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Factorizations of 800...009

Table of contents

  1. About 800...009
  2. Prime numbers of the form 800...009
  3. Factorizations of 800...009
  4. References

1. About 800...009

First ten terms

89, 809, 8009, 80009, 800009, 8000009, 80000009, 800000009, 8000000009, 80000000009

General term

8·10n+9

2. Prime numbers of the form 800...009

Last update

Mar 10, 2010

Searched up to

n≤100000

Difficulty of search

26.88%

Results

  1. 8·101+9 = 89 is prime.
  2. 8·102+9 = 809 is prime.
  3. 8·103+9 = 8009 is prime.
  4. 8·106+9 = 8000009 is prime.
  5. 8·1012+9 = 8(0)119<13> is prime.
  6. 8·1020+9 = 8(0)199<21> is prime.
  7. 8·1021+9 = 8(0)209<22> is prime.
  8. 8·1037+9 = 8(0)369<38> is prime.
  9. 8·1042+9 = 8(0)419<43> is prime.
  10. 8·1055+9 = 8(0)549<56> is prime.
  11. 8·1060+9 = 8(0)599<61> is prime.
  12. 8·1098+9 = 8(0)979<99> is prime.
  13. 8·10100+9 = 8(0)999<101> is prime. (Makoto Kamada / PPSIQS / Dec 6, 2004)
  14. 8·10104+9 = 8(0)1039<105> is prime. (searched by Makoto Kamada / Dec 6, 2004) (certified by Makoto Kamada / PFGW / Jan 5, 2005)
  15. 8·10223+9 = 8(0)2229<224> is prime. (searched by Makoto Kamada / Dec 6, 2004) (certified by Makoto Kamada / PFGW / Jan 5, 2005)
  16. 8·10237+9 = 8(0)2369<238> is prime. (searched by Makoto Kamada / Dec 6, 2004) (certified by Makoto Kamada / PFGW / Jan 5, 2005)
  17. 8·10260+9 = 8(0)2599<261> is prime. (searched by Makoto Kamada / Dec 6, 2004) (certified by Makoto Kamada / PFGW / Jan 5, 2005)
  18. 8·10501+9 = 8(0)5009<502> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Makoto Kamada / PFGW / Jan 5, 2005)
  19. 8·10570+9 = 8(0)5699<571> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Makoto Kamada / PFGW / Jan 5, 2005)
  20. 8·10600+9 = 8(0)5999<601> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Makoto Kamada / PFGW / Jan 5, 2005)
  21. 8·10698+9 = 8(0)6979<699> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Jun 1, 2006)
  22. 8·108857+9 = 8(0)88569<8858> is PRP. (Makoto Kamada / PFGW / Jan 2, 2005)
  23. 8·1020911+9 = 8(0)209109<20912> is PRP. (Dmitry Domanov / Prime95 v25.11, pfgw / Mar 8, 2010)
  24. 8·1024345+9 = 8(0)243449<24346> is PRP. (Dmitry Domanov / Prime95 v25.11, pfgw / Mar 8, 2010)
  25. 8·1031964+9 = 8(0)319639<31965> is PRP. (Dmitry Domanov / Prime95 v25.11, pfgw / Mar 8, 2010)
  26. 8·1067742+9 = 8(0)677419<67743> is PRP. (Dmitry Domanov / Prime95 v25.11, pfgw / Mar 8, 2010)

3. Factorizations of 800...009

Last update

Feb 9, 2012

Completed up to

Range

n≤200

Terms which have not been factored yet

n=191, 192, 193, 195, 196 (5/200)

Results

8·101+9 =
89
= definitely prime number
8·102+9 =
809
= definitely prime number
8·103+9 =
8009
= definitely prime number
8·104+9 =
80009
= 19 · 4211
8·105+9 =
800009
= 7 · 23 · 4969
8·106+9 =
8000009
= definitely prime number
8·107+9 =
80000009
= 29 · 181 · 15241
8·108+9 =
800000009
= 15299 · 52291
8·109+9 =
8000000009<10>
= 103 · 77669903
8·1010+9 =
80000000009<11>
= 1249 · 1571 · 40771
8·1011+9 =
800000000009<12>
= 7 · 43 · 281 · 9458389
8·1012+9 =
8000000000009<13>
= definitely prime number
8·1013+9 =
80000000000009<14>
= 4349 · 18395033341<11>
8·1014+9 =
800000000000009<15>
= 87427 · 9150491267<10>
8·1015+9 =
8000000000000009<16>
= 47 · 67 · 107 · 42683 · 556261
8·1016+9 =
80000000000000009<17>
= 17 · 971 · 36299 · 133514113
8·1017+9 =
800000000000000009<18>
= 7 · 9794467 · 11668395461<11>
8·1018+9 =
8000000000000000009<19>
= 59 · 135593220338983051<18>
8·1019+9 =
80000000000000000009<20>
= 179989 · 444471606598181<15>
8·1020+9 =
800000000000000000009<21>
= definitely prime number
8·1021+9 =
8000000000000000000009<22>
= definitely prime number
8·1022+9 =
80000000000000000000009<23>
= 19 · 4201 · 1002267630514038011<19>
8·1023+9 =
800000000000000000000009<24>
= 7 · 1141241 · 21511949 · 4655162243<10>
8·1024+9 =
8000000000000000000000009<25>
= 17681 · 7113134851<10> · 63609520339<11>
8·1025+9 =
80000000000000000000000009<26>
= 229 · 349344978165938864628821<24>
8·1026+9 =
800000000000000000000000009<27>
= 3309041 · 241761888111993777049<21>
8·1027+9 =
8000000000000000000000000009<28>
= 23 · 83 · 31012471823<11> · 135128724030187<15>
8·1028+9 =
80000000000000000000000000009<29>
= 1697 · 114713 · 410956171673262658769<21>
8·1029+9 =
800000000000000000000000000009<30>
= 7 · 1649705786423<13> · 69276422030085769<17>
8·1030+9 =
8000000000000000000000000000009<31>
= 46704648643<11> · 171289159268710698563<21>
8·1031+9 =
80000000000000000000000000000009<32>
= 139131947 · 574993750356990260475547<24>
8·1032+9 =
800000000000000000000000000000009<33>
= 17 · 43 · 9241 · 5521473833<10> · 21448583772694763<17>
8·1033+9 =
8000000000000000000000000000000009<34>
= 61 · 787 · 3375221 · 49372282483177977572947<23>
8·1034+9 =
80000000000000000000000000000000009<35>
= 64864965563<11> · 1233331418673152930661643<25>
8·1035+9 =
800000000000000000000000000000000009<36>
= 7 · 29 · 33149 · 118884029669292864417073708247<30>
8·1036+9 =
8000000000000000000000000000000000009<37>
= 23209 · 344693868757809470464044120815201<33>
8·1037+9 =
80000000000000000000000000000000000009<38>
= definitely prime number
8·1038+9 =
800000000000000000000000000000000000009<39>
= 467 · 659 · 2402177 · 1708219657<10> · 633488845598343577<18>
8·1039+9 =
8000000000000000000000000000000000000009<40>
= 281 · 1621 · 640009 · 41979101 · 653704443842705715401<21>
8·1040+9 =
80000000000000000000000000000000000000009<41>
= 19 · 1979 · 9547 · 21961 · 12350258161<11> · 821666387711990707<18>
8·1041+9 =
800000000000000000000000000000000000000009<42>
= 72 · 94907 · 536267 · 320785396043173450958826771089<30>
8·1042+9 =
8000000000000000000000000000000000000000009<43>
= definitely prime number
8·1043+9 =
80000000000000000000000000000000000000000009<44>
= 103 · 2769787 · 14999161 · 18695600658630129597481288229<29>
8·1044+9 =
800000000000000000000000000000000000000000009<45>
= 16411124027<11> · 48747422704491148015135282847862667<35>
8·1045+9 =
8000000000000000000000000000000000000000000009<46>
= 89 · 89887640449438202247191011235955056179775281<44>
8·1046+9 =
80000000000000000000000000000000000000000000009<47>
= 883 · 7883 · 26833 · 36203507 · 13373620155283<14> · 884644740743297<15>
8·1047+9 =
800000000000000000000000000000000000000000000009<48>
= 7 · 109 · 1048492791612057667103538663171690694626474443<46>
8·1048+9 =
8000000000000000000000000000000000000000000000009<49>
= 17 · 67 · 6896204160779<13> · 15826404526806353<17> · 64353754661101513<17>
8·1049+9 =
80000000000000000000000000000000000000000000000009<50>
= 23 · 347 · 3663755209<10> · 2735937847569708552076854414629531621<37>
8·1050+9 =
800000000000000000000000000000000000000000000000009<51>
= 593 · 57493690383153019<17> · 23464705494759199762755708318427<32>
8·1051+9 =
8(0)509<52>
= 1021 · 161492621449<12> · 48518968641063740609940065918345528021<38>
8·1052+9 =
8(0)519<53>
= 1291 · 42312553 · 1464517328457659216762948789723742912490883<43>
8·1053+9 =
8(0)529<54>
= 7 · 43 · 132547 · 2761585807<10> · 1632044746856723<16> · 4449005932754767674427<22>
8·1054+9 =
8(0)539<55>
= 193 · 58411 · 4901392633<10> · 144783323906052206079728815302390046451<39>
8·1055+9 =
8(0)549<56>
= definitely prime number
8·1056+9 =
8(0)559<57>
= 77801 · 22745209 · 35863735587456723491<20> · 12605478966889714222011011<26>
8·1057+9 =
8(0)569<58>
= 1307 · 7783228826728800543247<22> · 786420091835356878224229391392421<33>
8·1058+9 =
8(0)579<59>
= 19 · 113 · 163 · 18795713 · 557223887212474051819<21> · 21826384801279223060330627<26>
8·1059+9 =
8(0)589<60>
= 7 · 3047962268015449<16> · 37495777255840692530338184431492145723309063<44>
8·1060+9 =
8(0)599<61>
= definitely prime number
8·1061+9 =
8(0)609<62>
= 47 · 24623 · 64806809 · 4432020701<10> · 240673761620221523603054530469495145221<39>
8·1062+9 =
8(0)619<63>
= 257 · 3112840466926070038910505836575875486381322957198443579766537<61>
8·1063+9 =
8(0)629<64>
= 29 · 45641 · 9770143 · 39637688810676125341<20> · 15607293365345357129379978702887<32>
8·1064+9 =
8(0)639<65>
= 17 · 17099 · 626947 · 367629955083599531<18> · 1194066828105233314985958772772952139<37>
8·1065+9 =
8(0)649<66>
= 7 · 58049 · 96696537180983<14> · 20360398908127029575633689283605788478753756361<47>
8·1066+9 =
8(0)659<67>
= 643 · 460989309877618137688867995353<30> · 26989084909696898765035658837040571<35> (Makoto Kamada / msieve 0.81 / 45 seconds)
8·1067+9 =
8(0)669<68>
= 281 · 3347 · 412201 · 206356861337498973579391787560490189588781455748286982387<57>
8·1068+9 =
8(0)679<69>
= 83 · 107 · 131 · 24119681 · 27984917156969099<17> · 1018735020709277613957868020342820198201<40>
8·1069+9 =
8(0)689<70>
= 1787 · 244442761 · 274172226301<12> · 4354699959045631521349<22> · 15339335916668207656713763<26>
8·1070+9 =
8(0)699<71>
= 313 · 423796739 · 11175202735292329<17> · 86955523850308077227<20> · 620633840941868836400489<24>
8·1071+9 =
8(0)709<72>
= 7 · 23 · 29530701390613207663<20> · 168263666807397202077998630365541979672303536439463<51>
8·1072+9 =
8(0)719<73>
= 307 · 41491 · 58187068627020551565620030129<29> · 10793722059181020019089978512840633233<38>
8·1073+9 =
8(0)729<74>
= 547 · 146252285191956124314442413162705667276051188299817184643510054844606947<72>
8·1074+9 =
8(0)739<75>
= 43 · 18604651162790697674418604651162790697674418604651162790697674418604651163<74>
8·1075+9 =
8(0)749<76>
= 2243 · 58169 · 61315336444110722100217050925920213096546584591285801536343128961627<68>
8·1076+9 =
8(0)759<77>
= 19 · 59 · 2777 · 25698542603525775798847227625162342512103210486804280220763330235588177<71>
8·1077+9 =
8(0)769<78>
= 7 · 103 · 28807 · 33547 · 54157420592381<14> · 21200447559792061385992548548305073210570334277516321<53>
8·1078+9 =
8(0)779<79>
= 2569509204317024048080109659048777<34> · 3113435042987674863077695004448408426718580417<46> (Makoto Kamada / GGNFS-0.70.1 / 0.11 hours)
8·1079+9 =
8(0)789<80>
= 283 · 69109 · 4090429790150214387094857629267679617291207973965641514630930490457359647<73>
8·1080+9 =
8(0)799<81>
= 17 · 2089 · 5923 · 66263299111915502803081<23> · 57396820895286367790009433124714885887818517296611<50>
8·1081+9 =
8(0)809<82>
= 67 · 119402985074626865671641791044776119402985074626865671641791044776119402985074627<81>
8·1082+9 =
8(0)819<83>
= 97 · 9677924790041<13> · 927247573678212338051<21> · 91905246535217242008974209136125599933865211867<47>
8·1083+9 =
8(0)829<84>
= 72 · 881 · 573463594883<12> · 1268427869473822788024475947167<31> · 25476887542640341247194467235316523901<38> (Makoto Kamada / msieve 0.81 / 1.8 minutes)
8·1084+9 =
8(0)839<85>
= 15187 · 38299 · 197569 · 3530563 · 303017243 · 65072943181149412306366233080396183385247809456482234233<56>
8·1085+9 =
8(0)849<86>
= 4561 · 716063 · 1032881 · 20463535981553987931333665989<29> · 1158904670245516073488434857232218162707307<43>
8·1086+9 =
8(0)859<87>
= 3049 · 742357787 · 21510131384849<14> · 16431462919693623138045644370052527020796478510434631722634307<62>
8·1087+9 =
8(0)869<88>
= 7349809 · 1403370310478305653008290798213057061<37> · 775606873872654197928690034434567813621410341<45> (Makoto Kamada / GGNFS-0.70.3 / 0.15 hours)
8·1088+9 =
8(0)879<89>
= 57623273 · 1274643679984491297500607994656857<34> · 1089189052229670980683952642822861583468074773769<49> (Makoto Kamada / GGNFS-0.70.3 / 0.15 hours)
8·1089+9 =
8(0)889<90>
= 7 · 89 · 4241045810220763<16> · 36812927531102783<17> · 8224862018021160235769579111013613308155015002124002427<55>
8·1090+9 =
8(0)899<91>
= 14083153619<11> · 470241828452729<15> · 1208005225667448985939397598223949959591482312803746035746123701259<67>
8·1091+9 =
8(0)909<92>
= 29 · 10847 · 329341135169<12> · 772211688246570589486178169548509530972732763437683999332961141307802601347<75>
8·1092+9 =
8(0)919<93>
= 141554827 · 5651520452919630921522725607937057490805311782126652593768490847719378725248274295867<85>
8·1093+9 =
8(0)929<94>
= 23 · 61 · 1481 · 20269 · 66222307 · 87090827 · 372663492506553572550555698800861<33> · 88379464168044423546278721103437163<35> (Makoto Kamada / msieve 0.81 / 1.9 minutes)
8·1094+9 =
8(0)939<95>
= 19 · 5003539 · 2924931924148891961<19> · 287702300243348382825311232964367149316669779371535547591950703293609<69>
8·1095+9 =
8(0)949<96>
= 7 · 43 · 281 · 701 · 30951948054062593376170255876789<32> · 435924387164329767743036507138772994000848691533469803701<57> (Makoto Kamada / GGNFS-0.71.4 / 0.33 hours)
8·1096+9 =
8(0)959<97>
= 17 · 161886908888610809<18> · 304436655939137221942322295963257493673<39> · 9548439312657203748551510632950329383961<40> (Makoto Kamada / GGNFS-0.71.4 / 0.31 hours)
8·1097+9 =
8(0)969<98>
= 4201 · 19043084979766722208997857652939776243751487741014044275172577957629135920019043084979766722209<95>
8·1098+9 =
8(0)979<99>
= definitely prime number
8·1099+9 =
8(0)989<100>
= 469649 · 23865623 · 22554687854161487<17> · 909259427564533421572112683801<30> · 34803199853815840641302860940252945842441<41> (Makoto Kamada / msieve 0.83)
8·10100+9 =
8(0)999<101>
= definitely prime number
8·10101+9 =
8(0)1009<102>
= 7 · 149 · 487 · 941 · 8287 · 76346147 · 364439384627<12> · 1361074913684407<16> · 5333291197439114129508832175835592518590328200632104809<55>
8·10102+9 =
8(0)1019<103>
= 1797476095531930969<19> · 1025449864861251092819651<25> · 4340226870404998482546017714450915314158824225785096351190011<61>
8·10103+9 =
8(0)1029<104>
= 16829 · 101507309947<12> · 615774578203<12> · 76052343748605411280856605619513403568997745512065596011672356048977883354981<77>
8·10104+9 =
8(0)1039<105>
= definitely prime number
8·10105+9 =
8(0)1049<106>
= 10607 · 1593335590601<13> · 473358479210729823351520557012029207512118935876076983937545197630391879565240345481937487<90>
8·10106+9 =
8(0)1059<107>
= 7817 · 561624593 · 2080936219<10> · 30634478921<11> · 6630758324299<13> · 6261321390749812400818033<25> · 6885021419367412658060903003684364433<37>
8·10107+9 =
8(0)1069<108>
= 7 · 47 · 5987 · 300569 · 2464369 · 15629824663<11> · 5903522259789205105450881268709<31> · 5942505552902249507608316506415160671906673051809<49> (Makoto Kamada / Msieve 1.33 for P31 x P49 / 14 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Jan 16, 2008)
8·10108+9 =
8(0)1079<109>
= 444401 · 1138433 · 42414187 · 162259171523<12> · 7107371214632873<16> · 323279438555074240003686735217056819291764874161668173375266801<63>
8·10109+9 =
8(0)1089<110>
= 83 · 223 · 409 · 32885650365304248277027303729<29> · 321349248358889927171344597458044843571350263821450310799967017699489807941<75>
8·10110+9 =
8(0)1099<111>
= 8179 · 97811468394669274972490524513999266413987039980437706321066145005501895097200146717202592003912458735786771<107>
8·10111+9 =
8(0)1109<112>
= 103 · 227 · 523 · 663763 · 109467672449<12> · 341638038631061<15> · 352330846847081<15> · 1156997193104983<16> · 5660849404803835943<19> · 11420772954052473766626841<26>
8·10112+9 =
8(0)1119<113>
= 17 · 193 · 686088694115931837088239582171985283397511213262094457260962410915671123384475528073891752356285858854403403<108>
8·10113+9 =
8(0)1129<114>
= 7 · 167 · 115903 · 5904468344436599948216336502204909304155674791537394175228693159519168734700553817727010404492467880079687<106>
8·10114+9 =
8(0)1139<115>
= 67 · 1619 · 2131 · 654227059476304953156518569<27> · 59812477060225038016402609603651763<35> · 884432298709077437591050714383886146490310369<45> (Makoto Kamada / Msieve 1.33 for P35 x P45 / 15 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Jan 16, 2008)
8·10115+9 =
8(0)1149<116>
= 23 · 164754409 · 1219038421<10> · 562467957547373531345562723972322221908786381<45> · 30790016732270191561933012796406982113872329442024087<53> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 0.61 hours on Core 2 Quad Q6600 / Jan 16, 2008)
8·10116+9 =
8(0)1159<117>
= 43 · 2731 · 4019 · 52816123 · 12084972759551561<17> · 11886227219294900277209<23> · 223421829034726678059787595903408308037489589932291251953847921<63>
8·10117+9 =
8(0)1169<118>
= 570407 · 540758209 · 1090020499081<13> · 8959752026870266003989106938343<31> · 2655653222978175541447519201124671928388493948927052821291921<61> (Sinkiti Sibata / Msieve v. 1.30 for P31 x P61 / 12.6 hours on Pentium3 750MHz, Windows Me / Jan 17, 2008)
8·10118+9 =
8(0)1179<119>
= 3923 · 867599584961<12> · 33395249280707<14> · 114858715720081<15> · 32469888633351718442963<23> · 188722160020038206522232923463908019428002098207050843<54>
8·10119+9 =
8(0)1189<120>
= 7 · 29 · 14465304005221497427<20> · 30410348961140592876766942703<29> · 8958699720360463845716150863618753331482271338487833053726537641941463<70>
8·10120+9 =
8(0)1199<121>
= 4513 · 129802845572795609<18> · 1186666704803556185013425171<28> · 11508313470861399873651069777110269094750600309132327847624311334210422987<74>
8·10121+9 =
8(0)1209<122>
= 107 · 17321 · 39837349575609258121788494808572654717964321457787972441<56> · 1083534667380804556636556284146554026394969807509139591856667<61> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 2.09 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Jan 17, 2008)
8·10122+9 =
8(0)1219<123>
= 94291 · 128542241 · 66004550564547160260375655497679976030820711617686209181137104311790534903915264079379989614358981384439993939<110>
8·10123+9 =
8(0)1229<124>
= 281 · 1847789 · 87594212224781<14> · 1787112760915200910007<22> · 98424659857194915940422342879064966149733000138496990651664155068405048104815903<80>
8·10124+9 =
8(0)1239<125>
= 1579 · 418774289077175699561<21> · 120983974316377323584631711224014036378910595643970137940894681709354721752613108717289873341099175011<102>
8·10125+9 =
8(0)1249<126>
= 72 · 33469 · 107687 · 1906621 · 2979407 · 3626501 · 219890205232072592446593237163885841336188475702436959073241875155709724565132477716281147966901<96>
8·10126+9 =
8(0)1259<127>
= 401 · 389297 · 232424285281<12> · 9781973560753067<16> · 2728784228720769076664362884053977424213249851<46> · 8260139316381217641035166733618289230331842561<46> (Sinkiti Sibata / Msieve v. 1.30 for P46 x P46 / 6.74 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Jan 17, 2008)
8·10127+9 =
8(0)1269<128>
= 595961 · 134236971882388277085245511031762145509521596211832653479002820654371678683672253721300554902082518822540401133631227546769<123>
8·10128+9 =
8(0)1279<129>
= 17 · 47058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941177<128>
8·10129+9 =
8(0)1289<130>
= 34687 · 576227 · 31039762823<11> · 12894700178823504949187763524490624731935971039051006872918781881555422921723812776002504208163826677571612667<110>
8·10130+9 =
8(0)1299<131>
= 19 · 25216160984200256827<20> · 177844679544719357879627<24> · 45569197585367765957599099<26> · 20603697219057952184686365032752886363613940128976570662779041<62>
8·10131+9 =
8(0)1309<132>
= 7 · 1901 · 116259161 · 86992144223<11> · 16230203845269219667208170361<29> · 320533644260071425417953654576232041<36> · 1142628400174886692888574117774187454934002429<46> (Makoto Kamada / Msieve 1.33 for P36 x P46 / 19 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Jan 16, 2008)
8·10132+9 =
8(0)1319<133>
= 1934489 · 9941255627<10> · 415989607687626994379024208919654277878028055404905621947324703896224629797494192059360950252199449536431438674100403<117>
8·10133+9 =
8(0)1329<134>
= 89 · 683 · 48247 · 28063523 · 419570597518623739301843398921438222427110769704939738021<57> · 2316656939278359599773662465108090166954145351342952510252907<61> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 6.79 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Jan 17, 2008)
8·10134+9 =
8(0)1339<135>
= 59 · 16301584241<11> · 28571873631885209731492091721987844825451<41> · 29111825682462786935908160354061235293752365551347558913693510861695423975494302961<83> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 2.83 hours on Core 2 Quad Q6600 / Jan 17, 2008)
8·10135+9 =
8(0)1349<136>
= 14801185105213067737040565827661608911957391220799504238072333395727<68> · 540497260397233405983441758896201567297916533811770073388400426116967<69> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 3.58 hours on Cygwin on AMD 64 3200+ / Jan 19, 2008)
8·10136+9 =
8(0)1359<137>
= 42379 · 1887727412161683852851648221996743670214021095353830906817055617168880813610514641685740579060383680596521862243092097501120838150971<133>
8·10137+9 =
8(0)1369<138>
= 7 · 23 · 43 · 380503 · 1649243 · 2510141 · 32927563 · 127389389 · 431974381 · 111174418969258896469<21> · 37947353343130853705098428563822981<35> · 9596604764068692453459531281727700969<37> (Makoto Kamada / Msieve 1.33 for P35 x P37 / 3 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Jan 16, 2008)
8·10138+9 =
8(0)1379<139>
= 2546678620364651588556275988984437932502588301075923203<55> · 3141346511502304521005861647877216134965756685545711187785868781031519564330138156803<85> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 3.84 hours on Cygwin on AMD 64 X2 6000+ / Jan 17, 2008)
8·10139+9 =
8(0)1389<140>
= 163 · 3594343 · 102196891061<12> · 72184529568704507<17> · 18509771151205368273846244564703257984335172238825365225515524463829193697150899647161785603541663546563<104>
8·10140+9 =
8(0)1399<141>
= 26748433 · 953838796272576050827<21> · 31355711451501286145053779659588086442446436410960279262292590035067875289508553179273502206721185655888267145099<113>
8·10141+9 =
8(0)1409<142>
= 389 · 32563 · 4990867357422239873844609760866802279933879758965510129<55> · 126543531026932811719775808439501974442746850624376305592456058350578392937456103<81> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 6.10 hours on Core 2 Quad Q6600 / Jan 17, 2008)
8·10142+9 =
8(0)1419<143>
= 3329 · 29281922233<11> · 627552504355594804282068645958259<33> · 1795510682849862934729054445135297<34> · 728347356775380943407963675027056892979696390562810902400314219<63> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=2907880974 for P34 / Jan 16, 2008) (Jo Yeong Uk / Msieve v. 1.32 for P33 x P63 / 4.62 hours on Core 2 Quad Q6600 / Jan 18, 2008)
8·10143+9 =
8(0)1429<144>
= 7 · 383 · 341296326661470018931101663238896398460963020877249035438454385737449<69> · 874302175383230664843059392215687849285838943004522735011833597504969961<72> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 7.48 hours on Core 2 Quad Q6600 / Jan 17, 2008)
8·10144+9 =
8(0)1439<145>
= 17 · 5659 · 1783403562694297290006912071546504111216735779123<49> · 46628531887385325172139496576332321929456019180371596843235469372553694072124836083262715161<92> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 17.72 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Jan 18, 2008)
8·10145+9 =
8(0)1449<146>
= 103 · 263 · 19637441 · 66333767 · 342200413447<12> · 2824085392892504963662876213067<31> · 2345951909900622249766133589882940685013030624484792070733666366296781514821463224827<85> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=3142116591 for P31 / Jan 10, 2008)
8·10146+9 =
8(0)1459<147>
= 12823817 · 7793404954409<13> · 97339333989041<14> · 1034297732722561<16> · 269754004944570931<18> · 294743059681425655969283413607905086921958749719672881702479468320196720584811763<81>
8·10147+9 =
8(0)1469<148>
= 29 · 67 · 367 · 3001 · 446447 · 374232083 · 2261489201544452814997994627<28> · 9894177162514598079546385073110092760647751592920357286724133551767904127884385201353837797093807<97>
8·10148+9 =
8(0)1479<149>
= 19 · 23321975899<11> · 6264335206024583575242105787<28> · 28820137929138161280052635433696068751889719679695688629653783230633788507877847692016678795750468460331564747<110>
8·10149+9 =
8(0)1489<150>
= 7 · 122869 · 592463 · 20514356776409<14> · 76529783665759227547879863175857801580145592186970477872758281314038502151477085534461711269605420792053370393025114611931269<125>
8·10150+9 =
8(0)1499<151>
= 83 · 499 · 2482304185177<13> · 77813750743786303928117280787642992888695876575762740504349490131257779780805730683652263665564423971509372213489033589606739396053801<134>
8·10151+9 =
8(0)1509<152>
= 281 · 284697508896797153024911032028469750889679715302491103202846975088967971530249110320284697508896797153024911032028469750889679715302491103202846975089<150>
8·10152+9 =
8(0)1519<153>
= 179 · 10286545550776463644634627<26> · 434477611648684499985850664050081411437845728618159606645874026296642823905422801622721391632973272408528817371550125223113073<126>
8·10153+9 =
8(0)1529<154>
= 47 · 61 · 48895464172194500888865555728935598425504411122071941<53> · 57068140361452359856128021667726448531461834024720351768797284045710734038067945628429182751862647<98> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.33 / Jan 20, 2008)
8·10154+9 =
8(0)1539<155>
= 40563621115070073380669170035211<32> · 1972210512790699616561524977329804968488111698587183762968630675670612708240336060878219924495201162954628514414235940921019<124> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2632962093 for P32 / Jan 10, 2008)
8·10155+9 =
8(0)1549<156>
= 7 · 109 · 1470783867357781<16> · 10546742887006309<17> · 364319543132632908029981<24> · 21821922314714420047791463<26> · 8502032459994415884303071967448325665776936089423978775226417138915563289<73>
8·10156+9 =
8(0)1559<157>
= 10267 · 53192891 · 14648489037119868817989444797313568211533852452691343823722793688789773824519265527846042207453436769844148769259855946967147098540481226063718097<146>
8·10157+9 =
8(0)1569<158>
= 11489 · 716402649541<12> · 10593937852386983<17> · 3790480017172792738294451504361484879367<40> · 242046575091074164088712317063624793945838546238186463919115736744802008317537350438981<87> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 22.81 hours on Core 2 Quad Q6600 / Jan 19, 2008)
8·10158+9 =
8(0)1579<159>
= 43 · 133397260513579219<18> · 167167903992258454388890478299<30> · 2033479913775371639587434065835085127837961461819<49> · 410281407262533748598335324491991573466072616789247908444678817<63> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=1484630729 for P30 / Jan 17, 2008) (Robert Backstrom / GGNFS-0.77.1-20050930-k8 gnfs for P49 x P63, Msieve 1.33 / Jan 20, 2008)
8·10159+9 =
8(0)1589<160>
= 23 · 75289 · 3073981 · 912782811803<12> · 106892778448396257701<21> · 15403294683357107492284292972438681857771414432918182754479601358964133084092682488569350637536794203521767133005829<116>
8·10160+9 =
8(0)1599<161>
= 17 · 4705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058823529411764705882352941177<160>
8·10161+9 =
8(0)1609<162>
= 7 · 361469 · 2281823 · 93410043703<11> · 104070924106063664505185233829029<33> · 379610134970967214429953242481364208742167<42> · 37547251435502570973405299828344898136743364461002377728913347569<65> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=897222511 for P33 / Jan 17, 2008) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona gnfs for P42 x P65 / 10.59 hours on Core 2 Quad Q6600 / Jan 19, 2008)
8·10162+9 =
8(0)1619<163>
= 4339 · 31891930524271969<17> · 21467718354271832026587974954408013867919721<44> · 2692983165965493372324419233124120624401536996288557907855362716504013533241417008457888322335917819<100> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.33 / Jan 20, 2008)
8·10163+9 =
8(0)1629<164>
= 503 · 1087 · 399924341 · 29222738487023707<17> · 36035228405537339175432279337085862878520760605668457943<56> · 347429290363042316932943294898674175631435388823749992448700892981477531332209<78> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.34 / Apr 10, 2008)
8·10164+9 =
8(0)1639<165>
= 547 · 145375908511929289<18> · 665862476027077901987<21> · 15108650584694095421336839101744907722955551986198408204720288516498163374331216992376317984676111223948581486828821510198329<125>
8·10165+9 =
8(0)1649<166>
= 3089 · 314438682222884322729688296198134025767975025422514323112159291576842309<72> · 8236374989606056257892776904055137083699957579463131990199160763315628777145426750588217509<91> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.33 / Jan 20, 2008)
8·10166+9 =
8(0)1659<167>
= 19 · 233 · 247318002448511232349795071846013961161<39> · 73067581878550869883137762289663789192178328142338528983715149951558468070091483340423029109213779504121706037391601196627747<125> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.33 / Jan 25, 2008)
8·10167+9 =
8(0)1669<168>
= 72 · 967 · 59723 · 85525507 · 104791781467<12> · 32070636141063417698309974804038142769<38> · 983547553579979304561951273616176372155814093748174239324385537878449421978287184323475247763731622141<102> (Robert Backstrom / GMP-ECM 6.0 B1=4262000, sigma=1855270650 for P38 / Apr 16, 2008)
8·10168+9 =
8(0)1679<169>
= 13523 · 365108141391685392803<21> · 3925702274486438236222373323<28> · 412741427767146656482060605643146065993784214777445361386847613635487121913351520321871886583067352379474102886920307<117>
8·10169+9 =
8(0)1689<170>
= 2083 · 21187 · 347913094655913140947256232930961<33> · 5210272953749998271101503426402444733270293388626467088714412188109283843702487962421130258535164821785639637952029491481694049489<130> (Robert Backstrom / GMP-ECM 6.2.1 B1=792000, sigma=246426398 for P33 / Jun 20, 2008)
8·10170+9 =
8(0)1699<171>
= 113 · 452926193 · 3182006963<10> · 3558984497657<13> · 3739349584888004768232061820906349177229967138340283<52> · 369114253681640613419529242815258516418059888685901830643751071825955380199942725832817<87> (Wataru Sakai / Msieve / 70.90 hours / Jun 11, 2009)
8·10171+9 =
8(0)1709<172>
= 1609 · 47441 · 179947 · 2675683 · 717143003 · 8834088052212443456467<22> · 113402724882979773257549023<27> · 66045585799722886585090670007395970328026662921<47> · 4587394211090038825215575348339222477208606014167<49> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon gnfs for P47 x P49 / 4.94 hours on Cygwin on AMD 64 X2 6000+ / Jan 17, 2008)
8·10172+9 =
8(0)1719<173>
= 4201 · 31121 · 5041411 · 346459071611<12> · 122454245483536330061045540807347553945459<42> · 608296663654957875693373827303732266946233<42> · 4703167420425903988646488862192041281322859917358747628829697267<64> (Jo Yeong Uk / GMP-ECM 6.2.1 B1=3000000, sigma=2462122556 for P42, GGNFS-0.77.1-20050930-nocona gnfs for P42 x P64 / 7.72 hours on Core 2 Quad Q6700 / Nov 19, 2008)
8·10173+9 =
8(0)1729<174>
= 7 · 643 · 661 · 443227 · 260680181687<12> · 8189545458237210393744457523666003154315736867<46> · 4183880356288717606362756534826033091154894241628947<52> · 67921338602004285032869683860445350931844687971789469<53> (Wataru Sakai / Msieve / 100.92 hours / Oct 8, 2009)
8·10174+9 =
8(0)1739<175>
= 107 · 878011819 · 5486878492542635057<19> · 15519599315742890524424924611307277485313260541377213615503272288516557671053444128075729565367482316113010438811763463229080260479799829964497889<146>
8·10175+9 =
8(0)1749<176>
= 29 · 9907 · 828349 · 149397358667<12> · 3432767866354222343<19> · 75056191036086198203<20> · 266890443093272218468549330943<30> · 32721226544458263861906681169586495852149103259513363783751003948859549712960564477403<86> (Jo Yeong Uk / GMP-ECM 6.1.3 B1=1000000, sigma=2573028571 for P30 / Jan 16, 2008)
8·10176+9 =
8(0)1759<177>
= 17 · 3217 · 103961611179868503438377681867481435196874462689578948106251372965474787726477889<81> · 140707421063833161706485449146184930821888979205845979668829757316153913675077037413502917929<93> (matsui / GGNFS-0.77.1-20060513-pentium4 snfs / Feb 24, 2008)
8·10177+9 =
8(0)1769<178>
= 89 · 89887640449438202247191011235955056179775280898876404494382022471910112359550561797752808988764044943820224719101123595505617977528089887640449438202247191011235955056179775281<176>
8·10178+9 =
8(0)1779<179>
= 97 · 4817 · 8349953 · 643080328444181532267745772077361920255259647015699<51> · 31885435315622042511691137957740545112655694428559568324606418192336033358782251093798798406485062920172031044546403<116> (centylion torun / GMP-ECM B1=110000000, sigma=82896577 for P51 / Dec 11, 2010)
8·10179+9 =
8(0)1789<180>
= 7 · 43 · 103 · 281 · 64874204399140027<17> · 413369852432898383586010724769000432120059903<45> · 3424278682210520474518825384650397525932147218696471465227722326587804054510388061024712800327342516298551999623<112> (G.L.I.S. / GMP-ECM B1=110000000, sigma=1275872707 for P45 / Dec 11, 2010)
8·10180+9 =
8(0)1799<181>
= 67 · 86841941731033<14> · 5751212540972257<16> · 239070638384079464305466092471025322060071531552167545678913212961798899107584106689129062608889974510490101143409045500133259615588677789072157093467<150>
8·10181+9 =
8(0)1809<182>
= 23 · 3478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478260869565217391304347826086956521739130434783<181>
8·10182+9 =
8(0)1819<183>
= 181628417 · 4404597106630070998196278944610302913117389554741315616927939200174827268356360778060406703869472143227455426206792299467103762733339243935600672002773662889987088308984160777<175>
8·10183+9 =
8(0)1829<184>
= 1709 · 1235389 · 53996821 · 912256291892709420829481<24> · 2078200117056154131058483<25> · 37014490001362985704295939467561832570982470665215294205702264521205912573311818585632408541503114700987023171504597223<119>
8·10184+9 =
8(0)1839<185>
= 19 · 4502146292418701187836585771<28> · 935226454742198158831789694095815568184377471382396693364340767699219936355705178940216380025951801759748479274447141979232563950450419757911310397828855641<156>
8·10185+9 =
8(0)1849<186>
= 7 · 24329 · 53381 · 25502165263849<14> · 11958203612381011725704592874030579567<38> · 1303028394848660857467715486468010946754987<43> · 221454293090384742218717863326746087344454398748013997486958446978047338608032823703<84> (Jo Yeong Uk / GMP-ECM 6.2.1 B1=3000000, sigma=927156312 for P43 / Nov 18, 2008) (Serge Batalov / Msieve-1.38+pol51 gnfs for P38 x P84 / 70.00 hours on Opteron-2.6GHz; Linux x86_64 / Nov 28, 2008)
8·10186+9 =
8(0)1859<187>
= 50153 · 302299 · 1722241 · 11771231219249<14> · 468906861490212793165420171<27> · 55507792726914566497798504244765417670582545786727387225014401377586633446438223809853812791819939065204663497110847337090122841673<131>
8·10187+9 =
8(0)1869<188>
= 181 · 441988950276243093922651933701657458563535911602209944751381215469613259668508287292817679558011049723756906077348066298342541436464088397790055248618784530386740331491712707182320441989<186>
8·10188+9 =
8(0)1879<189>
= 443 · 280009 · 46738919942089<14> · 1186986927040459<16> · 1443968284072142039096537<25> · 80506696766249900552485161273132377878249301551978500401524539107690180714415943050142655051843089545519564016550793067276582361<128>
8·10189+9 =
8(0)1889<190>
= 2543 · 137944789 · 32904674261<11> · 6409379328215201885827901<25> · 75125429721777718514365695923<29> · 5312784824487735277961519362969<31> · 270929041462985763172625031527468593947500499762685217039308716400013884113298635281<84> (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=708702101 for P31 / Jan 15, 2008)
8·10190+9 =
8(0)1899<191>
= 10979 · 93384737 · 1829065993<10> · 33295915167128085016755403<26> · 538680813586121424240758361537710132899<39> · 6350022202664860146059913355300429133521100785097<49> · 374562434586295016714727912805051180637746786286264130259<57> (Jo Yeong Uk / GMP-ECM 6.2.1 B1=3000000, sigma=329758939 for P39, GGNFS-0.77.1-20050930-nocona gnfs for P49 x P57 / 8.41 hours, 8.41 hours on Core 2 Quad Q6700 / Dec 11, 2008)
8·10191+9 =
8(0)1909<192>
= 7 · 83 · 32815576605582649<17> · 5200740096042613643<19> · [8068051545891094511578479700823384394584768631450390852593942134609561393701118548374424516117929869950068836225453848430310390267238081742813962168542327<154>] SUBMIT/RESERVE
8·10192+9 =
8(0)1919<193>
= 17 · 59 · 255560483051<12> · 22520567661717783905291022490556943117012307<44> · [1385849343139333038164505296411820227818026836471709217118622691807166707789127712232186430757575800220188870355273314831516389469074379<136>] (yoyo@home / GMP-ECM B1=43000000, sigma=2172363567 for P44 / Feb 26, 2010) SUBMIT/RESERVE
8·10193+9 =
8(0)1929<194>
= 56569 · 65022989 · [21749263554136100543387610629817550376863625386837037939139612924587722216787820750108106569775981104166959783796781140803427641380217823609695398210457031000585586966984267770649749<182>] SUBMIT/RESERVE
8·10194+9 =
8(0)1939<195>
= 36288787236817<14> · 1733287778383420857881<22> · 4640813787596588296684196149207787<34> · 2740644562907019485541894329504307053275818363204588691032659775150280382696305597977509234141114088628824622335852067596963491<127> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=636370792 for P34 / Nov 6, 2008)
8·10195+9 =
8(0)1949<196>
= 727 · 39461 · 3393105024121<13> · [82184551070809001593097046469258474974045157610650887799287801522783019674463835505638949175776431921373326567851260576229312266996468771180522288103817253454147342122647650507<176>] SUBMIT/RESERVE
8·10196+9 =
8(0)1959<197>
= 491 · 24378181914136070883131<23> · 1608217088942848772529667<25> · [4155875309349698676972742050348235793071578516401734367543983032713103888383436309991840583688225894483651426003183699967227677779086222799374298187<148>] SUBMIT/RESERVE
8·10197+9 =
8(0)1969<198>
= 7 · 12219247 · 15213705288655807<17> · 4865154059575323971503<22> · 37114608851460783280897610347<29> · 16621692800680584305294747562998773325126469691178650296201467<62> · 204831038833285778102275560455244890057538477743970633200511049<63> (Tyler Cadigan / GGNFS gnfs, Msieve for P62 x P63 / 81.57 hours on C2Q Q660 2.4 Ghz, 4 GB RAM, Windows Vista / Jun 2, 2008)
8·10198+9 =
8(0)1979<199>
= 131 · 14779577 · 46164732442019<14> · 89504807737012816465501621504961017111653905292881275753399321462371170990355484423739181105724254078782548384128641434162117806977859235261476637210465344401589470702839661353<176>
8·10199+9 =
8(0)1989<200>
= 47 · 10029840581<11> · 34574850197219026620537581<26> · 4908375636455220759055677921494644701510929631554628307158601099794397912071382010172519640742111531902047338075363097067968113058601380373184350807396468927516327<163>
8·10200+9 =
8(0)1999<201>
= 43 · 409695657661963<15> · 22793391171990396467<20> · 1992283906237365201538932207676295118684402950955556269932521925276598386991605490564720907345426515529769955531939362161987484955156634153382402844597947890557157003<166>

4. References