(0)1461<148>
= 283183 · 1902961 · 4224729381223999559<19> · 1257698080821893649965656268769551561386291<43> · 2444700608743657571446769617615111125524512245960929287873490693266909697683<76> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 15.32 hours on Core 2 Duo E6300@2.33GHz / Apr 5, 2007)
7·10148+1 =
7(0)1471<149>
= 3684925389750999011<19> · 22029725720760974922384230516355618304117854041<47> · 862303702875318574684178933529694530368164638218030948135135277879348224342523674051<84> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 23.53 hours on Cygwin on AMD XP 2700+ / Apr 10, 2007)
7·10149+1 =
7(0)1481<150>
= 353 · 4957 · 2883242209<10> · 27592287833712963754580710491390334851359<41> · 5028466680407615659824747536024164572850397380074196151582478698822339725661178413486182331051<94> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 18.01 hours on Core 2 Duo E6300@2.33GHz / Apr 10, 2007)
7·10150+1 =
7(0)1491<151>
= 12583 · 7011677 · 48703953167<11> · 565102429506584132764175102442628047540137331998418471757<57> · 2882707341673302681845839339823884543514446084956768454184275090583469569<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 15.03 hours on Cygwin on AMD 64 3400+ / Apr 10, 2007)
7·10151+1 =
7(0)1501<152>
= 3319 · 9029 · 20543 · 1049778553<10> · 5575410493<10> · 10983502889<11> · 1768772004902478309893971384441205809591822385192631640941577176302280245653996748505868572705067900666570182697<112>
7·10152+1 =
7(0)1511<153>
= 121386524700439541<18> · 5766702702194301289915542121264216675448468498235675287504272647229475254071295684910157483266006251101179901778543432381439265648468061<136>
7·10153+1 =
7(0)1521<154>
= 53 · 167 · 569 · 173483 · 58181687021<11> · 240810772871<12> · 438563879448152243<18> · 20339748706129911647205888791801144203<38> · 64105581640209598722446044764182036063686833229677824048410717867<65> (Robert Backstrom / GMP-ECM 6.0.1 B1=477500, sigma=1974761456 for P38 / Apr 4, 2007)
7·10154+1 =
7(0)1531<155>
= 43 · 5623 · 12401 · 79861933 · 1575233648179<13> · 193370246682439687632641395275617696499919070409857<51> · 959688618561589603204660736875782818852796083063317811556994979114317575491<75> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 28.11 hours on Cygwin on AMD 64 3400+ / May 3, 2007)
7·10155+1 =
7(0)1541<156>
= 1129 · 1193 · 55130793260966415361235729756577932205405829083406166227977587<62> · 9426911131444313172543736731542159160773688947699429609478209619825750212976152411926859<88> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 27.19 hours on Athlon XP 3000+ / Apr 3, 2007)
7·10156+1 =
7(0)1551<157>
= 421 · 5579837 · 2979850197200760481438850057555189304248982827177376528452273550927508874773969476203341379500713217992302967761753767199093514926176273846380507313<148>
7·10157+1 =
7(0)1561<158>
= 107 · 131 · 257 · 44701 · 36067159 · 412688953 · 11433124763162139881<20> · 50150999103831809543<20> · 58723657563182981121109730736410322969118927<44> · 867361611497461809778725449710059255808380370747<48> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P44 x P48 / 4.26 hours on Athlon XP 3000+ / Apr 1, 2007)
7·10158+1 =
7(0)1571<159>
= definitely prime number
7·10159+1 =
7(0)1581<160>
= 173 · 19 · 59 · 461 · 124753 · 8695702266873779<16> · 3614107149313696436903098527751<31> · 173125876189407980940183608574563<33> · 4061870467967602945551870950350685652940570551689772588617215412107<67> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1329172899 for P31 / Mar 30, 2007) (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=472219747 for P33 / Mar 30, 2007)
7·10160+1 =
7(0)1591<161>
= 94514160553<11> · 1036143335433866880995009<25> · 714794695072678527154522192706524446062218435179592437787846626018548054950234092183347409551014373062624055379118229312253913<126>
7·10161+1 =
7(0)1601<162>
= 229 · 242467 · 1517671 · 32593933 · 46943545972117<14> · 638839674622067064620477103409<30> · 8498215560590040816704776139546515219193719251278278781985430547992584465308428088850076281224633<97> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=4012320279 for P30 / Mar 30, 2007)
7·10162+1 =
7(0)1611<163>
= 29 · 331 · 40665431 · 1645805022353<13> · 2473251925797485004201944893565647<34> · 4405547920203456458779052457232424346149863777109139414484987392817028714950420487387989307793267723460519<106> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1594068802 for P34 / Mar 30, 2007)
7·10163+1 =
7(0)1621<164>
= 2621 · 637097 · 6177922939<10> · 156791141329<12> · 402780568113496127134113047287312945816114000773181<51> · 107446665123360825440701365404164787206317314310967090805791720700790075639081056243<84> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs / 46.82 hours on Msieve 1.33 / Apr 4, 2008)
7·10164+1 =
7(0)1631<165>
= 1493 · 4603 · 119429 · 79514415457<11> · 4011137403054399824497281514214954974908736320403030763817761<61> · 2674077881194096559726374285341983014251581688108917524458192840920208139039746043<82> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 51.39 hours on Cygwin on AMD 64 X2 6000+ / Jan 23, 2008)
7·10165+1 =
7(0)1641<166>
= 1090967 · 11436012877<11> · 1934565819362618078884501610509<31> · 290020221573261953762717502067915448761963064267460125187429746035634212740848140784915846874690427361518315806184905871<120> (Makoto Kamada / GMP-ECM 5.0.3 B1=91890, sigma=2976108834)
7·10166+1 =
7(0)1651<167>
= 23 · 53 · 31327 · 34726262056239405863392591<26> · 1913290242196232539268012066652201280412112493917178819<55> · 27589042770237067407217839796789774556735213612294539601853969868354417611828713<80> (Justin Card / GGNFS / 93.42 hours on AMD Athlon(tm) 64 X2 Dual Core Processor 3600+ 3 GB RAM Running Ubuntu Linux 8.04 64-bit / Sep 24, 2008)
7·10167+1 =
7(0)1661<168>
= 94126111912362384454419640507<29> · 45944168788570289296719424358942927<35> · 161866703314530544206931137643404221120769747950795429104385791774237543764981165611916824698958062426909<105> (Robert Backstrom / GMP-ECM 6.0 B1=1160000, sigma=3892956357 for P35 / Feb 9, 2008)
7·10168+1 =
7(0)1671<169>
= 39874420514155621405930029196213<32> · 175551140549239192504522004124894766597610705708295751211644739831183679452961360088433039867758405935282447575807483052676447787480773277<138> (Jo Yeong Uk / GMP-ECM 6.1.1 B1=1000000, sigma=1122796349 for P32 / Apr 6, 2007)
7·10169+1 =
7(0)1681<170>
= 47 · 151 · 13679 · 69581271307931<14> · 39537414818425401700082179<26> · 262100745709398798485248290413230243877973456030393217395713586895123047106795590404763309503410957879426068029019824408023<123>
7·10170+1 =
7(0)1691<171>
= 499 · 384941 · 3687989 · 27612726356486912972395700594939<32> · 35785279872327545208647282141323368359931221872796464844278919978115969773916536537918582989981782789362311769452347991469809<125> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3105718241 for P32 / Mar 30, 2007)
7·10171+1 =
7(0)1701<172>
= 191 · 11351 · 200087 · 199743193690849<15> · 503783621180657<15> · 640757244242093195737825269513973688101421<42> · 250266153200200437607062854749076319929624557778915248618363969037755267406743304872865851<90> (Robert Backstrom / GMP-ECM 6.2.1 B1=7574000, sigma=1044013304 for P42 / Aug 13, 2008)
7·10172+1 =
7(0)1711<173>
= 2221 · 13553 · 40608976450967<14> · 1250211931636399<16> · [45804522546961108363690889338886536418357525610678706451761158031531237864633614184826046249774735378054117018000729448410692562395216669<137>] SUBMIT/RESERVE
7·10173+1 =
7(0)1721<174>
= 62473 · 1835807801<10> · 3510906612731053298436347<25> · 992595949608553727415223604789713<33> · 1626878119033344343859043164870647<34> · 1076543722683910823425060595208148712881299436943475382391159481127061<70> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=3918156657 for P34, pol51+Msieve 1.36 gnfs for P33 x P70 / 4.00 hours on Opteron-2.6GHz; Linux x86_64 / Aug 7, 2008)
7·10174+1 =
7(0)1731<175>
= 9404860453<10> · 744295998327876518892565858680263822942658179598191216245577184642146226217908562518466109983014332769919728228422657277677312922486591625348383039958328236558259117<165>
7·10175+1 =
7(0)1741<176>
= 17 · 43 · 16106554067<11> · [5945358239123625634011428660866607620137468294219930437924782752600840851464522625179701735071778160104909516766334428716890094478708550908337237518092811760086913<163>] SUBMIT/RESERVE
7·10176+1 =
7(0)1751<177>
= 71 · 8573471 · 805581827 · 284095648103<12> · 8413635332369<13> · 1772201439222433182847040694601969<34> · 5991250959750702185019813412247610703<37> · 56246368184668911475605266297942702738852214410521358324628735307<65> (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=2065754217 for P34 / Aug 6, 2008)
7·10177+1 =
7(0)1761<178>
= 19 · 1979 · 516977 · 9303190260631<13> · [38707535429769271817933736813700841775495968708953177384101306584707082371531056965919785749273345311849031914872617006519943577262553709195836398681509623<155>] SUBMIT/RESERVE
7·10178+1 =
7(0)1771<179>
= 67 · 557 · 38661967709<11> · 36637648795722647<17> · 5818134233320100182457<22> · 1662167533338508964204747<25> · 1783080582215628427498691<25> · 76793947157016219502762538117085488564563018478796006649288560115315417360157<77>
7·10179+1 =
7(0)1781<180>
= 53 · 4944817 · 243957911 · 215486917894351463<18> · 50808471665857893437517964208287426218431300280849428134175259933029146285367548593237918762046686401653261335756691370412456767128823237057384557<146>
7·10180+1 =
7(0)1791<181>
= 2151725922138758923261663<25> · 7087520924662674679818007<25> · [459004278820866487459437679274030108176266123818772470407638613819424111428109898761423535317510385492788692576664286169842068059961<132>] SUBMIT/RESERVE
7·10181+1 =
7(0)1801<182>
= 353 · 321719196896439418987<21> · [616376906317938281784449531477521656598628885351985919643241270030520509882761600524786113407223423824129005771794575684162436994758092692579807465847277894691<159>] SUBMIT/RESERVE
7·10182+1 =
7(0)1811<183>
= 109 · 11621 · 84792619 · 8678619303260101422863539087<28> · 750964406660170807841205276154203602906351985572563625545734283586039282401294289072997102053862402904598025459534302886442020907461631823053<141>
7·10183+1 =
7(0)1821<184>
= 183343 · 20379849399125231<17> · 1873409578113106928328966276808224641434894106903238236146532586172224571192149315108338077096513679903851828807831202801279484505307072253390163416596493461284897<163>
7·10184+1 =
7(0)1831<185>
= 149 · 1873 · 31839019 · 22998826951<11> · [342537899792275838330655968732054614832594917561401326091339011818975072989115740027383246620388207950150934801109882195561960802407243747352061514872764651757377<162>] SUBMIT/RESERVE
7·10185+1 =
7(0)1841<186>
= 219465968201<12> · 2982379230977<13> · 5719598275459<13> · [186983145711998872151621380107283617743523846765162311326490113484149406571856132208433656235044004288419878293310788422126371943698074376213243933907<150>] SUBMIT/RESERVE
7·10186+1 =
7(0)1851<187>
= 337 · 1382021 · [15029810222214949702621999991639131284956426551141418861793888968054239287122187850310656622628113173706600072984329015926589614512357045114146115997408577298411666617930717758013<179>] SUBMIT/RESERVE
7·10187+1 =
7(0)1861<188>
= 61 · 97 · 13477 · 11051321 · 1250700283367<13> · 63509076905737709607773998521570759812813213872065422716685196728502463710090990822013222977121418889253667306124842970619057148376308515425352173304503501688127<161>
7·10188+1 =
7(0)1871<189>
= 23 · 1607 · 2521 · 61075211 · 123003227052651152950005200833711850969402456441204373766640629730402381369407452911904359537763602419186641694035978494527928170552400569670237539931553001319142163758580411<174>
7·10189+1 =
7(0)1881<190>
= 126751 · 442961 · 407211125311<12> · 306169214480545484095401530789754572073207974170533359013961672659299954901090426329959390170917046029755821875856455791456029698311298216039897481418256760523924811281<168>
7·10190+1 =
7(0)1891<191>
= 29 · 18168419302228497779<20> · 102557119002802823101<21> · 73316966906831314464051823<26> · 355098879311614202406460897590438184483<39> · 49758043313543013512337916205691953866857075376389549242886554315519833104914284256879<86> (Robert Backstrom / GMP-ECM 6.0 B1=1540000, sigma=898811196 for P39 / Jan 27, 2008)
7·10191+1 =
7(0)1901<192>
= 17 · 277 · 4177 · 6818267 · 73528321631<11> · 41697361934200639<17> · [1702423627678361954809315929461828350203816552561645118207624300268108951077018933765444654474353331670394168430397977906220931972578982457628054627719<151>] SUBMIT/RESERVE
7·10192+1 =
7(0)1911<193>
= 53 · 60342221562520298675808271913387<32> · 2188773768650039140461457627089616957466162048627827553532370714156265666695112700205642303636943536844392668804225938184082442940320634356324063411380105589591<160> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=103207662 for P32 / Apr 1, 2007)
7·10193+1 =
7(0)1921<194>
= 9241 · 219293 · 6936938890086167066622757<25> · [4979507974541433597365738024509158975992078914609300907050322765775804139600173271129286207481076441936244003985028550033691274922505111872628211217845313005561<160>] SUBMIT/RESERVE
7·10194+1 =
7(0)1931<195>
= 44402740939<11> · 4350604316543<13> · 3229114677266322853<19> · 142681828165844793819666383<27> · 7864779302790260093837923822449676279939337792435192801017306821724144034045223318387861266653023159472973073168992395224536087<127>
7·10195+1 =
7(0)1941<196>
= 19 · 1172079999382367<16> · [314330978112176756170892020233836852861158290880123136679735296147442066696688057651060066275013851055571784551760136372633451365657437290034850295352831994444579765584125457252037<180>] SUBMIT/RESERVE
7·10196+1 =
7(0)1951<197>
= 43 · 317 · 1372963 · [3740343504479472490515528554550606468852393955614664401067010292209659255073829918281456549774990170747297067496585596574102001581384853005867903842404724145367019780504670851921501819317<187>] SUBMIT/RESERVE
7·10197+1 =
7(0)1961<198>
= 653 · 2819 · 21323 · 39733 · [448838516941868417499425440664681100362291479464010908684153096612991077612112813896771510976203294280081563729687939129376663691811114690702635692568366367480681394210763927626542577<183>] SUBMIT/RESERVE
7·10198+1 =
7(0)1971<199>
= 23549 · 131245193 · 15232681991<11> · 148684531570815410532680649579255676722504892797241305592208580365871104569745716862242777344488021346683252216593937137486891010964381392274126000451717972340113579633503929323<177>
7·10199+1 =
7(0)1981<200>
= 725090659 · [96539652154034989437093272497942908956988783936327057276295708010217243744688758981792371979791288415977235751426222689761612278610253066299672190370887125164303075100020010049529544415217739<191>] SUBMIT/RESERVE
7·10200+1 =
7(0)1991<201>
= 118799 · 6220943 · 3123018700066548676649<22> · 303287456024033375811688864745842636310948539879346801763295868948372563194612386405922432317470705052355289515702782896341928269340989242839814851203707940413910774457<168>

Factorizations

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