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Factorizations of 300...001

Table of contents

  1. About 300...001
  2. Prime numbers of the form 300...001
  3. Factorizations of 300...001
  4. References

1. About 300...001

First ten terms

31, 301, 3001, 30001, 300001, 3000001, 30000001, 300000001, 3000000001, 30000000001

General term

3·10n+1

Related tables

2. Prime numbers of the form 300...001

Last update

Jan 18, 2009

Searched up to

n≤10000

Difficulty of search

20.74%

Results

  1. 3·101+1 = 31 is prime.
  2. 3·103+1 = 3001 is prime.
  3. 3·107+1 = 30000001 is prime.
  4. 3·1010+1 = 30000000001<11> is prime.
  5. 3·1028+1 = 3(0)271<29> is prime.
  6. 3·1036+1 = 3(0)351<37> is prime.
  7. 3·1067+1 = 3(0)661<68> is prime.
  8. 3·1081+1 = 3(0)801<82> is prime.
  9. 3·10147+1 = 3(0)1461<148> is prime.
  10. 3·10483+1 = 3(0)4821<484> is prime.
  11. 3·10643+1 = 3(0)6421<644> is prime.
  12. 3·101020+1 = 3(0)10191<1021> is prime. (Harvey Dubner / Dubner Cruncher / 1984)
  13. 3·101900+1 = 3(0)18991<1901> is prime. (Harvey Dubner / Dubner Cruncher / 1984)
  14. 3·102620+1 = 3(0)26191<2621> is prime. (Harvey Dubner / Dubner Cruncher / 1984)
  15. 3·1010453+1 = 3(0)104521<10454> is prime. (Chris Caldwell / Dubner Cruncher / May 1, 1994)
  16. 3·1027720+1 = 3(0)277191<27721> is prime. (Jim Liddle / Yves Gallot's Proth.exe / Mar 13, 2000)
  17. 3·1052824+1 = 3(0)528231<52825> is prime. (Peter Benson / Paul Jobling's NewPGen, OpenPFGW / Jun 9, 2004)

3. Factorizations of 300...001

Last update

Nov 5, 2009

Completed up to

Range

n≤200

Terms which have not been factored yet

n=173, 174, 175, 176, 182, 183, 193, 194, 195, 196, 197, 200 (12/200)

Results

3·101+1 =
31
= definitely prime number
3·102+1 =
301
= 7 · 43
3·103+1 =
3001
= definitely prime number
3·104+1 =
30001
= 19 · 1579
3·105+1 =
300001
= 13 · 47 · 491
3·106+1 =
3000001
= 853 · 3517
3·107+1 =
30000001
= definitely prime number
3·108+1 =
300000001
= 72 · 6122449
3·109+1 =
3000000001<10>
= 7589 · 395309
3·1010+1 =
30000000001<11>
= definitely prime number
3·1011+1 =
300000000001<12>
= 132 · 1775147929<10>
3·1012+1 =
3000000000001<13>
= 67 · 44776119403<11>
3·1013+1 =
30000000000001<14>
= 17 · 23 · 62191 · 1233721
3·1014+1 =
300000000000001<15>
= 7 · 95773 · 447486691
3·1015+1 =
3000000000000001<16>
= 29 · 103448275862069<15>
3·1016+1 =
30000000000000001<17>
= 31 · 379 · 15901 · 160581649
3·1017+1 =
300000000000000001<18>
= 13 · 2281 · 23911 · 423111547
3·1018+1 =
3000000000000000001<19>
= 16921 · 5188801 · 34168681
3·1019+1 =
30000000000000000001<20>
= 163 · 184049079754601227<18>
3·1020+1 =
300000000000000000001<21>
= 7 · 42857142857142857143<20>
3·1021+1 =
3000000000000000000001<22>
= 263 · 13472579 · 846671161213<12>
3·1022+1 =
30000000000000000000001<23>
= 19 · 181 · 1381 · 10452973 · 604304143
3·1023+1 =
300000000000000000000001<24>
= 13 · 43 · 233 · 2303316007278478583<19>
3·1024+1 =
3000000000000000000000001<25>
= 6709 · 15056940637<11> · 29697967297<11>
3·1025+1 =
30000000000000000000000001<26>
= 2309 · 12992637505413598960589<23>
3·1026+1 =
300000000000000000000000001<27>
= 7 · 109 · 877 · 17011 · 26355258412811941<17>
3·1027+1 =
3000000000000000000000000001<28>
= 2069 · 85577 · 4296989 · 3943115191193<13>
3·1028+1 =
30000000000000000000000000001<29>
= definitely prime number
3·1029+1 =
300000000000000000000000000001<30>
= 13 · 17 · 6389 · 212469253928379447424129<24>
3·1030+1 =
3000000000000000000000000000001<31>
= 1637539 · 1832017435920610135086859<25>
3·1031+1 =
30000000000000000000000000000001<32>
= 31 · 383 · 2526741345910890255200875937<28>
3·1032+1 =
300000000000000000000000000000001<33>
= 7 · 103 · 326707 · 1273583870573108963459083<25>
3·1033+1 =
3000000000000000000000000000000001<34>
= 6287 · 42299 · 11281002465075774324342877<26>
3·1034+1 =
30000000000000000000000000000000001<35>
= 20107 · 28711 · 51966762052062599154639013<26>
3·1035+1 =
300000000000000000000000000000000001<36>
= 13 · 23 · 2618448681461<13> · 383182793960858193559<21>
3·1036+1 =
3000000000000000000000000000000000001<37>
= definitely prime number
3·1037+1 =
30000000000000000000000000000000000001<38>
= 179 · 613 · 1569611 · 3874630228127<13> · 44955771308579<14>
3·1038+1 =
300000000000000000000000000000000000001<39>
= 7 · 3571 · 2173333 · 1283942706199<13> · 4300920803658799<16>
3·1039+1 =
3000000000000000000000000000000000000001<40>
= 2990993 · 1003011374483323765719277845183857<34>
3·1040+1 =
30000000000000000000000000000000000000001<41>
= 19 · 979150369 · 5634413557<10> · 286199942061324334063<21>
3·1041+1 =
300000000000000000000000000000000000000001<42>
= 13 · 257 · 17107 · 4735035242785279<16> · 1108530656089810937<19>
3·1042+1 =
3000000000000000000000000000000000000000001<43>
= 151 · 1669 · 119299 · 39546174097<11> · 2523171052478922495193<22>
3·1043+1 =
30000000000000000000000000000000000000000001<44>
= 29 · 12654046331183595167<20> · 81751143590441508737707<23>
3·1044+1 =
300000000000000000000000000000000000000000001<45>
= 7 · 43 · 37021 · 4191314061691<13> · 6423273420722757827509291<25>
3·1045+1 =
3000000000000000000000000000000000000000000001<46>
= 17 · 67 · 269 · 1249 · 7839399777505813901392825897156132039<37>
3·1046+1 =
30000000000000000000000000000000000000000000001<47>
= 31 · 97 · 700963 · 77575909 · 968862613 · 189366722010724917133<21>
3·1047+1 =
300000000000000000000000000000000000000000000001<48>
= 13 · 109311862154664874542821<24> · 211110876917197143984737<24>
3·1048+1 =
3000000000000000000000000000000000000000000000001<49>
= 61 · 8221 · 864195651219961261<18> · 6922368189145372572420061<25>
3·1049+1 =
30000000000000000000000000000000000000000000000001<50>
= 1879 · 35278466088721848125359<23> · 452568977610245073188041<24>
3·1050+1 =
300000000000000000000000000000000000000000000000001<51>
= 72 · 586335359385372763185511<24> · 10441889409517628903684359<26>
3·1051+1 =
3000000000000000000000000000000000000000000000000001<52>
= 47 · 994953497 · 64153538257318726918841475967120159360039<41>
3·1052+1 =
30000000000000000000000000000000000000000000000000001<53>
= 397 · 409369 · 589291 · 313246327159464677685910911080355191527<39>
3·1053+1 =
300000000000000000000000000000000000000000000000000001<54>
= 13 · 6581 · 3506598249038607646721915070190408284922796395217<49>
3·1054+1 =
3000000000000000000000000000000000000000000000000000001<55>
= 1011559 · 754590459935761<15> · 3930236875017125218405813407578599<34>
3·1055+1 =
30000000000000000000000000000000000000000000000000000001<56>
= 59 · 409 · 3299 · 321114319 · 1645263250196710211<19> · 713293966588391497181<21>
3·1056+1 =
300000000000000000000000000000000000000000000000000000001<57>
= 7 · 157 · 272975432211101000909918107370336669699727024567788899<54>
3·1057+1 =
3000000000000000000000000000000000000000000000000000000001<58>
= 23 · 1117 · 23447 · 3339120189577212023<19> · 1491491939550947497031924913731<31>
3·1058+1 =
30000000000000000000000000000000000000000000000000000000001<59>
= 19 · 21871 · 72193652252802918548715073312653862721363786220156949<53>
3·1059+1 =
300000000000000000000000000000000000000000000000000000000001<60>
= 13 · 1039 · 338082920595701<15> · 17500711862350918541<20> · 3753906133691874100123<22>
3·1060+1 =
3000000000000000000000000000000000000000000000000000000000001<61>
= 577 · 5199306759098786828422876949740034662045060658578856152513<58>
3·1061+1 =
30000000000000000000000000000000000000000000000000000000000001<62>
= 17 · 31 · 10103893 · 392494829757049332889<21> · 14354496404471703713440320501419<32>
3·1062+1 =
300000000000000000000000000000000000000000000000000000000000001<63>
= 7 · 14811936975361976113<20> · 2893419201582547140630722876441221402622311<43>
3·1063+1 =
3000000000000000000000000000000000000000000000000000000000000001<64>
= 389 · 1867 · 4130735009218423628905782065174736975448288016875429424327<58>
3·1064+1 =
30000000000000000000000000000000000000000000000000000000000000001<65>
= 7927 · 1026139 · 3688129845545438409852942740111089271467757989074336517<55>
3·1065+1 =
300000000000000000000000000000000000000000000000000000000000000001<66>
= 13 · 43 · 1525331 · 1434687874937293<16> · 1663870743431261569<19> · 147390107888415272711657<24>
3·1066+1 =
3000000000000000000000000000000000000000000000000000000000000000001<67>
= 103 · 29126213592233009708737864077669902912621359223300970873786407767<65>
3·1067+1 =
30000000000000000000000000000000000000000000000000000000000000000001<68>
= definitely prime number
3·1068+1 =
300000000000000000000000000000000000000000000000000000000000000000001<69>
= 7 · 42857142857142857142857142857142857142857142857142857142857142857143<68>
3·1069+1 =
3000000000000000000000000000000000000000000000000000000000000000000001<70>
= 131 · 1193 · 13010688596546599947627907<26> · 1475398144671508730120834597876984040721<40>
3·1070+1 =
30000000000000000000000000000000000000000000000000000000000000000000001<71>
= 246245887325083<15> · 121829445867639276545602652290090242139072129211660761747<57>
3·1071+1 =
300000000000000000000000000000000000000000000000000000000000000000000001<72>
= 13 · 29 · 199 · 185621 · 736259 · 738845467 · 1270904911<10> · 31160357553605870175480621392732932109<38>
3·1072+1 =
3000000000000000000000000000000000000000000000000000000000000000000000001<73>
= 294984638384826331048078719260608561<36> · 10170021111697037216236753300358009041<38>
3·1073+1 =
30000000000000000000000000000000000000000000000000000000000000000000000001<74>
= 22739 · 117485247043<12> · 11229658739992996031059261706955788780792567645986856808713<59>
3·1074+1 =
300000000000000000000000000000000000000000000000000000000000000000000000001<75>
= 7 · 1873 · 22189 · 46861 · 3179107 · 363937864783<12> · 19019704578369356396789725755065110611923659<44>
3·1075+1 =
3000000000000000000000000000000000000000000000000000000000000000000000000001<76>
= 5815181 · 242995654571<12> · 30296635088429<14> · 558665640875791<15> · 125433387853024282821592391909<30>
3·1076+1 =
30000000000000000000000000000000000000000000000000000000000000000000000000001<77>
= 19 · 31 · 1291 · 415543 · 4516945831<10> · 21019329800602844759367800353109139799041028297946332303<56>
3·1077+1 =
300000000000000000000000000000000000000000000000000000000000000000000000000001<78>
= 13 · 17 · 40949 · 7243627 · 189330424333774697273<21> · 24171811200974383408786576437714478568683739<44>
3·1078+1 =
3000000000000000000000000000000000000000000000000000000000000000000000000000001<79>
= 67 · 547 · 1783 · 5851837 · 29488903 · 774480196801059841<18> · 343515729084853263740131391420318235853<39>
3·1079+1 =
30000000000000000000000000000000000000000000000000000000000000000000000000000001<80>
= 23 · 31588957 · 64560983 · 822776055137967966312899<24> · 777331654853277695714263410548853568823<39>
3·1080+1 =
300000000000000000000000000000000000000000000000000000000000000000000000000000001<81>
= 7 · 997 · 156742903 · 274245916962662936878665224768927142918789143313534242324532556092973<69>
3·1081+1 =
3000000000000000000000000000000000000000000000000000000000000000000000000000000001<82>
= definitely prime number
3·1082+1 =
30000000000000000000000000000000000000000000000000000000000000000000000000000000001<83>
= 396556147820323<15> · 7877327463333877<16> · 9603679718327062465169317706939506976097026342997631<52>
3·1083+1 =
300000000000000000000000000000000000000000000000000000000000000000000000000000000001<84>
= 13 · 9532847 · 2420779760434954733153372027991540924036326511578658182920267479056684422091<76>
3·1084+1 =
3000000000000000000000000000000000000000000000000000000000000000000000000000000000001<85>
= 367 · 84631 · 440527 · 981319 · 223430768225151152811482584017892586519419195709078993848314952801<66>
3·1085+1 =
30000000000000000000000000000000000000000000000000000000000000000000000000000000000001<86>
= 1661583485297<13> · 54023475012308291507621<23> · 334207792110584172091449693805941060369350577909373<51>
3·1086+1 =
300000000000000000000000000000000000000000000000000000000000000000000000000000000000001<87>
= 7 · 43 · 147929130938493357761877823<27> · 6737535295047400422939574997854853936889567773370251541787<58>
3·1087+1 =
3000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<88>
= 57704100757<11> · 78212992366947111793224659<26> · 664715300063407687268091985902707716360249006586927<51>
3·1088+1 =
30000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<89>
= 613 · 3751676989<10> · 13044737394181493541891572756624031685359114648899761380720804186090822001393<77>
3·1089+1 =
300000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<90>
= 132 · 113 · 250451 · 278917 · 4115541273187<13> · 81816795564710189<17> · 667865368081651529733187254777823845221359793<45>
3·1090+1 =
3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<91>
= 3967 · 180331 · 381318197437<12> · 564094907179255318210761991225027<33> · 19496154286820318385804086168513204587<38>
3·1091+1 =
30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<92>
= 31 · 283 · 883 · 16347505193<11> · 52155548314181870086767536446091569<35> · 4542139018383436278421775174894971465367<40>
3·1092+1 =
300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<93>
= 72 · 769 · 17929 · 1795678883533<13> · 1896995229026274291292255877683<31> · 130361051090105258563806462474876437765791<42>
3·1093+1 =
3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<94>
= 17 · 863 · 9439 · 1290996163<10> · 16780720353433491782468421724289387703811042473187542015809353308503757977083<77>
3·1094+1 =
30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<95>
= 19 · 140395141 · 770083117 · 4819894883232336708373<22> · 1001770522456725752538019<25> · 3024629329448324924475066105061<31>
3·1095+1 =
300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<96>
= 13 · 40093 · 6579763843<10> · 10684622854603<14> · 8187283801493673414908347666397742188102045797947618728529480372841<67>
3·1096+1 =
3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<97>
= 2833205979816856630365091<25> · 1058871123868630697170279213402229282716267254260527378849368062541824011<73>
3·1097+1 =
30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<98>
= 47 · 199771102072963<15> · 336014103925942214219<21> · 9508964463243707970091052874294858739920079951513408696616239<61>
3·1098+1 =
300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<99>
= 7 · 3756512436102370044614142122779<31> · 11408758412526373980350866244775600239574193508591183341548280948117<68>
3·1099+1 =
3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<100>
= 29 · 643 · 160883788276934627554030138896337212420228454979353247171126722797232798841636724406070681610983<96>
3·10100+1 =
30000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<101>
= 103 · 163 · 313 · 271975894534095225991176221835439<33> · 20990446375297618944778008551499605099634313008134910244350187<62>
3·10101+1 =
3(0)1001<102>
= 13 · 23 · 112455688781<12> · 608906393745935368545043<24> · 14652714986922379314736190545012031169061014220429491786130421653<65>
3·10102+1 =
3(0)1011<103>
= 3184685509<10> · 4357048548962608484941710525445154377541575699<46> · 216203292699210532299880330172360087254034249311<48> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 0.57 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Mar 20, 2007)
3·10103+1 =
3(0)1021<104>
= 83301251819<11> · 1141870773049<13> · 5959534140575605571563<22> · 52922512935658165935800313758093233844200674356148904094417<59>
3·10104+1 =
3(0)1031<105>
= 7 · 32089 · 1335571157005293313685597645833240585336319076853216277941261580514907200064107415536254079056908687<100>
3·10105+1 =
3(0)1041<106>
= 167 · 3851 · 2172689417<10> · 522970842054278052596796307<27> · 4105406260953967323411421624379333441658282336124257972514962287<64>
3·10106+1 =
3(0)1051<107>
= 31 · 4744051332993243749733574090207<31> · 203990612149063181178190673768547952947112612321147898789683681650672394753<75> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 0.93 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Mar 20, 2007)
3·10107+1 =
3(0)1061<108>
= 13 · 43 · 149 · 319469 · 406859 · 27710893469268378687085304936496533197645542536668954891993497757911796495887926681123282141<92>
3·10108+1 =
3(0)1071<109>
= 61 · 2050264538747272760451120621063903142800302077<46> · 23987308437233184406133324376083302948918445967347350246327033<62> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 1.33 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Mar 20, 2007)
3·10109+1 =
3(0)1081<110>
= 17 · 470317 · 11861956980462821<17> · 4194875121286899383<19> · 2554805335672876431983<22> · 29515385542052210711260544097911301044937947161<47>
3·10110+1 =
3(0)1091<111>
= 7 · 7482121 · 228966966455977967620471917769017793<36> · 25016448656495401004069927663455363536577225267399577915957403823231<68> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 0.92 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Mar 20, 2007)
3·10111+1 =
3(0)1101<112>
= 67 · 6883 · 50769977 · 822533722631126307625175578433<30> · 1934766413697553399092247719779<31> · 80515494338141194672046088158648781419<38> (Makoto Kamada / GMP-ECM 6.1.2 B1=50000, sigma=2173873469 for P31 / Mar 18, 2007) (Makoto Kamada / Msieve 1.17 for P30 x P38 / Mar 18, 2007)
3·10112+1 =
3(0)1111<113>
= 19 · 7807361641<10> · 8118226003<10> · 10210034882989784864647209757<29> · 2439916668000842264184198385585361045416127281052552280029060389<64>
3·10113+1 =
3(0)1121<114>
= 13 · 59 · 10243 · 47825881 · 319042484686421<15> · 8860269191229929657<19> · 831972291458432430035984753<27> · 339493482302125699689696823651386878401<39>
3·10114+1 =
3(0)1131<115>
= 919 · 967 · 295357 · 11429625511698592200629533241927411979327821030913432739903978629728413991676984595399531610900916380341<104>
3·10115+1 =
3(0)1141<116>
= 832033003 · 403233877351<12> · 1577831737746491<16> · 5185040008134360225023375060014351<34> · 10929766662867956939358630793031023525224309137<47>
3·10116+1 =
3(0)1151<117>
= 7 · 176989 · 805614854347532273657889152825813219506231<42> · 300572659388749176537866923029182472055638130513953259347940318716277<69> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 1.37 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Mar 20, 2007)
3·10117+1 =
3(0)1161<118>
= 151 · 787 · 983 · 5364595726158023<16> · 4787172289684415190372122785770632962010454236261129833023534339757976679455179640719536246397<94>
3·10118+1 =
3(0)1171<119>
= 229 · 131004366812227074235807860262008733624454148471615720524017467248908296943231441048034934497816593886462882096069869<117>
3·10119+1 =
3(0)1181<120>
= 13 · 1553 · 438721 · 642459091110046921<18> · 2909223957003733935959638857517450326431467<43> · 18121551992896711422356563612737888923327762681447<50> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 1.78 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Mar 20, 2007)
3·10120+1 =
3(0)1191<121>
= 129457 · 97356367 · 23194910287<11> · 14024472877652688033418848086042342088954204619<47> · 731732109565129767405444811518543619679358772542643<51> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 1.54 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Mar 20, 2007)
3·10121+1 =
3(0)1201<122>
= 31 · 2533733441819<13> · 5680551281721563208659<22> · 67236972872290888335676434473866511834711951165578089027465183928012262948453258565151<86>
3·10122+1 =
3(0)1211<123>
= 7 · 43711 · 2655233370133<13> · 92771425356838998606541<23> · 3980297609513933332382807187105798139082232720008215213498031449569053628602395321<82>
3·10123+1 =
3(0)1221<124>
= 23 · 19553 · 166235481615022500575018646587621550923191<42> · 40128811045536569808228286660052417775119260016039979721737391386749724030769<77> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 3.14 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Mar 21, 2007)
3·10124+1 =
3(0)1231<125>
= 2767 · 5449 · 17167 · 57571 · 158941 · 64072783 · 197691309554911543479077660268414631217739335706830786585014015880624021918384268676142039645857<96>
3·10125+1 =
3(0)1241<126>
= 13 · 17 · 1471 · 7673 · 600701 · 634218826805839667438296844687<30> · 19233942138039946177234105344928717<35> · 16412899871082734672605658515241235597824962933<47> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2146302078 for P30, sigma=1408671498 for P35 / Mar 18, 2007)
3·10126+1 =
3(0)1251<127>
= 3187 · 1775837843273505241987971241538076876967<40> · 530073245617957365009268096007895652834218165933718492937784526257953798248555640269<84> (Makoto Kamada / GGNFS-0.77.1-20060722-pentium4 / 2.45 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Mar 21, 2007)
3·10127+1 =
3(0)1261<128>
= 29 · 19573583 · 103934947 · 322172298116923693<18> · 1578349333128622133308952388255710631082915998992096274067434685677424530735030916200883893133<94>
3·10128+1 =
3(0)1271<129>
= 7 · 43 · 1693 · 3709 · 481153 · 1688691118297<13> · 330470429522606563<18> · 591119036400766694459860015179609950216121761960385602854728605249929171033537198231<84>
3·10129+1 =
3(0)1281<130>
= 428657 · 1109161 · 4750400686003697<16> · 30976605475761427<17> · 42631129647954533977037566338810486942407<41> · 1005832896845130922388650295627982989490898661<46>
3·10130+1 =
3(0)1291<131>
= 19 · 31627 · 273253 · 48049664319064769869<20> · 15662296387277294671225933171<29> · 41041333591559226903556091015401<32> · 5915309275092388734119687813085634306291<40> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1810344172 for P32 / Mar 19, 2007)
3·10131+1 =
3(0)1301<132>
= 13 · 3559 · 10267451 · 885106597 · 3970843397400821<16> · 14248760853504781734593<23> · 5960458521395615500271408429<28> · 2115690668630032081669968821003525873818602277<46>
3·10132+1 =
3(0)1311<133>
= 193 · 13426297 · 297991711 · 3885111721371994174857293714863962860157745941710769201332177744305621026491718623507381980843580642456489942771671<115>
3·10133+1 =
3(0)1321<134>
= 602551 · 49788316673609370825042195598380883941774223260769627799140653654213502259559771703971945943164976906519116224186832317928274951<128>
3·10134+1 =
3(0)1331<135>
= 72 · 103 · 109 · 157 · 567979 · 4821502235119<13> · 19159624248086059537256114689<29> · 921148200730835944300579540106197<33> · 71867188082562346821361859984554535876161847527<47> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3094951228 for P33 / Mar 19, 2007)
3·10135+1 =
3(0)1341<136>
= 523 · 13477 · 1075774213<10> · 5752978421<10> · 147095946235219350911667697013541493<36> · 467532449005166182402814318007788918674002841796260849988478421239468688979<75> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 4.34 hours on Core 2 Duo E6300@2.33GHz / Mar 21, 2007)
3·10136+1 =
3(0)1351<137>
= 31 · 631 · 5683 · 21061 · 5619844367191367822413<22> · 28731552996140783336205349164799<32> · 79357900169239460936673489505340712129651144134050386938660184759316861<71> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3689886608 for P32 / Mar 19, 2007)
3·10137+1 =
3(0)1361<138>
= 13 · 182924718029<12> · 126155302167881834100782103641129548809713983877462483723115599111940271236775421520981050242583796793870945402002290692420313<126>
3·10138+1 =
3(0)1371<139>
= 2341 · 30427 · 40687364143<11> · 296243498740348121248054677331<30> · 3494236713686476798561678201951209134404038145161222453838652958294043118897029832719756771<91>
3·10139+1 =
3(0)1381<140>
= 613 · 701 · 176531 · 13156471 · 5476593989<10> · 2191957616240599<16> · 6168537428391373109<19> · 405935904781531709647711583561114892568580809007984843638690234553821712672323<78>
3·10140+1 =
3(0)1391<141>
= 7 · 25860237801109<14> · 12123679087138214273443<23> · 136696145417512502469827638712574449098511977307412418748966651137389231633470826169247101765890038190889<105>
3·10141+1 =
3(0)1401<142>
= 17 · 32069 · 1247451965855923922740201<25> · 106149839857628546463274992773903<33> · 41556957164328385196956218832346458694372291760513828318831460900821120143747579<80> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=662962843 for P33 / Mar 19, 2007)
3·10142+1 =
3(0)1411<143>
= 97 · 203543020951<12> · 33690430121780543888212711166213824692220327981<47> · 45101059976427355505564135250839549784926008407968873075769527543445669278405405443<83> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 9.87 hours on Core 2 Duo E6300@2.33GHz / Mar 22, 2007)
3·10143+1 =
3(0)1421<144>
= 13 · 47 · 2099 · 4231 · 4259 · 17736799 · 74115735887240684807<20> · 120940167904876203213061027933433<33> · 81650848796699811506688800647364367461674661533783095495619303656848309<71> (Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 gnfs for P33 x P71 / 13.81 hours on Pentium 4 2.80GHz / Mar 23, 2007)
3·10144+1 =
3(0)1431<145>
= 67 · 307 · 26505761839<11> · 5502597989341811453280325654661188430257915760736811008735182048955323276663102194362600358957490858193629421824587327740094756711<130>
3·10145+1 =
3(0)1441<146>
= 23 · 163365916333<12> · 1512111483928357227059586147307533255856999<43> · 5280173022660233758936952412889720282802454835751048118163212654450579862340614890525644261<91> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 9.90 hours on Core 2 Duo E6300@2.33Ghz / Mar 23, 2007)
3·10146+1 =
3(0)1451<147>
= 7 · 62162502049965253<17> · 6699066280481465227<19> · 102915420634079625638666204942525818485234829450766386797107818368315755086070464205897735709733756055701964353<111>
3·10147+1 =
3(0)1461<148>
= definitely prime number
3·10148+1 =
3(0)1471<149>
= 19 · 61197589 · 97631503 · 108817550461206481<18> · 2428535299870600499821029291580376841317100236944884307563528984399789039459262784278489760915114603226966299572177<115>
3·10149+1 =
3(0)1481<150>
= 13 · 43 · 280811 · 18451977947946169372964490164450899739<38> · 103574394682250651492366474771488310679253472549528420564006228321981430254572052540584974107852577311191<105> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 22.38 hours on Cygwin on AMD XP 2700+ / Mar 25, 2007)
3·10150+1 =
3(0)1491<151>
= 3757884014173930271262822327673582373969961097805606684684809<61> · 798321605638876885936868160206937968803884648888029502380986396890251623546215931267628089<90> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 16.21 hours on Core 2 Duo E6300@2.33GHz / Mar 22, 2007)
3·10151+1 =
3(0)1501<152>
= 31 · 397 · 38197 · 60017 · 2703403 · 2730124326417233<16> · 373344263955479291<18> · 62705195924448530372188252023190597<35> · 6154025449218468087679049299048266043351577284513852625291792459<64> (Shaopu Lin / Msieve v. 1.17 for P35 x P64 / Mar 22, 2007)
3·10152+1 =
3(0)1511<153>
= 7 · 585049 · 88220869831<11> · 12289698182411593<17> · 87212223991413427425069271951<29> · 28233780160855150696140036523537581907<38> · 27439236958583695018558967396484435036752651468698597<53> (Makoto Kamada / GMP-ECM 5.0.3 B1=81740, sigma=2715751568 for P38)
3·10153+1 =
3(0)1521<154>
= 21391504829<11> · 120702410173837<15> · 1161887222229059094198302587921696702480855120609398699198129858656050707831596728698528953452207727214370278996536041206825232937<130>
3·10154+1 =
3(0)1531<155>
= 709 · 8035475151373083659527183835942623308307448782043954239<55> · 5265789050328925623147256769024288482438775097245447059422020562309429069222311849609536376272051<97> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 25.09 hours on Core 2 Duo E6300@2.33GHz / Mar 28, 2007)
3·10155+1 =
3(0)1541<156>
= 13 · 292 · 847002118930358570602520920381717175156063<42> · 213090300524279549137442960054809434214996463074123<51> · 152031551632891694465641580404499699339343734544590141354153<60> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 19.48 hours on Cygwin on AMD 64 3200+ / Apr 1, 2007)
3·10156+1 =
3(0)1551<157>
= 1297177961174555143<19> · 2667221954249769199<19> · 14120876924458604253497663539366736456941609<44> · 61404594566872242448503276730228599364013338843483356019440687469832045039377<77> (Robert Backstrom / GMP-ECM 5.0 B1=988000, sigma=501477544 for P44 / May 10, 2007)
3·10157+1 =
3(0)1561<158>
= 17 · 772006355756021<15> · 7401761985090177770309<22> · 248529780208636811981353203838303673<36> · 1242618760787690302557066234608127824342363929964979635799811131131051551936554388849<85> (Robert Backstrom / GMP-ECM 5.0 B1=618000, sigma=3187509690 for P36 / May 8, 2007)
3·10158+1 =
3(0)1571<159>
= 7 · 518209 · 1248630547<10> · 14187037984758391993529228654317591874792986868087928456850474187179<68> · 4668663539228271717902874354562882580267735906322278836949839530064145731879<76> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 35.69 hours on Cygwin on AMD 64 3400+ / May 18, 2007)
3·10159+1 =
3(0)1581<160>
= 509 · 55231796185538374229<20> · 106712256956479168420438191693967482450298743599582395615105036976264392819677967849715055994621546022928882386524388902088895096621815041<138>
3·10160+1 =
3(0)1591<161>
= 12697 · 44454007667553277<17> · 29275289584766911761299359521184239465004060018132044373477<59> · 1815549170260446417865866950799703327121370197342878399772057644753731002595701977<82> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 31.82 hours on Cygwin on AMD 64 3200+ / Aug 20, 2007)
3·10161+1 =
3(0)1601<162>
= 13 · 16217 · 1423008144349946162858538760370171851950232661831601216197627371087320523097793863040209466798848312075172776905526489296607074247821611699024290749024053581<157>
3·10162+1 =
3(0)1611<163>
= 7130941393003213<16> · 103809697153908617469853075665675511<36> · 3853176322382181446159610642291595255342267<43> · 1051762253929606176068974362696177686302006839768383025664246236931321<70> (Wataru Sakai / GMP-ECM 6.1 B1=11000000, sigma=447522327 for P36 / Apr 1, 2007) (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 gnfs for P43 x P70 / 22.19 hours on Core 2 Duo E6300@2.33GHz / Apr 11, 2007)
3·10163+1 =
3(0)1621<164>
= 2693727049321118094591486398079193352608837<43> · 11136985838101413491867306813366781640721780664180020279181015243224647866545476655493916704578164265918304339860447237773<122> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 69.52 hours on Core 2 Duo E6300@2.33GHz / Apr 3, 2007)
3·10164+1 =
3(0)1631<165>
= 7 · 153643579 · 3358957632992895950040793<25> · 9126754553793380350961701881130062943<37> · 9098879264948989983429360562774153133639098883364585761384303273204226621258077428446473075683<94> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=1587404188 for P37 / Jan 14, 2008)
3·10165+1 =
3(0)1641<166>
= 116891557 · 518126347 · 1922556849772274468793737<25> · 1996780824920828139624227695148118615121<40> · 12903063841818771390850986103947680780972868837668201185568690923523136035069365410047<86> (matsui / GGNFS-0.77.1-20060513-pentium4 snfs / Jan 3, 2008)
3·10166+1 =
3(0)1651<167>
= 192 · 31 · 373 · 193939 · 23755628747941<14> · 447212374355192497<18> · 625649191871122082626948379908529671729699051<45> · 5575285937796913330137969587393113913079322142661733106598322245299860531890319<79> (matsui / GGNFS-0.77.1-20060513-prescott snfs / Dec 23, 2007)
3·10167+1 =
3(0)1661<168>
= 132 · 23 · 11240783 · 107653808874199343653823320575009810381715666999<48> · 63779447095061318423367850224578695523579815789150289866244003646649681085810329261922617536898003393691354119<110> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.32 / Jan 2, 2008)
3·10168+1 =
3(0)1671<169>
= 61 · 103 · 3587283476490020290143529<25> · 133103200368004275753921527821276712486591327532406362051431716830496515837378906946751049169170845802264215168161428832251246693080356564843<141>
3·10169+1 =
3(0)1681<170>
= 547 · 849763 · 14923933 · 55353326319623081657<20> · 78128429892476209929315813823129326676823648239826037322173456012994919551810835086092109845502537595408447887249501891256847905505461<134>
3·10170+1 =
3(0)1691<171>
= 7 · 43 · 199 · 57529 · 1526651229058273<16> · 261968755177133227477927295381326837835413<42> · 217683509057887059702713392168572709659690627314116574373411276814837715368246493032016769217598949465919<105> (Dmitry Domanov / Jun 14, 2009)
3·10171+1 =
3(0)1701<172>
= 59 · 2421821 · 1600388452377973<16> · 19226964394318121967711782431<29> · 454231567465961238949597490091615349190531<42> · 1502151578223577638654775137097332901436078950967469661170957656557872845681903<79> (Sinkiti Sibata / GGNFS-0.77.1-20060722-nocona gnfs for P42 x P79 / 72.45 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Dec 28, 2007)
3·10172+1 =
3(0)1711<173>
= 19055977 · 42387494983<11> · 170190139057<12> · 64419666286924261<17> · 220505600678738400241<21> · 161183636530960926117651862009<30> · 43118791680011201738092517077520575807<38> · 2210508874952327084358149851144464520021<40> (Makoto Kamada / GMP-ECM 5.0.3 B1=81890, sigma=3324633473 for P30) (Makoto Kamada / Msieve 1.17 for P38 x P40 / Mar 18, 2007)
3·10173+1 =
3(0)1721<174>
= 13 · 172 · 174049 · 774588953 · [592293857025346624210362390252170839341086653051594159764333383779932202844867907476956745798214635664406561760854277089030385709822053497300982445076387469<156>] SUBMIT/RESERVE
3·10174+1 =
3(0)1731<175>
= 695560069 · 1643541565177<13> · [2624254320971457534633066971233070743567071534381656264721815627687476310413252491135977490762315634934808973396788267848403939506862746371253371676364277<154>] SUBMIT/RESERVE
3·10175+1 =
3(0)1741<176>
= 15121 · 219026567 · 1760550942973475119<19> · [5145118112144435327757146311895219103549937585511052732642348395235306744282728177909772755647069527877777047480068081437145725065089109941105897<145>] SUBMIT/RESERVE
3·10176+1 =
3(0)1751<177>
= 73 · 306883 · 27571321 · 2223696949<10> · 34295441066827<14> · [1355453852456951783664690332454894179973798988136253554527922055352506546590584854140232808416242698356849939860838412601812507168764244963<139>] SUBMIT/RESERVE
3·10177+1 =
3(0)1761<178>
= 67 · 971 · 1181 · 1487 · 230479 · 825733 · 3109400284219346651<19> · 126785306124523882133503879<27> · 559219839704943337643116206350631409<36> · 625845632053760575390249120386323002760427242323498242975273828154385498197<75> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 21.23 hours on Core 2 Duo E6300@2.33GHz / Mar 24, 2007)
3·10178+1 =
3(0)1771<179>
= 2050459 · 12264541 · 340688242377207018081711127<27> · 5069346827014420672241942756293<31> · 690732220068543526727568186205626712603241853899400661384995347253624067067728995244495344555464573552973589<108> (Wataru Sakai / GMP-ECM 6.1 B1=11000000, sigma=1794784119 for P31 / Apr 1, 2007)
3·10179+1 =
3(0)1781<180>
= 13 · 7127 · 5174677 · 1117157777<10> · 167717010985879<15> · 3339613976591229119259320197203139774767853553791481874729761460795419995848020835478379082095535623034053752302201130407369915797564759568306961<145>
3·10180+1 =
3(0)1791<181>
= 661 · 430259544631759600727768857693217721153099730144795861<54> · 1538326517326993101925943385140082111132168130040478949<55> · 6857104304052897516728603587977821413916030196167551914714888140645269<70> (matsui / GGNFS-0.77.1-20060513-prescott snfs / Mar 2, 2008)
3·10181+1 =
3(0)1801<182>
= 31 · 163 · 45831510539<11> · 129541161070962276375524706597797231237380084278534888904236011409595074063067722554009382796484727145428087893614131520398789497295078620266068259167231776212559687903<168>
3·10182+1 =
3(0)1811<183>
= 7 · 184711 · 7889052315362488613741228856217<31> · [29410717466469283588075381685466768757690100812083217388444840671740509653974079948813432796129179492301617138223082785385874048810154482083840889<146>] (Makoto Kamada / GMP-ECM 5.0.3 B1=81970, sigma=4128059153 for P31) SUBMIT/RESERVE
3·10183+1 =
3(0)1821<184>
= 29 · 114790045871334151<18> · [901195526814424772421657606972377984538975003819932526094678491123761306774370718542767272851404406061113000403399044804171325813994939206177419054478158819871733219<165>] SUBMIT/RESERVE
3·10184+1 =
3(0)1831<185>
= 19 · 196797409 · 10762263913<11> · 745494836636572130172819523037276149944686381269674094578751262163539451085510590830500109309643116762278895320239001816323158684183587595033024231399271515596849987<165>
3·10185+1 =
3(0)1841<186>
= 13 · 2023746225668777<16> · 36720090322313647694051<23> · 310540401257397737348038834696050663179011279285556879255610037091646723630434622079930149152479120433809319536685872800872343331623558391188304351<147>
3·10186+1 =
3(0)1851<187>
= 439 · 169819005840667<15> · 40241155283092480818038774787149275870934631476611728723408637074158659177368013036434976879754984472537487184954630114161470383022045784968026778476870122069983476991877<170>
3·10187+1 =
3(0)1861<188>
= 1990243 · 16565261 · 909948611529811412934384541301540732469732845232998558343616864089988451756330466262286003545679220186522513929107253571677653491327174671386973154651393239832076783199266487<174>
3·10188+1 =
3(0)1871<189>
= 7 · 37135242979<11> · 9561060331429<13> · 13649588948170686463<20> · 8843237995130879985234228749128009724370323877568816254715812236482263635980946446461438878364758061388356047345722471760315601906705188372132071<145>
3·10189+1 =
3(0)1881<190>
= 17 · 23 · 47 · 163247537682973281819665886706208848016542417151874625891059476519562496599009631604723295423627360287315666322032976002611960602927572509114654187299341568264678674429994014256951624313<186>
3·10190+1 =
3(0)1891<191>
= 337 · 613 · 71359 · 799217773 · 2546343508839486516207701265886984349789271759336639159658352387359208880453389197974991386928337275420727244285163037733738941426151492090978763689643407394343548617013903<172>
3·10191+1 =
3(0)1901<192>
= 13 · 43 · 41981 · 90059 · 222941 · 1235130679<10> · 8247897299<10> · 94927819198801891456854631<26> · 3509579947593832172401267969183483650808143002961993244596581<61> · 187600851274178017217228137473536104234402691756912413319983272561371<69> (matsui / GGNFS-0.77.1-20060513-prescott gnfs for P61 x P69 / 321.19 hours / Jul 3, 2008)
3·10192+1 =
3(0)1911<193>
= 151 · 791442937966190685229637395742267041720820331589<48> · 95011290548333356448178869786693410025075222062601524884381341878748749<71> · 264210140483694895177251228728197166603387493603667452462313902636578791<72> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp, Msieve 1.36 snfs / 179.21 hours, 14.43 hours / Sep 1, 2008)
3·10193+1 =
3(0)1921<194>
= 228341 · 2462075533<10> · 5473356377065602643<19> · [9749498059632349472537365567195612466704803993553469885573399879070807606858132275262056647525992812387897660033035386037689136339636083520394004764399862945419<160>] SUBMIT/RESERVE
3·10194+1 =
3(0)1931<195>
= 7 · 866651964229863762194029183<27> · [49451388361217369800398549437932552036460598526900817731202449047593444598421139490901229397738265221314543439946882377336042856715055406986301404178693200878935122121<167>] SUBMIT/RESERVE
3·10195+1 =
3(0)1941<196>
= 2365233400223<13> · [1268373767982962125319133175632406214893622512720614455919362112986389524519666911532753714169686561055733399031390074237916652726510874758486022956067514047787818473789232166409032287<184>] SUBMIT/RESERVE
3·10196+1 =
3(0)1951<197>
= 31 · 223 · 11497565766727360956446718343<29> · [377440757717925047082140021675179638164089682134825775849748283342945432040728137839385506451487038903870147400431841581942537701399703414953478013944560563044413239<165>] SUBMIT/RESERVE
3·10197+1 =
3(0)1961<198>
= 13 · 10902448059185532910215851<26> · [2116673516961202367100246760216781454495794908092658404774238951202752624652151450401618480202236071837151682557892057810224137504758224353690938374009671620023050971010127<172>] SUBMIT/RESERVE
3·10198+1 =
3(0)1971<199>
= 1833911383348466522566074446250134380140228731863510782284501695384966021186952971<82> · 1635847853521917851052479217771526282232255683407487990801439756907074080101789715314755512178980013517705612191904931<118> (Serge Batalov / Msieve-1.37 snfs / 20 CPU-days on Opteron-2.6GHz; Linux x86_64 / Sep 8, 2008)
3·10199+1 =
3(0)1981<200>
= 131 · 229007633587786259541984732824427480916030534351145038167938931297709923664122137404580152671755725190839694656488549618320610687022900763358778625954198473282442748091603053435114503816793893129771<198>
3·10200+1 =
3(0)1991<201>
= 7 · 433 · 610447 · 185263117033<12> · 2828858023360747867<19> · [309376439141173135122801092378292676231512120185807112772569914227805906546089791125493270760503843458985380944707345486783522559087459175400651703880428787804563<162>] SUBMIT/RESERVE

4. References

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