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Factorizations of 677...779

Table of contents

  1. About 677...779
  2. Prime numbers of the form 677...779
  3. Factorizations of 677...779
  4. References

1. About 677...779

First ten terms

69, 679, 6779, 67779, 677779, 6777779, 67777779, 677777779, 6777777779, 67777777779

General term

(61·10n+11)/9

2. Prime numbers of the form 677...779

Last update

Sep 19, 2010

Searched up to

n≤30000

Difficulty of search

16.45%

Results

  1. (61·103+11)/9 = 6779 is prime.
  2. (61·105+11)/9 = 677779 is prime.
  3. (61·1015+11)/9 = 6(7)149<16> is prime.
  4. (61·1047+11)/9 = 6(7)469<48> is prime.
  5. (61·1069+11)/9 = 6(7)689<70> is prime.
  6. (61·10123+11)/9 = 6(7)1229<124> is prime. (searched by Makoto Kamada / Dec 6, 2004) (certified by Makoto Kamada / PPSIQS / Jan 5, 2005)
  7. (61·10713+11)/9 = 6(7)7129<714> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 31, 2006)
  8. (61·102316+11)/9 = 6(7)23159<2317> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Ray Chandler / Primo 3.0.9 / Sep 19, 2010)
  9. (61·106147+11)/9 = 6(7)61469<6148> is PRP. (Makoto Kamada / PFGW / Dec 24, 2004)
  10. (61·108877+11)/9 = 6(7)88769<8878> is PRP. (Makoto Kamada / PFGW / Jan 1, 2005)
  11. (61·1010704+11)/9 = 6(7)107039<10705> is PRP. (Ray Chandler / srsieve, PFGW / Sep 9, 2010)

3. Factorizations of 677...779

Last update

Dec 8, 2011

Completed up to

Range

n≤200

Terms which have not been factored yet

n=182, 184, 192, 194, 195, 197, 198 (7/200)

Results

(61·101+11)/9 =
69
= 3 · 23
(61·102+11)/9 =
679
= 7 · 97
(61·103+11)/9 =
6779
= definitely prime number
(61·104+11)/9 =
67779
= 32 · 17 · 443
(61·105+11)/9 =
677779
= definitely prime number
(61·106+11)/9 =
6777779
= 139 · 48761
(61·107+11)/9 =
67777779
= 3 · 647 · 34919
(61·108+11)/9 =
677777779
= 7 · 787 · 123031
(61·109+11)/9 =
6777777779<10>
= 499 · 1439 · 9439
(61·1010+11)/9 =
67777777779<11>
= 3 · 29 · 1181 · 659657
(61·1011+11)/9 =
677777777779<12>
= 173 · 15823 · 247601
(61·1012+11)/9 =
6777777777779<13>
= 7451 · 909646729
(61·1013+11)/9 =
67777777777779<14>
= 32 · 2399 · 3139168069<10>
(61·1014+11)/9 =
677777777777779<15>
= 7 · 88657 · 1092134821<10>
(61·1015+11)/9 =
6777777777777779<16>
= definitely prime number
(61·1016+11)/9 =
67777777777777779<17>
= 3 · 859 · 1283 · 20499640769<11>
(61·1017+11)/9 =
677777777777777779<18>
= 19 · 373 · 360653 · 265176689
(61·1018+11)/9 =
6777777777777777779<19>
= 5096783 · 1329814861213<13>
(61·1019+11)/9 =
67777777777777777779<20>
= 3 · 43 · 207973 · 2526333370487<13>
(61·1020+11)/9 =
677777777777777777779<21>
= 72 · 17 · 4461161 · 182387229883<12>
(61·1021+11)/9 =
6777777777777777777779<22>
= 344801 · 19657071115738579<17>
(61·1022+11)/9 =
67777777777777777777779<23>
= 33 · 179 · 14023955675104030163<20>
(61·1023+11)/9 =
677777777777777777777779<24>
= 23 · 29468599033816425120773<23>
(61·1024+11)/9 =
6777777777777777777777779<25>
= 41771 · 162260366708428761049<21>
(61·1025+11)/9 =
67777777777777777777777779<26>
= 3 · 151 · 449 · 3209 · 36109 · 2875792880347<13>
(61·1026+11)/9 =
677777777777777777777777779<27>
= 7 · 270471427 · 357987525334411111<18>
(61·1027+11)/9 =
6777777777777777777777777779<28>
= 14087 · 866606197 · 555196884845761<15>
(61·1028+11)/9 =
67777777777777777777777777779<29>
= 3 · 47 · 337 · 1426390087290396653361487<25>
(61·1029+11)/9 =
677777777777777777777777777779<30>
= 1907 · 355415719862494901823690497<27>
(61·1030+11)/9 =
6777777777777777777777777777779<31>
= 61541611 · 110133252406697279630489<24>
(61·1031+11)/9 =
67777777777777777777777777777779<32>
= 32 · 109 · 69090497225053799977347377959<29>
(61·1032+11)/9 =
677777777777777777777777777777779<33>
= 7 · 781051 · 2703761 · 45850237904585994527<20>
(61·1033+11)/9 =
6777777777777777777777777777777779<34>
= 1327 · 4099 · 94383038389<11> · 13202145972094307<17>
(61·1034+11)/9 =
67777777777777777777777777777777779<35>
= 3 · 301843492002617<15> · 74848698717005015129<20>
(61·1035+11)/9 =
677777777777777777777777777777777779<36>
= 19 · 95640931627<11> · 372983763468615976154083<24>
(61·1036+11)/9 =
6777777777777777777777777777777777779<37>
= 17 · 398692810457516339869281045751633987<36>
(61·1037+11)/9 =
67777777777777777777777777777777777779<38>
= 3 · 547 · 1291 · 298579 · 484695396841<12> · 221067218970131<15>
(61·1038+11)/9 =
677777777777777777777777777777777777779<39>
= 7 · 29 · 9327746808067<13> · 357943547973999310327379<24>
(61·1039+11)/9 =
6777777777777777777777777777777777777779<40>
= 409 · 9746579 · 10230281 · 166197408442873321826369<24>
(61·1040+11)/9 =
67777777777777777777777777777777777777779<41>
= 32 · 43 · 317 · 2333 · 236811265989910614085259322368297<33>
(61·1041+11)/9 =
677777777777777777777777777777777777777779<42>
= 4733 · 249833 · 573193184852068359164684974090711<33>
(61·1042+11)/9 =
6777777777777777777777777777777777777777779<43>
= 379 · 859 · 10723 · 131249 · 461643928939<12> · 32043172966831963<17>
(61·1043+11)/9 =
67777777777777777777777777777777777777777779<44>
= 3 · 117523793 · 260089393 · 4691108813<10> · 157558603704880789<18>
(61·1044+11)/9 =
677777777777777777777777777777777777777777779<45>
= 7 · 269 · 359945713105564406679648315336047678055113<42>
(61·1045+11)/9 =
6777777777777777777777777777777777777777777779<46>
= 23 · 2011 · 145819 · 1004924196717545511044870343249605197<37>
(61·1046+11)/9 =
67777777777777777777777777777777777777777777779<47>
= 3 · 59908248608851<14> · 377119897797424583318357726212043<33>
(61·1047+11)/9 =
677777777777777777777777777777777777777777777779<48>
= definitely prime number
(61·1048+11)/9 =
6777777777777777777777777777777777777777777777779<49>
= 229 · 16091 · 87589 · 1010507237<10> · 20781639755906901590265555677<29>
(61·1049+11)/9 =
67777777777777777777777777777777777777777777777779<50>
= 33 · 59 · 383 · 6693592878397<13> · 16596384271179072691824272115353<32>
(61·1050+11)/9 =
677777777777777777777777777777777777777777777777779<51>
= 7 · 96825396825396825396825396825396825396825396825397<50>
(61·1051+11)/9 =
6(7)509<52>
= 43851036473149658881<20> · 154563684758691289729450753279859<33>
(61·1052+11)/9 =
6(7)519<53>
= 3 · 17 · 139 · 233 · 23093630689<11> · 1776864095693847207905542686790361803<37>
(61·1053+11)/9 =
6(7)529<54>
= 19 · 839 · 1031 · 10265839 · 132662559173<12> · 1130969959099<13> · 26774366833903433<17>
(61·1054+11)/9 =
6(7)539<55>
= 173 · 257 · 182086174336026566509<21> · 837203678194293655462178589371<30>
(61·1055+11)/9 =
6(7)549<56>
= 3 · 72006673 · 313756929063957622269155423867348969068361103041<48>
(61·1056+11)/9 =
6(7)559<57>
= 7 · 193 · 463 · 23189 · 20988497 · 3573588445597<13> · 622992889809839986420693483<27>
(61·1057+11)/9 =
6(7)569<58>
= 449 · 4854812173666529<16> · 2311385974729398491<19> · 1345228558523647403689<22>
(61·1058+11)/9 =
6(7)579<59>
= 32 · 13607768621<11> · 553423886551757102920163195324135442435728948711<48>
(61·1059+11)/9 =
6(7)589<60>
= 131 · 46853 · 213511988943669389737<21> · 517197431854811999143484979970069<33>
(61·1060+11)/9 =
6(7)599<61>
= 451218642633919<15> · 15021049968621750345853499599612449445497540941<47>
(61·1061+11)/9 =
6(7)609<62>
= 3 · 43 · 577 · 617 · 3180732309511<13> · 463990958345624080451900752287211664885549<42>
(61·1062+11)/9 =
6(7)619<63>
= 72 · 693829 · 21539807 · 925543829571173185652729916555399017625065751257<48>
(61·1063+11)/9 =
6(7)629<64>
= 208151291333116570267576177<27> · 32561785873962738696903396937429973027<38>
(61·1064+11)/9 =
6(7)639<65>
= 3 · 82972672771<11> · 272289560382692527215908559737923024036805046608790683<54>
(61·1065+11)/9 =
6(7)649<66>
= 39384328135931011345405582141<29> · 17209326903800328068832401146663883119<38>
(61·1066+11)/9 =
6(7)659<67>
= 29 · 233716475095785440613026819923371647509578544061302681992337164751<66>
(61·1067+11)/9 =
6(7)669<68>
= 32 · 23 · 106279 · 3080842670268969736968309497737441769358854973407100424162843<61>
(61·1068+11)/9 =
6(7)679<69>
= 7 · 17 · 859 · 1281791417<10> · 8145769381<10> · 9790576280662660331369<22> · 64861871475112288206323<23>
(61·1069+11)/9 =
6(7)689<70>
= definitely prime number
(61·1070+11)/9 =
6(7)699<71>
= 3 · 541 · 719 · 58081779717137924136245382379492447131060012475204554982640689067<65>
(61·1071+11)/9 =
6(7)709<72>
= 19 · 169003 · 37405783 · 75355252279<11> · 74883654782345714420147776944425326834906786771<47>
(61·1072+11)/9 =
6(7)719<73>
= 300836558735679106451<21> · 22529767679375916881969788341752659787244288342925729<53>
(61·1073+11)/9 =
6(7)729<74>
= 3 · 2213 · 528302611 · 2157408906847<13> · 8957141447347197710775624459938699279444720011633<49>
(61·1074+11)/9 =
6(7)739<75>
= 7 · 47 · 163 · 141697 · 636180036302896607051<21> · 140204880360841073362875155502220407061406491<45>
(61·1075+11)/9 =
6(7)749<76>
= 523 · 5644103 · 1202518621<10> · 10159405559<11> · 187944922947132872987110792675355442083438976269<48>
(61·1076+11)/9 =
6(7)759<77>
= 34 · 16883 · 49562440834836253414222486771906416036715856170446696529256018200628273<71>
(61·1077+11)/9 =
6(7)769<78>
= 21959353496387<14> · 812639713894133141738663770139<30> · 37981291922580851422378716755060803<35>
(61·1078+11)/9 =
6(7)779<79>
= 166906456925824468145956175932288081<36> · 40608241901569546338667813271961776788701059<44> (Makoto Kamada / GGNFS-0.70.1 / 0.13 hours)
(61·1079+11)/9 =
6(7)789<80>
= 3 · 227 · 274117 · 363081602435986610890928011118449109339490740184958041929916973659750527<72>
(61·1080+11)/9 =
6(7)799<81>
= 7 · 16339 · 14591461415316292951393<23> · 406129953800649895185125452327810613698990980272902711<54>
(61·1081+11)/9 =
6(7)809<82>
= 199 · 910751 · 37396812974077060771564019584818853525524554964729438003189789976561768171<74>
(61·1082+11)/9 =
6(7)819<83>
= 3 · 43 · 1447 · 19819 · 3928349114755223024056971518741916317<37> · 4663771558990740724544637805424149771<37> (Makoto Kamada / msieve 0.83)
(61·1083+11)/9 =
6(7)829<84>
= 114809 · 314515209746494921549354603<27> · 18770236250816632496564977027498333621680369581193377<53>
(61·1084+11)/9 =
6(7)839<85>
= 17 · 113 · 104104159 · 2280162457<10> · 251735881796227422753227626499<30> · 59044706304915208037571728421916327<35>
(61·1085+11)/9 =
6(7)849<86>
= 32 · 1867 · 6128509 · 658181498298614255419126535649288755738882702846479275870831851968699417477<75>
(61·1086+11)/9 =
6(7)859<87>
= 7 · 557 · 126800233880731507<18> · 1871021147460179293937<22> · 3098506206961175291299<22> · 236473766691979787921281<24>
(61·1087+11)/9 =
6(7)869<88>
= 2129 · 3359 · 538940287 · 1758575470039488571882157839058851440900263594516213805473002185731234147<73>
(61·1088+11)/9 =
6(7)879<89>
= 3 · 7478683 · 101269691 · 29830563749446183604044404080127727991414998683505981491503015536385409881<74>
(61·1089+11)/9 =
6(7)889<90>
= 19 · 23 · 449 · 727241 · 4749864189908579163484774100091960347012678139746399093438770972236203872811663<79>
(61·1090+11)/9 =
6(7)899<91>
= 21977 · 8919809 · 7999976718149505483409<22> · 4321899257686104574281574901296804544084225428374599126267<58>
(61·1091+11)/9 =
6(7)909<92>
= 3 · 2705113 · 8351811030664002794926715664962089418295129479837845070646805731439903838616942283961<85>
(61·1092+11)/9 =
6(7)919<93>
= 7 · 7733130135286443806632770974039247233832511<43> · 12520854444642073023565802421099034916112816031627<50> (Makoto Kamada / GGNFS-0.71.1 / 0.30 hours)
(61·1093+11)/9 =
6(7)929<94>
= 149 · 4019 · 50186940214093<14> · 225523774972368688002771471605091383056703694351274309019024055419312697713<75>
(61·1094+11)/9 =
6(7)939<95>
= 32 · 29 · 859 · 302310794329045971559988125628471927964789217515590068545255678115325125347471566678610421<90>
(61·1095+11)/9 =
6(7)949<96>
= 1856523751<10> · 12154411616183<14> · 274151178046439<15> · 109562708426523440019978575745601251440323564404168873788917<60>
(61·1096+11)/9 =
6(7)959<97>
= 349 · 3054130207340383<16> · 243237438464288403309268637970448313009<39> · 26142308112299958914209531646655482258593<41> (Makoto Kamada / GGNFS-0.71.1 / 0.35 hours)
(61·1097+11)/9 =
6(7)969<98>
= 3 · 173 · 2730587 · 14044061 · 26655564990585363323<20> · 189969039860898051385492589<27> · 672512749843472318707273307026965029<36>
(61·1098+11)/9 =
6(7)979<99>
= 7 · 97 · 139 · 191403059 · 37519226526972543294522280323079392669085632467184300393966964846284284811757354089701<86>
(61·1099+11)/9 =
6(7)989<100>
= 5254180699905335216633638997<28> · 1289978050792941565657125614571816466799380408780895168873428681245098407<73>
(61·10100+11)/9 =
6(7)999<101>
= 3 · 17 · 151 · 929 · 10337 · 9132432863<10> · 10711857130118529297846802327599268363<38> · 9368686618876984719920834795754345486291467<43> (Makoto Kamada / GGNFS-0.71.1 / 0.44 hours)
(61·10101+11)/9 =
6(7)1009<102>
= 14153 · 143349674701<12> · 44880551511011<14> · 257495933469051938270899873<27> · 28907700549928933731370448188765822066437761581<47>
(61·10102+11)/9 =
6(7)1019<103>
= 20673895105772984563476130687<29> · 294639908354044475887618757043321869<36> · 1112688107679640172471959251581777678593<40> (Makoto Kamada / Msieve 1.42 for P36 x P40 / Oct 16, 2009)
(61·10103+11)/9 =
6(7)1029<104>
= 33 · 43 · 15809 · 215177500491476100559<21> · 17161444807920561137417693037009715325584846678372302659972076259635042575669<77>
(61·10104+11)/9 =
6(7)1039<105>
= 72 · 13832199546485260770975056689342403628117913832199546485260770975056689342403628117913832199546485260771<104>
(61·10105+11)/9 =
6(7)1049<106>
= 43045273 · 157456958811198102467088030264734940298271026827446948188196594264317426393782605996662578438700523<99>
(61·10106+11)/9 =
6(7)1059<107>
= 3 · 3121 · 13316029 · 139589330092567<15> · 679543722659116356499317289021<30> · 5730967450648430058059569007138574233846729439604111<52> (Makoto Kamada / Msieve 1.42 for P30 x P52 / Oct 19, 2009)
(61·10107+11)/9 =
6(7)1069<108>
= 19 · 59 · 223 · 1442531 · 1879540529252887433618106939322453852777696144471977267669273568749855959703392703488623904223823<97>
(61·10108+11)/9 =
6(7)1079<109>
= 57855953 · 674919914887<12> · 91108247087160828584254860711097<32> · 1905150723036496927643831385952647134842981729524119029837<58> (Serge Batalov / Msieve 1.43 snfs / 0.57 hours / Oct 20, 2009)
(61·10109+11)/9 =
6(7)1089<110>
= 3 · 4047537538542415495109532620351832243679<40> · 5581811750343532307079939582977515751345075804424834298521615160645967<70> (Dmitry Domanov / GGNFS/msieve snfs / 0.84 hours / Oct 20, 2009)
(61·10110+11)/9 =
6(7)1099<111>
= 7 · 1965797247224922563675203<25> · 351440429148987573975248485100660149<36> · 140151852450797442864198764926068611764798232457451<51> (Robert Backstrom / Msieve 1.42 for P36 x P51 / 0.68 hours / Oct 20, 2009)
(61·10111+11)/9 =
6(7)1109<112>
= 23 · 263 · 2193383 · 11767080137<11> · 50085229859103377<17> · 160116958157390637554209<24> · 5413442829593323341949718811605848214276934155217757<52>
(61·10112+11)/9 =
6(7)1119<113>
= 32 · 2784696249953239187<19> · 2704375458421119715525125389097337917071564647192259169959966873810706437372952701267420836313<94>
(61·10113+11)/9 =
6(7)1129<114>
= 307 · 25657039 · 37773578848785727777230654144955249<35> · 2278002948413952062643500998301129304750379898099741553485911129576927<70> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2497921219 for P35 / Oct 15, 2009)
(61·10114+11)/9 =
6(7)1139<115>
= 222679 · 11178637 · 18903334723259647<17> · 41036055173181597710179425086539396815889<41> · 3510065170731752561733587750619799871556698231<46> (Sinkiti Sibata / Msieve 1.42 for P41 x P46 / 0.58 hours / Oct 19, 2009)
(61·10115+11)/9 =
6(7)1149<116>
= 3 · 11689 · 16395185245811434412457687799934663376577264400981837<53> · 117888755802769552667826097972841639069866714575824487244301<60> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 0.49 hours on Core 2 Quad Q6700 / Oct 19, 2009)
(61·10116+11)/9 =
6(7)1159<117>
= 7 · 17 · 991 · 1753 · 3278572513698309969986426166947676072905720181522864716606886116025973481369417364765721783519390254222732467<109>
(61·10117+11)/9 =
6(7)1169<118>
= 33212926581041112127<20> · 5048520055612043895414911011<28> · 40421841448082072144169026476440208608566504887483281690938032805245007<71>
(61·10118+11)/9 =
6(7)1179<119>
= 3 · 2309837 · 448500547927<12> · 17632003377816731628383189280973540932700525483<47> · 1236858729965652988254596588296867185555187756209443929<55> (Lionel Debroux / GGNFS + Msieve snfs / 5.80 hours on Core 2 Duo T7200, 2 GB RAM / Oct 20, 2009)
(61·10119+11)/9 =
6(7)1189<120>
= 317 · 7633871488060427353<19> · 182910787984500992308889<24> · 203268902482364108466077<24> · 7533086525830537889915373360396796134284486516814443<52>
(61·10120+11)/9 =
6(7)1199<121>
= 47 · 673 · 859 · 1021 · 23180233 · 61632673 · 373788539923650340956391<24> · 1626838112515995782825928657361477<34> · 281226587302051223904026448176305109737<39> (Makoto Kamada / Msieve 1.42 for P34 x P39 / Oct 16, 2009)
(61·10121+11)/9 =
6(7)1209<122>
= 32 · 359 · 449 · 7673 · 1271557826448075794255113281727<31> · 83209827218379502749044972247973<32> · 57547716151864030774518059446990346216884672026127<50> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3163179662 for P32 / Oct 16, 2009) (Makoto Kamada / Msieve 1.42 for P31 x P50 / Oct 16, 2009)
(61·10122+11)/9 =
6(7)1219<123>
= 7 · 29 · 361533924210305081649450654391335109543178661701<48> · 9235113397381922794432779026073798516430287706951852241880434020450688293<73> (Dmitry Domanov / GGNFS/msieve snfs / 1.57 hours / Oct 20, 2009)
(61·10123+11)/9 =
6(7)1229<124>
= definitely prime number
(61·10124+11)/9 =
6(7)1239<125>
= 3 · 43 · 149791 · 135329388429488114701900710450078109693022954591<48> · 25919091566712232464070995868800192058033785202911487150859363568422771<71> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 1.25 hours on Core 2 Quad Q6700 / Oct 20, 2009)
(61·10125+11)/9 =
6(7)1249<126>
= 19 · 1158217 · 11334851941801<14> · 6229576253728276513568100853<28> · 436183699492521568044594791285779540018721340677072943462845856249376706176141<78>
(61·10126+11)/9 =
6(7)1259<127>
= 4583 · 6317 · 17909 · 3879167 · 10801069060460037677<20> · 2195586039900908690698168329609801270916603<43> · 142101798548019649379224996185134551483183791973<48> (Erik Branger / YAFU, Msieve 1.38 for P43 x P48 / Oct 26, 2009)
(61·10127+11)/9 =
6(7)1269<128>
= 3 · 10651 · 338321697226366674240487061083<30> · 839143732972937638963072284751393<33> · 7471528886835488366156323258479905800735219309969221378129497<61> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3931209069 for P30 / Oct 25, 2009) (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2278851720 for P33 / Oct 25, 2009)
(61·10128+11)/9 =
6(7)1279<129>
= 7 · 547 · 24203 · 1839589 · 613627414237052498183<21> · 6478988373848378571910955102118203964321911347218457626225439950839678323491061924458689700391<94>
(61·10129+11)/9 =
6(7)1289<130>
= 2898421 · 293848081 · 1733540197979<13> · 1337589118704611<16> · 18318119666941001<17> · 187355075800931821973712405030481359218162990275852694404393820947840591<72>
(61·10130+11)/9 =
6(7)1299<131>
= 33 · 12141019215809417<17> · 258286671235162236352303<24> · 2603800835257585405318811667397972553087<40> · 307438786873328469652390333446782493394750798060721<51> (Norbert Schneider / Msieve 1.43 for P40 x P51 / 2.98 hours on Intel Celeron 2.80 GHz, 512 MB RAM, WIndows XP / Oct 27, 2009)
(61·10131+11)/9 =
6(7)1309<132>
= 1543 · 690358459339<12> · 433771686143552718713393<24> · 1466849469169072024246005253564805281153641375560932085760799091000286599838768047452854062639<94>
(61·10132+11)/9 =
6(7)1319<133>
= 17 · 74887 · 1144727 · 560920115891<12> · 8291422195165363202683928804609973500442832530082335093351642924858599846835530116866780581971737532330683793<109>
(61·10133+11)/9 =
6(7)1329<134>
= 3 · 23 · 982286634460547504025764895330112721417069243156199677938808373590982286634460547504025764895330112721417069243156199677938808373591<132>
(61·10134+11)/9 =
6(7)1339<135>
= 7 · 956689 · 147489889 · 1605024511121898730823739355562491316477<40> · 427537867971104787643044373647126483897763339452030506462774083723736087616393641<81> (Robert Backstrom / GMP-ECM 6.2.1 B1=2118000, sigma=3579718577 for P40 / Oct 26, 2009)
(61·10135+11)/9 =
6(7)1349<136>
= 169485499 · 184510757 · 62710119529<11> · 3456172895578360546051159037009143411221239651186370224711897212668099474880125976446366684003777114176965357<109>
(61·10136+11)/9 =
6(7)1359<137>
= 3 · 2213363 · 20975235357953<14> · 56099438243208509545785301147285196647<38> · 8674572279336327283237021925543194621541044909983854234310679612701120002673821<79> (Sinkiti Sibata / Msieve 1.40 snfs / 5.94 hours / Oct 26, 2009)
(61·10137+11)/9 =
6(7)1369<138>
= 41854649 · 1497100862179284466393211599484926776042967<43> · 10816644611377158968597922580922419233088088735788862949569901953744310105884107215906413<89> (Sinkiti Sibata / Msieve 1.40 snfs / 7.87 hours / Oct 26, 2009)
(61·10138+11)/9 =
6(7)1379<139>
= 2293 · 2656921 · 179200673 · 671340304528453919<18> · 9247455962328383153776027164770662363025925297333169463910057730019434118798349142612261108592191648289<103>
(61·10139+11)/9 =
6(7)1389<140>
= 32 · 109 · 48878329 · 83506061 · 19526948443<11> · 78880357352977<14> · 31457024130252067117<20> · 349351880228624267909827068790040751750788974024574959850980598238368667866453<78>
(61·10140+11)/9 =
6(7)1399<141>
= 7 · 173 · 4668508477118735351<19> · 11868308233560420583480229<26> · 34654709996381233356360236722003259611<38> · 291483479342020082267398383224796794589186280350551363081<57> (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 gnfs for P38 x P57 / 10.42 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Oct 26, 2009)
(61·10141+11)/9 =
6(7)1409<142>
= 36910453 · 1478179639<10> · 121391528936094278359<21> · 1023345662186109312162508553034940319973704706852215009817064418962973167327609638021175664506014530557943<106>
(61·10142+11)/9 =
6(7)1419<143>
= 3 · 33353 · 19906792880765389<17> · 6333596761890210427769088539424107<34> · 5372537550577884027041044748259697776204681547417165620095560642583786697767311429280647<88> (Sinkiti Sibata / Msieve 1.40 snfs / 11.35 hours / Oct 27, 2009)
(61·10143+11)/9 =
6(7)1429<144>
= 19 · 857 · 997 · 9043 · 740599 · 6233932453230396110177094525680454896957686994750382371034287503572836072109821993572875581653773493937340794294460975119116097<127>
(61·10144+11)/9 =
6(7)1439<145>
= 139 · 35451613663413251648447982109961<32> · 902835582445713727649667691606922077<36> · 1523448755300188337671604898103869412215946977128520856830739463707719389413<76> (Dmitry Domanov / GGNFS/msieve snfs / 8.06 hours / Oct 28, 2009)
(61·10145+11)/9 =
6(7)1449<146>
= 3 · 43 · 748927063 · 19663589654197<14> · 18103407230733287<17> · 1970765574483183451384821623210853480121864739035126571658087407910295142996853354595101825892567995659143<106>
(61·10146+11)/9 =
6(7)1459<147>
= 72 · 859 · 5557 · 275800236853<12> · 43877517103969019<17> · 47018556761287004919324019214769957965617<41> · 5092742427046728561746607640479066938348493902951058681904891312864643<70> (juno1369 / GGNFS + Msieve gnfs for P41 x P70 / 213.24 hours on AMD Turion 64, Windows Vista and Cygwin / Nov 15, 2009)
(61·10147+11)/9 =
6(7)1469<148>
= 3167033747<10> · 16507115558371<14> · 5034286213921156475322253<25> · 25752864337365954777081141007747100398975704638555930997679477791475931149947503577455163408108118039<101>
(61·10148+11)/9 =
6(7)1479<149>
= 32 · 17 · 15319 · 159589 · 97217642812415666311<20> · 268978493809359271513416809599<30> · 15778348857742482280322540725154142893917<41> · 439175725135905508379395921376984663405910180421<48> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3309641469 for P30 / Oct 25, 2009) (Erik Branger / YAFU, Msieve 1.38 for P41 x P48 / Oct 26, 2009)
(61·10149+11)/9 =
6(7)1489<150>
= 617 · 9733 · 2326369 · 9080937358237<13> · 23566523069347<14> · 7825711172208650238355070173<28> · 28968554729342512964467783515157310592652126016125078524302111749358574581872358573<83>
(61·10150+11)/9 =
6(7)1499<151>
= 29 · 233716475095785440613026819923371647509578544061302681992337164750957854406130268199233716475095785440613026819923371647509578544061302681992337164751<150>
(61·10151+11)/9 =
6(7)1509<152>
= 3 · 6311 · 85588793 · 1905078723901<13> · 4462269539240969<16> · 4920194397210908181861235855429933862365811431896577048259614172044467717466934173078585996093085295416572064339<112>
(61·10152+11)/9 =
6(7)1519<153>
= 7 · 503803 · 187141081 · 514484652541<12> · 8213141350468269411037<22> · 243039957906730044456550060448517146300279272179573570741376053036711457969772357550239944624517444543887<105>
(61·10153+11)/9 =
6(7)1529<154>
= 449 · 1071850645202543663<19> · 14083373942751179469741816072162036961041806687347334057352788277930869299090708635884279638980186323513461751152853338266017838816317<134>
(61·10154+11)/9 =
6(7)1539<155>
= 3 · 342211 · 73645603103078917<17> · 1489801417608295942964128487<28> · 601723397846165336228825432531805885541778532681500951298963791731019265706738939603441175573287196125897<105>
(61·10155+11)/9 =
6(7)1549<156>
= 23 · 163 · 659 · 287586298285800146257914734984871284131275628557401661706046609<63> · 953933893847574957429258954829395060019674797190928406852259555726105076178805065202941<87> (Sinkiti Sibata / Msieve 1.40 snfs / 21.05 hours / Dec 25, 2009)
(61·10156+11)/9 =
6(7)1559<157>
= 1031 · 856255798213763<15> · 661542050937201180007812167768624715936624530911929887<54> · 11605602178758045128535674160139984140449568658770410887945323629142397528821410828089<86> (Sinkiti Sibata / Msieve 1.42 snfs / 21 hours / Dec 22, 2009)
(61·10157+11)/9 =
6(7)1569<158>
= 34 · 176950121 · 122235222451519882069441<24> · 111122136683290248307436451467<30> · 348140454532406548012799873791754897004718519801836297157597144025759655461435508999534054897857<96> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=119786723 for P30 / Dec 18, 2009)
(61·10158+11)/9 =
6(7)1579<159>
= 7 · 47947 · 370424065561157043005740122638615381<36> · 5451658618654229583422200616066216555531534316702994687574391619950836910293242281617785667350933415824446950885802371<118> (Dmitry Domanov / GGNFS/msieve snfs / 26.64 hours / Dec 21, 2009)
(61·10159+11)/9 =
6(7)1589<160>
= 167 · 5153 · 127787011978227509711432050637<30> · 27682035015166481474010757311683<32> · 5486643505504392984455778494096868727<37> · 405806725364661937722524130979655905519377159864333334037<57> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=86820970 for P30 / Dec 18, 2009) (Jo Yeong Uk / GMP-ECM v6.2.3/YAFU v1.10 B1=1000000, sigma=3551862618 for P32, Msieve 1.38 for P37 x P57 / Dec 21, 2009)
(61·10160+11)/9 =
6(7)1599<161>
= 3 · 37096537 · 318602231 · 306165298424039<15> · 329941288039669879685932268781811517<36> · 18923055277115022873260438445332513123376717790659675808990381692014965745788428750512725960013<95> (Sinkiti Sibata / Msieve 1.40 snfs / 32.20 hours / Dec 22, 2009)
(61·10161+11)/9 =
6(7)1609<162>
= 19 · 1730068170162643<16> · 316028248396519459<18> · 65244604748528830440752322584056350438847024108845417403522650551534963034314207194563660746256087217754099031406101195984601993<128>
(61·10162+11)/9 =
6(7)1619<163>
= 3566273 · 462804838788405557<18> · 113990293046369827455829809216336468347<39> · 36025247970230741843823484703167564104166807793409098338045741430171486725099060883837298016220812837<101> (Sinkiti Sibata / Msieve 1.40 snfs / 51.17 hours / Dec 24, 2009)
(61·10163+11)/9 =
6(7)1629<164>
= 3 · 68531 · 1194517 · 53428043521649<14> · 229355260976131<15> · 10688166830659133<17> · 1484592475394454432301<22> · 1871588248380026241365627576216769897016787<43> · 758381797619450576082406619267293711227799391<45> (Sinkiti Sibata / Msieve 1.42 for P43 x P45 / 0.89 hours / Dec 20, 2009)
(61·10164+11)/9 =
6(7)1639<165>
= 7 · 172 · 44711 · 167411401 · 149334670797750991643<21> · 120914647031434162711029575123136458526463272062610139034489<60> · 2478862669511374046524623309725596551727978452206500258616198344907609<70> (Sinkiti Sibata / Msieve 1.40 snfs / 48.01 hours on Core i7 2.93GHz,Windows 7 64bit,and Cygwin / Dec 25, 2009)
(61·10165+11)/9 =
6(7)1649<166>
= 59 · 318756319633<12> · 2752738908947720923391736911537353829351043020914446781171<58> · 130921655593937280434022421470604766061837566769549361700021420587916908256274349687404863625667<96> (Dmitry Domanov / GGNFS/msieve snfs / 31.56 hours / Dec 21, 2009)
(61·10166+11)/9 =
6(7)1659<167>
= 32 · 43 · 47 · 1861 · 457077097048639926533<21> · 142764139093831387098492576380731<33> · 30684817049934862236835487841888609107837093149971626018403841800708999218658693557067867089469650182858837<107> (Markus Tervooren / Msieve 1.44 for P33 x P107 / Dec 28, 2009)
(61·10167+11)/9 =
6(7)1669<168>
= 6151 · 57763746961<11> · 1494794490361357<16> · 15944572173789759241324007<26> · 113794270147369588653878589256850130478318915747067<51> · 703349993642721287585740997082676211944799701617899993459389933<63> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.43 gnfs for P51 x P63 / 10.16 hours, 0.75 hours / Dec 21, 2009)
(61·10168+11)/9 =
6(7)1679<169>
= 654827 · 757001800721<12> · 330710580524033<15> · 95878663818846980597<20> · 431214913338582759962238446121038619771016504846308665730630385691152442009462841240061173537797793064594003968608837<117>
(61·10169+11)/9 =
6(7)1689<170>
= 3 · 44939 · 665221 · 1479879893<10> · 15992251210919<14> · 17093209147337<14> · 1241527496479518969376421541593971<34> · 1504737326775329431837876707667921530091717850110212903089127410272542747798721969528414183<91> (Wataru Sakai / GMP-ECM 6.2.1 B1=1000000, sigma=1130343346 for P34 / Dec 22, 2009)
(61·10170+11)/9 =
6(7)1699<171>
= 7 · 1447029833<10> · 66913200140910173893301753942067361230986726191012003411007350548104992246435182394333417586716331939921258967454471842528228923408379255852443366193816976679309<161>
(61·10171+11)/9 =
6(7)1709<172>
= 181 · 3659 · 9151461262907<13> · 69301977072056291<17> · 2356283733006025761544983487300907009263364301997553<52> · 6848298564134704811361929667540887734115283671201626733386140788297350150636060125941<85> (Sinkiti Sibata / Msieve 1.40 snfs / Apr 9, 2010)
(61·10172+11)/9 =
6(7)1719<173>
= 3 · 859 · 432511 · 4304231 · 113797127 · 3974138368996769<16> · 31239631111979261740843970235475216787963622655471207009826427538202550922649397967982560427753222470355380193571664143030152867005069<134>
(61·10173+11)/9 =
6(7)1729<174>
= 1087 · 11087 · 2109799282109300269861<22> · 7367921404106198588301290759232603149<37> · 158911917873070601700674732285479115606428865368227739<54> · 22766755324559494358929643088337361837502181978114872121<56> (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=1882517408 for P37 / Mar 1, 2010) (ruffenach timothee / Msieve 1.44 gnfs for P54 x P56 / Mar 1, 2010)
(61·10174+11)/9 =
6(7)1739<175>
= 3465859 · 55462769337400261<17> · 194087652985380197956811990904295997<36> · 413282358321178217200759952934543432163324032996082126927<57> · 439572089173596797458633485736036541862498997540378028916559<60> (Ignacio Santos / GMP-ECM 6.2.3 B1=3000000, sigma=979673009 for P36 / Jun 7, 2010) (Dmitry Domanov / Msieve 1.40 gnfs for P57 x P60 / Jun 10, 2010)
(61·10175+11)/9 =
6(7)1749<176>
= 32 · 151 · 49873272831330226473714332433979233096230888725369961573052080778350094023383206606164663559807047665767312566429564222058703294906385414111683427356716539939497996893140381<173>
(61·10176+11)/9 =
6(7)1759<177>
= 7 · 721219 · 25323181963994263163<20> · 1676981384740138826737048034493177011<37> · 1141439980357459268841031966937707421134300960351<49> · 2769634934735791989088132715019803527446730809962389708086691926841<67> (Rich Dickerson / GMP-ECM 6.3 [config GMP 5.0.2] [ECM] B1=11000000, sigma=2430288424 for P37 / Aug 21, 2011) (Warut Roonguthai / Msieve 1.48 gnfs for P49 x P67 / Aug 23, 2011)
(61·10177+11)/9 =
6(7)1769<178>
= 23 · 68351 · 20483909 · 456932594308727<15> · 460627264529157661793264405424192736825060350143773018581698097772939502816707905262900816689598301166510923604490216680847245504580573707676678455161<150>
(61·10178+11)/9 =
6(7)1779<179>
= 3 · 29 · 1187 · 5779 · 16522307 · 2829676568475942590138948809657032444287508841693183632423841841724139<70> · 2429165885853619193662244316309260460121425009342270209434351530162935206800853034298450568973<94> (matsui / Msieve 1.47 snfs / Sep 3, 2010)
(61·10179+11)/9 =
6(7)1789<180>
= 19 · 7177 · 578509 · 8591730751881721618800282967981313137584064010402098857016006400206371430083960757337606296997424348150493913277221833139828802179509965582177987916056431118369146146237<169>
(61·10180+11)/9 =
6(7)1799<181>
= 17 · 199 · 1487 · 219153877 · 29349579134651833<17> · 209470718919694656389751866351891178172797558683929430257425147051813043267748642368492150430201019569729107836577079348467329898225727543733806889239<150>
(61·10181+11)/9 =
6(7)1809<182>
= 3 · 22592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592592593<182>
(61·10182+11)/9 =
6(7)1819<183>
= 7 · 2453640648629952941<19> · 363190446580501671647<21> · [108653547754349420142056902031394272116119405302211234307408460983711129053872074001730481249008499770920692931630653116773273303608397829377911<144>] SUBMIT/RESERVE
(61·10183+11)/9 =
6(7)1829<184>
= 173 · 174912671 · 223985523781346585900769611075079185958304323863367354289244897892247971431001675386172519079891583689286674637403986203032281903917514965110385578164514757360107330088582913<174>
(61·10184+11)/9 =
6(7)1839<185>
= 33 · 2917 · 2210122826933775239<19> · 283570549895996183652577997<27> · [1373123490285079421140337590869728041256722606371942919647106480781855859122503323720529874856512586234384083969944055757349175773110607<136>] SUBMIT/RESERVE
(61·10185+11)/9 =
6(7)1849<186>
= 449 · 4241 · 93294348110671834780090636675095012293<38> · 211932646641119217655915149848691440234801<42> · 18001948543574024260951655439691780805894373278122437636957145375740930619748197779058194059900366167<101> (Dmitry Domanov / ECMNET, GMP-ECM B1=11000000, sigma=96355152 for P38 / Dec 21, 2009)
(61·10186+11)/9 =
6(7)1859<187>
= 11064356141<11> · 6593937000538782954599208778732781<34> · 92900143664152041610733982563617930749541509401481860046283875992578438137971694644621795839901683792618731990044520768286581883999169058387899<143> (Dmitry Domanov / ECMNET, GMP-ECM B1=11000000, sigma=2002082671 for P34 / Dec 21, 2009)
(61·10187+11)/9 =
6(7)1869<188>
= 3 · 43 · 3061 · 4657 · 36793 · 33202954976031389<17> · 99148948774857003287<20> · 1258589563692485861503142639027<31> · 241776379881139611252223968195255522328772774789827069691625743047250647087797588362655583834348637827529231<108> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=141765597 for P31 / Dec 19, 2009)
(61·10188+11)/9 =
6(7)1879<189>
= 72 · 13832199546485260770975056689342403628117913832199546485260770975056689342403628117913832199546485260770975056689342403628117913832199546485260770975056689342403628117913832199546485260771<188>
(61·10189+11)/9 =
6(7)1889<190>
= 131 · 20101 · 11384293539641391457483319514553211009689575658311591843638042233407115590250383161<83> · 226095688655221735585493152042682368158637747926233856958274932057159101039244430511781829552567993669<102> (Robert Backstrom / Msieve 1.42 snfs / Mar 10, 2010)
(61·10190+11)/9 =
6(7)1899<191>
= 3 · 139 · 1699 · 1246377540553231270517304854428178026702512130082057989845012070878697<70> · 76755282987069738064818275995174521908382367033378985164674128789540497512724588327483330081841463307730148032229929<116> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.42 snfs / 5.6 hours / Dec 23, 2009)
(61·10191+11)/9 =
6(7)1909<192>
= 1223 · 286547 · 1934037998683109722031755148085518185068279352013529766369360670217266838939547827857526265229198187265245060786463952382508262434647076551011229221511763509179089711655349594173783959<184>
(61·10192+11)/9 =
6(7)1919<193>
= 227 · 6863 · 242261 · 306693683 · [58554345784506121272077702036099626242943730753694803963060720780678826406944977846861423795445159258944691791044356993834047703540185673034855686699955733873739862962818033<173>] SUBMIT/RESERVE
(61·10193+11)/9 =
6(7)1929<194>
= 32 · 95713 · 6630282983<10> · 1823859185520691661<19> · 6506546200207376173757470167128490541054812945218326456404276337610895903967156329734797740670333735906058749604921639976824960772849050381030081226389715080449<160>
(61·10194+11)/9 =
6(7)1939<195>
= 7 · 97 · 2698089807299527157704813<25> · [369965434275597308021049267273344291331530222387820434590668875858363930859204035891312534876190657311717450891355014567984340043627521224838036832446828175724338231177<168>] SUBMIT/RESERVE
(61·10195+11)/9 =
6(7)1949<196>
= 3559 · 6217 · 98868560959601<14> · [3098277100858512813951037237451861267712327769735653728540310684374407588848929780185585645106843432565829852954145069332551103670109696626022046683473908572112592317285074493<175>] SUBMIT/RESERVE
(61·10196+11)/9 =
6(7)1959<197>
= 3 · 17 · 113 · 503353507745319114994474886041714166826433972216443149419123614959555772238010119<81> · 23364990379592324769436625725229708239002478431946642025096897816014994030181941389129396722784648087318500837607<113> (Robert Backstrom / Msieve 1.42 snfs / Mar 3, 2010)
(61·10197+11)/9 =
6(7)1969<198>
= 19 · 6776503 · 3254533138327<13> · 894952124696692179329<21> · [1807338867177732838408658270134667940488061383814556452391408275225346926812236178639241063339003095979042880935139477773391310942951504908540056002916012209<157>] SUBMIT/RESERVE
(61·10198+11)/9 =
6(7)1979<199>
= 317 · 859 · 3079 · 453360115411798181756595299<27> · [17831254574941664679096948388464121739002053819573203803658669511157374126746642055673379792754296385156839476917421366758563919871120534052611405660103633910609833<164>] SUBMIT/RESERVE
(61·10199+11)/9 =
6(7)1989<200>
= 3 · 23 · 587101 · 47153613391<11> · 48883754729<11> · 725848326585809869511673176621964548763493443906933125095798134138100537136960495467422719204954339204946164012691097454842994285049667928793016482149138340292081630227269<171>
(61·10200+11)/9 =
6(7)1999<201>
= 7 · 179 · 22701997 · 21080828624826489173<20> · 9761613852295366422508363<25> · 115787823646659061798940933857776518627155890628044138880006479736794600134121147689375686604700554754255034749527924716522860472209369831527450581<147>

4. References

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