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Factorizations of 688...889

Table of contents

  1. About 688...889
  2. Prime numbers of the form 688...889
  3. Factorizations of 688...889
  4. References

1. About 688...889

First ten terms

69, 689, 6889, 68889, 688889, 6888889, 68888889, 688888889, 6888888889, 68888888889

General term

(62·10n+1)/9

2. Prime numbers of the form 688...889

Last update

Apr 3, 2011

Searched up to

n≤200000

Difficulty of search

11.43%

Results

  1. (62·105+1)/9 = 688889 is prime. (Makoto Kamada / Dec 6, 2004)
  2. (62·1057+1)/9 = 6(8)569<58> is prime. (Makoto Kamada / PPSIQS / Dec 6, 2004)
  3. (62·10501+1)/9 = 6(8)5009<502> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 31, 2006)
  4. (62·10515+1)/9 = 6(8)5149<516> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 31, 2006)
  5. (62·10627+1)/9 = 6(8)6269<628> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 31, 2006)
  6. (62·10641+1)/9 = 6(8)6409<642> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 31, 2006)
  7. (62·10725+1)/9 = 6(8)7249<726> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 31, 2006)
  8. (62·1053111+1)/9 = 6(8)531109<53112> is PRP. (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / May 15, 2010)
  9. (62·1065331+1)/9 = 6(8)653309<65332> is PRP. (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / May 21, 2010)
  10. (62·10109673+1)/9 = 6(8)1096729<109674> is PRP. (Serge Batalov / srsieve, sr1sieve, Prime95 and PFGW 3.3.3 / Jun 5, 2010)

3. Factorizations of 688...889

Last update

Dec 8, 2011

Completed up to

Range

n≤200

Terms which have not been factored yet

n=180, 181, 182, 185, 186, 190, 191, 197 (8/200)

Results

(62·101+1)/9 =
69
= 3 · 23
(62·102+1)/9 =
689
= 13 · 53
(62·103+1)/9 =
6889
= 832
(62·104+1)/9 =
68889
= 3 · 22963
(62·105+1)/9 =
688889
= definitely prime number
(62·106+1)/9 =
6888889
= 7 · 984127
(62·107+1)/9 =
68888889
= 32 · 19 · 402859
(62·108+1)/9 =
688888889
= 13 · 52991453
(62·109+1)/9 =
6888888889<10>
= 2179 · 3161491
(62·1010+1)/9 =
68888888889<11>
= 3 · 14411 · 1593433
(62·1011+1)/9 =
688888888889<12>
= 17 · 167 · 11689 · 20759
(62·1012+1)/9 =
6888888888889<13>
= 72 · 5441 · 25838921
(62·1013+1)/9 =
68888888888889<14>
= 3 · 967 · 23746600789<11>
(62·1014+1)/9 =
688888888888889<15>
= 13 · 699151 · 75794003
(62·1015+1)/9 =
6888888888888889<16>
= 53 · 129979035639413<15>
(62·1016+1)/9 =
68888888888888889<17>
= 36 · 139 · 2593 · 8713 · 30091
(62·1017+1)/9 =
688888888888888889<18>
= 43 · 71 · 673 · 335279740381<12>
(62·1018+1)/9 =
6888888888888888889<19>
= 7 · 984126984126984127<18>
(62·1019+1)/9 =
68888888888888888889<20>
= 3 · 5689 · 4036379497796267<16>
(62·1020+1)/9 =
688888888888888888889<21>
= 13 · 29 · 557 · 8527 · 89603 · 4293721
(62·1021+1)/9 =
6888888888888888888889<22>
= 419 · 2843 · 4409 · 517609 · 2534057
(62·1022+1)/9 =
68888888888888888888889<23>
= 3 · 277 · 57881 · 1432227903107999<16>
(62·1023+1)/9 =
688888888888888888888889<24>
= 23 · 98929 · 5899991 · 51315241337<11>
(62·1024+1)/9 =
6888888888888888888888889<25>
= 7 · 523 · 1471 · 6983 · 25343 · 7228309051<10>
(62·1025+1)/9 =
68888888888888888888888889<26>
= 32 · 19 · 4057 · 99299728703531530787<20>
(62·1026+1)/9 =
688888888888888888888888889<27>
= 13 · 52991452991452991452991453<26>
(62·1027+1)/9 =
6888888888888888888888888889<28>
= 17 · 52503306941<11> · 7718156851059037<16>
(62·1028+1)/9 =
68888888888888888888888888889<29>
= 3 · 53 · 1223 · 354262839028108470710177<24>
(62·1029+1)/9 =
688888888888888888888888888889<30>
= 191 · 521 · 8389 · 1505683 · 548067876850577<15>
(62·1030+1)/9 =
6888888888888888888888888888889<31>
= 7 · 61 · 197 · 1039 · 78820562762825180127329<23>
(62·1031+1)/9 =
68888888888888888888888888888889<32>
= 3 · 7680522307<10> · 2989765805645092954609<22>
(62·1032+1)/9 =
688888888888888888888888888888889<33>
= 13 · 97 · 546303639087144241783417041149<30>
(62·1033+1)/9 =
6888888888888888888888888888888889<34>
= 38259209 · 180058319786195498419449521<27>
(62·1034+1)/9 =
68888888888888888888888888888888889<35>
= 32 · 47 · 120319 · 1353550921752568214965840097<28>
(62·1035+1)/9 =
688888888888888888888888888888888889<36>
= 863 · 1699 · 469834609881546359073525554797<30>
(62·1036+1)/9 =
6888888888888888888888888888888888889<37>
= 7 · 263899 · 308303 · 225861137 · 53554273809522643<17>
(62·1037+1)/9 =
68888888888888888888888888888888888889<38>
= 3 · 89189 · 257464070266097421912600914495767<33>
(62·1038+1)/9 =
688888888888888888888888888888888888889<39>
= 13 · 43 · 2130981749747677<16> · 578305924975742049923<21>
(62·1039+1)/9 =
6888888888888888888888888888888888888889<40>
= 639811247 · 1928413213<10> · 5583380319939417490499<22>
(62·1040+1)/9 =
68888888888888888888888888888888888888889<41>
= 3 · 787 · 13259 · 33461 · 2503252457<10> · 26272346017815392543<20>
(62·1041+1)/9 =
688888888888888888888888888888888888888889<42>
= 53 · 17881 · 10936703390411<14> · 66465315912868313843543<23>
(62·1042+1)/9 =
6888888888888888888888888888888888888888889<43>
= 7 · 1033 · 68674451 · 13872528390188464832295969889469<32>
(62·1043+1)/9 =
68888888888888888888888888888888888888888889<44>
= 33 · 17 · 19 · 7899196065690733733389392144122106282409<40>
(62·1044+1)/9 =
688888888888888888888888888888888888888888889<45>
= 13 · 83 · 20611 · 3055777 · 917445382993<12> · 11049097219357931221<20>
(62·1045+1)/9 =
6888888888888888888888888888888888888888888889<46>
= 23 · 131 · 98893 · 2500163 · 2053871880397<13> · 4502387021375414111<19>
(62·1046+1)/9 =
68888888888888888888888888888888888888888888889<47>
= 3 · 2411 · 9524248429267093721676882191191606372029433<43>
(62·1047+1)/9 =
688888888888888888888888888888888888888888888889<48>
= 421 · 15161 · 3891749 · 789918873979<12> · 35108471578998729810539<23>
(62·1048+1)/9 =
6888888888888888888888888888888888888888888888889<49>
= 7 · 29 · 769 · 518113 · 5812397 · 14653691461177189794786706614007<32>
(62·1049+1)/9 =
68888888888888888888888888888888888888888888888889<50>
= 3 · 3669073 · 6258518967314894787583393124901838410672931<43>
(62·1050+1)/9 =
688888888888888888888888888888888888888888888888889<51>
= 13 · 1245175641943361<16> · 6776860807884967<16> · 6279812047929467419<19>
(62·1051+1)/9 =
6(8)509<52>
= 114974082255943769<18> · 59916885212038792020790531598944481<35>
(62·1052+1)/9 =
6(8)519<53>
= 32 · 71 · 12377 · 187423 · 409301441 · 113544675155368804234547016584641<33>
(62·1053+1)/9 =
6(8)529<54>
= 149 · 593796253 · 7786198276448866758750340763735200026021337<43>
(62·1054+1)/9 =
6(8)539<55>
= 72 · 53 · 499 · 28564787 · 186099709334719829299872294169982045263549<42>
(62·1055+1)/9 =
6(8)549<56>
= 3 · 59 · 424593779745854598497831<24> · 916647347771038295842616954447<30>
(62·1056+1)/9 =
6(8)559<57>
= 13 · 72869512669<11> · 727210201503056129255358571903406006748238337<45>
(62·1057+1)/9 =
6(8)569<58>
= definitely prime number
(62·1058+1)/9 =
6(8)579<59>
= 3 · 1199909 · 45402691 · 421500428485076883758839988255302167043405277<45>
(62·1059+1)/9 =
6(8)589<60>
= 17 · 43 · 204289199 · 7163532713<10> · 8920673878808299<16> · 72187414345750187168263<23>
(62·1060+1)/9 =
6(8)599<61>
= 7 · 5715547 · 172184216860955587800105044036377292844259173116236141<54>
(62·1061+1)/9 =
6(8)609<62>
= 32 · 19 · 11877587 · 9085025783561930356771<22> · 3733349815450127768821931173667<31>
(62·1062+1)/9 =
6(8)619<63>
= 13 · 139 · 1777 · 66749 · 7942933756343<13> · 308273431392977<15> · 1312628407334020434561109<25>
(62·1063+1)/9 =
6(8)629<64>
= 99523 · 1163273 · 59503713937593457981533953288199778961006593800820091<53>
(62·1064+1)/9 =
6(8)639<65>
= 3 · 8221 · 284518374088747<15> · 14412429204535701016429<23> · 681170406775645062371681<24>
(62·1065+1)/9 =
6(8)649<66>
= 1747 · 2389 · 50549 · 58321 · 1640189 · 1354888837308576001<19> · 25194458884378167570005543<26>
(62·1066+1)/9 =
6(8)659<67>
= 7 · 7817 · 108136394929<12> · 1164230952084291601691793206724532673859338709750839<52>
(62·1067+1)/9 =
6(8)669<68>
= 3 · 23 · 53 · 883 · 1297 · 4261 · 40577 · 95133192445517844848649005358017818351707623841791<50>
(62·1068+1)/9 =
6(8)679<69>
= 132 · 102499 · 170167 · 43839551794960317914159<23> · 5330910598457774699015103174182323<34>
(62·1069+1)/9 =
6(8)689<70>
= 5347 · 1288365230762836897117802298277331005963884213369906281819504187187<67>
(62·1070+1)/9 =
6(8)699<71>
= 33 · 6290419648531<13> · 405607331748358659381828767685371641134930948003125232697<57>
(62·1071+1)/9 =
6(8)709<72>
= 248051 · 2777206658666519743475692050783463436506560702794541803455293019939<67>
(62·1072+1)/9 =
6(8)719<73>
= 7 · 311 · 593 · 11654899 · 273215447 · 18647534693<11> · 84867100453<11> · 1058915987475025442276480681677<31>
(62·1073+1)/9 =
6(8)729<74>
= 3 · 44203960925123143680964174885210781<35> · 519477496640172242479843730463109415023<39> (Makoto Kamada / GGNFS-0.70.1 / 0.08 hours)
(62·1074+1)/9 =
6(8)739<75>
= 13 · 10439321 · 5076139817087049191512690623408648077110709881557717350869031902693<67>
(62·1075+1)/9 =
6(8)749<76>
= 17 · 2609 · 13562129370750386547901588512581<32> · 11452447161452842771331343032666304564773<41> (Makoto Kamada / GGNFS-0.70.1 / 0.07 hours)
(62·1076+1)/9 =
6(8)759<77>
= 3 · 29 · 2613547 · 2065382029<10> · 256017624151<12> · 64857448126846759<17> · 8834246214224669967433851840641<31>
(62·1077+1)/9 =
6(8)769<78>
= 188299 · 24403603984061<14> · 53388315035353<14> · 7097279235659767007911<22> · 395648105694003788094697<24>
(62·1078+1)/9 =
6(8)779<79>
= 7 · 72452489 · 13583066609719703721760711134809794139496394445841386166652286909383943<71>
(62·1079+1)/9 =
6(8)789<80>
= 32 · 19 · 5964669947<10> · 10006621146257<14> · 6749618010498230052967496899926213732189587558665621121<55>
(62·1080+1)/9 =
6(8)799<81>
= 13 · 43 · 47 · 53 · 12293259168297089<17> · 4814813453546980346278517123<28> · 8358284347652808525963876865223<31>
(62·1081+1)/9 =
6(8)809<82>
= 521 · 2027 · 51581 · 130729 · 53567383 · 1383653872258533080197129763<28> · 13051731138575078139808249070827<32>
(62·1082+1)/9 =
6(8)819<83>
= 3 · 9721 · 44236789 · 25372505497<11> · 2104602255406609555050677076965532954115219520723216710759991<61>
(62·1083+1)/9 =
6(8)829<84>
= 3089 · 309595277 · 720339027210952876802374942790406321417021802118196514380915048384476813<72>
(62·1084+1)/9 =
6(8)839<85>
= 7 · 4657 · 75244472813<11> · 13656442344656419733<20> · 394175886506997379181<21> · 521726227853295198741045094139<30>
(62·1085+1)/9 =
6(8)849<86>
= 3 · 83 · 1289 · 29077 · 3548227843<10> · 1823623259848156324629427<25> · 1140776843198028041018364914357491503010717<43>
(62·1086+1)/9 =
6(8)859<87>
= 13 · 113 · 8443 · 141959 · 8058811517<10> · 48550830715445873748101084434337766889389882269136192949535626789<65>
(62·1087+1)/9 =
6(8)869<88>
= 71 · 479 · 17195530291<11> · 11779849567434633678012744260502682593562068530167588389146860386304002331<74>
(62·1088+1)/9 =
6(8)879<89>
= 32 · 480463 · 29278692607<11> · 51687237389080453<17> · 10044163843913878933<20> · 1048088445087647982690988704575079769<37>
(62·1089+1)/9 =
6(8)889<90>
= 23 · 90163 · 3073240061<10> · 108092734759176483441255394935185723498740604205062139907032966502617911801<75>
(62·1090+1)/9 =
6(8)899<91>
= 7 · 61 · 5691137 · 2138822053<10> · 1325401968750612014842518608094745019000497431134634761004836959986371087<73>
(62·1091+1)/9 =
6(8)909<92>
= 3 · 17 · 277 · 4876399015282005301117639193663827344014220208741338492878097889777651935222544693770007<88>
(62·1092+1)/9 =
6(8)919<93>
= 13 · 68557517387<11> · 24371124339250756783<20> · 945684718731376246915793<24> · 33537355039205999650679910148392490601<38>
(62·1093+1)/9 =
6(8)929<94>
= 53 · 9832412509<10> · 147140627507974843<18> · 1540393625323266367219971859<28> · 58324215140546834961579538198286695961<38>
(62·1094+1)/9 =
6(8)939<95>
= 3 · 108379 · 11594567 · 783309510283733<15> · 2443133391616379677321<22> · 9548775271241801118135295892944526047919870587<46>
(62·1095+1)/9 =
6(8)949<96>
= 263 · 6133 · 57503 · 104303475607<12> · 1289783852141116807757327<25> · 55209555213943750837224859048991481738482338487173<50>
(62·1096+1)/9 =
6(8)959<97>
= 72 · 225164847423539<15> · 647842073864492492492810856555647<33> · 963792096584974466388656581993015177003501583917<48> (Makoto Kamada / GGNFS-0.71.1 / 0.28 hours)
(62·1097+1)/9 =
6(8)969<98>
= 34 · 19 · 11677 · 60337 · 153509456999469660188672869<27> · 725744150799699600132433097<27> · 570265222860987767825369717545243<33>
(62·1098+1)/9 =
6(8)979<99>
= 13 · 486907 · 7240799 · 2340345902680952203330623833<28> · 6422339606060821951922186396730061399032889587059823233537<58>
(62·1099+1)/9 =
6(8)989<100>
= 337 · 20441806791955159907682162875041213320145070886910649521925486317177711836465545664358720738542697<98>
(62·10100+1)/9 =
6(8)999<101>
= 3 · 10399107123321098233<20> · 2208166786883663157118660556242926557938734114380760506430498174910660054529512811<82>
(62·10101+1)/9 =
6(8)1009<102>
= 43 · 794923 · 22298899069<11> · 521414373128318801070969157<27> · 1733361879406850829640718045984603028969013088436358102097<58>
(62·10102+1)/9 =
6(8)1019<103>
= 7 · 126307 · 208654741 · 400156717 · 3093275436869<13> · 152720239844761591<18> · 2105829240635400821<19> · 93805220659517407554990943863307<32>
(62·10103+1)/9 =
6(8)1029<104>
= 3 · 109 · 210669384981311586816173972137274889568467550118926265715256540944614339109751953788651036357458375807<102>
(62·10104+1)/9 =
6(8)1039<105>
= 13 · 29 · 229 · 38244373169<11> · 139607668881823642420652311961<30> · 1494498642480030417679315385059712646147073901718284772400837<61> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2548317768 for P30 / Oct 19, 2009)
(62·10105+1)/9 =
6(8)1049<106>
= 2377 · 10037387 · 3145444153<10> · 9237199316962640481719<22> · 9937497576468544999293386043573912503214162458588803212293674573<64>
(62·10106+1)/9 =
6(8)1059<107>
= 32 · 53 · 9187 · 15720164440019471705618318312082333296340236691416544271241193950546036108558486022403110604718975311<101>
(62·10107+1)/9 =
6(8)1069<108>
= 17 · 2011398162679<13> · 113745703825053221<18> · 177119838385459031677538125003545212751586915051072292099117905677489024518963<78>
(62·10108+1)/9 =
6(8)1079<109>
= 7 · 139 · 359 · 571261 · 786719 · 2979701 · 88487325486117617422437582413031689<35> · 166430884397911127150765051393953307715521219894077<51> (Erik Branger / YAFU, Msieve 1.38 for P35 x P51 / Oct 22, 2009)
(62·10109+1)/9 =
6(8)1089<110>
= 3 · 88359769 · 321656962118179<15> · 3255012946193881919<19> · 6053539948885294234840535779447<31> · 41003248435304780435015393009752973041<38> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3071172844 for P31 / Oct 19, 2009)
(62·10110+1)/9 =
6(8)1099<111>
= 13 · 181 · 21559 · 2174310109<10> · 63432888137017016044348166423759881<35> · 98460643496494633707032806939239407637455939456098771653683<59> (Erik Branger / GGNFS, Msieve snfs / 1.02 hours / Oct 22, 2009)
(62·10111+1)/9 =
6(8)1109<112>
= 23 · 4639 · 315057233 · 3077974809623148102960387293801097224185933679<46> · 66579795337873101825458429741248933989066545646212591<53> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.42 snfs / 0.57 hours, 0.02 hours / Oct 22, 2009)
(62·10112+1)/9 =
6(8)1119<113>
= 3 · 886283 · 424474417621500274841350325647806085712007847<45> · 61038518645710499741252246219722199134494898635738764960652863<62> (Erik Branger / GGNFS, Msieve snfs / 0.89 hours / Oct 22, 2009)
(62·10113+1)/9 =
6(8)1129<114>
= 59 · 5568859 · 64608067 · 307759447 · 988598368841<12> · 2164455170504407347901<22> · 869855747552322801388305721<27> · 56652239651942988193519461521<29>
(62·10114+1)/9 =
6(8)1139<115>
= 7 · 221346679 · 2747140819<10> · 1618442251239215176321169765044624862842585487452750491900336374410865424387068148000972693111427<97>
(62·10115+1)/9 =
6(8)1149<116>
= 32 · 19 · 4263603869989940029<19> · 94487905451492604539631341703095550490501649534901773783367983171085887628647970858109029195271<95>
(62·10116+1)/9 =
6(8)1159<117>
= 13 · 52991452991452991452991452991452991452991452991452991452991452991452991452991452991452991452991452991452991452991453<116>
(62·10117+1)/9 =
6(8)1169<118>
= 40464497 · 45130259711000452950944547303930885114601<41> · 3772308490515012510449614847679149216069295945683508079802035124362337<70> (Erik Branger / GGNFS, Msieve snfs / 1.96 hours / Oct 22, 2009)
(62·10118+1)/9 =
6(8)1179<119>
= 3 · 179 · 128284709290295882474653424374094765156217670184150631078005379681357334988619904821022139457893647837781915994206497<117>
(62·10119+1)/9 =
6(8)1189<120>
= 53 · 81639827347528296394011236911324937968186783394226152874541<59> · 159210326457590438894678389977581407772306683697429931033193<60> (Serge Batalov / Msieve 1.44 snfs / 0.77 hours / Oct 23, 2009)
(62·10120+1)/9 =
6(8)1199<121>
= 7 · 1520128541<10> · 230482446188707<15> · 24674280757669201<17> · 5408366139107340547253<22> · 43704165670885458627270709<26> · 481614497298797956613036738145073<33>
(62·10121+1)/9 =
6(8)1209<122>
= 3 · 91572199 · 164024522923<12> · 196938095405058523<18> · 35168395587744027943<20> · 220736020804699605701533904538393822824303411988043793634311608171<66>
(62·10122+1)/9 =
6(8)1219<123>
= 13 · 43 · 71 · 12852950743<11> · 298297116435961716457125618861217437142706371<45> · 4527173357582149631512924797923598004872719944155101719816241917<64> (Dmitry Domanov / GGNFS/msieve snfs / 1.11 hours / Oct 23, 2009)
(62·10123+1)/9 =
6(8)1229<124>
= 17 · 797 · 9853043 · 138595979 · 158482889 · 76444739699<11> · 140344436011805338070535887144534289733<39> · 218975609300055754225391098819657487228955178651<48> (Sinkiti Sibata / Msieve 1.42 for P39 x P48 / 0.64 hours / Oct 22, 2009)
(62·10124+1)/9 =
6(8)1239<125>
= 33 · 191 · 13358326330984853381595673625923771357162863852799862107599164027319931915627087238489216383340874324004050589274556697477<122>
(62·10125+1)/9 =
6(8)1249<126>
= 321313 · 1505022925791217057<19> · 62028237283581396428045821<26> · 5493493946692694352198298538123<31> · 4180610217385291406336119989356729610182804263<46> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3681457563 for P31 / Oct 19, 2009)
(62·10126+1)/9 =
6(8)1259<127>
= 7 · 47 · 83 · 1541963399<10> · 660931435820087<15> · 24438968728948515381731252918147334447671<41> · 10128889662287420283252120128975774558249253186011221512749<59> (Sinkiti Sibata / GGNFS-0.77.1-20050930-pentium4 snfs / 4.21 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Oct 29, 2009)
(62·10127+1)/9 =
6(8)1269<128>
= 3 · 17891 · 4844804631723757<16> · 27800134277149853<17> · 674359408887951554012507<24> · 14131189685330691405394812326678489380392983787551231073736394591419<68>
(62·10128+1)/9 =
6(8)1279<129>
= 13 · 97 · 197 · 1571 · 221839062921055719484107373612660853699302142746356139<54> · 7957078823320286782689262399302302972074139970168996053248181231993<67> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.43 snfs / 1.84 hours, 0.13 hours / Oct 29, 2009)
(62·10129+1)/9 =
6(8)1289<130>
= 233081622689<12> · 19764208627430219<17> · 5370357403518944491<19> · 278457248897235614613011852681120886534870266139194795069899210088061280309737048769<84>
(62·10130+1)/9 =
6(8)1299<131>
= 3 · 1021 · 4517 · 97829 · 172646517491005006256239973571080363<36> · 294799441210256853477729159395431700808480725079520017412819392555476174232512350517<84> (Sinkiti Sibata / Msieve 1.42 snfs / 1 hour 17 min, 0.11 hours / Oct 29, 2009)
(62·10131+1)/9 =
6(8)1309<132>
= 599 · 2588270609<10> · 3211874737<10> · 6371971009<10> · 50689315607939<14> · 372424554632699<15> · 1150073381041910242784515200836687330384007738097251570257564292314268383<73>
(62·10132+1)/9 =
6(8)1319<133>
= 7 · 29 · 53 · 467527552724707428829431341<27> · 1369525308671422068186030112317004583080693882949677712554639225014790222503753653177677959052215413531<103>
(62·10133+1)/9 =
6(8)1329<134>
= 32 · 192 · 23 · 521 · 13903 · 1920271 · 203516197045434218419<21> · 325659599688318185005347374634219565874756198740615971131502478117151397677641846574905657420061<96>
(62·10134+1)/9 =
6(8)1339<135>
= 13 · 52991452991452991452991452991452991452991452991452991452991452991452991452991452991452991452991452991452991452991452991452991452991453<134>
(62·10135+1)/9 =
6(8)1349<136>
= 277213 · 115204781 · 2088359971517143<16> · 103290344105197014113671483575138229359748242061096187664452948852666987834697786088327637591580311220726791<108>
(62·10136+1)/9 =
6(8)1359<137>
= 3 · 3371 · 1014970768241<13> · 77426502504949242515724093217<29> · 86681415857318770436422722340003219274859669482496823776897806280141335067727737427389633449<92>
(62·10137+1)/9 =
6(8)1369<138>
= 691 · 16724552400041<14> · 863429022865229<15> · 10646286546452465309<20> · 6484729058154525456285413801199338765366657004870082297198717713573004352799850640872579<88>
(62·10138+1)/9 =
6(8)1379<139>
= 72 · 2777 · 14838630112248264447941<23> · 3411798792251944441458942947320335495936808460622007046143663562888090249873159413763774770655315745825598658173<112>
(62·10139+1)/9 =
6(8)1389<140>
= 3 · 17 · 45022889 · 484214506163729990618092275284042969<36> · 61959492079224298660493435009803532533981674214668390763156707898945653153181452537824772870179<95> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 4.64 hours / Oct 30, 2009)
(62·10140+1)/9 =
6(8)1399<141>
= 13 · 12015911326813<14> · 10098947505940741188253378705758426820362239035432097<53> · 436689750002543719167336765795082713550194093289913311609891257071910504673<75> (Erik Branger / GGNFS, Msieve snfs / 5.09 hours / Oct 29, 2009)
(62·10141+1)/9 =
6(8)1409<142>
= 568661993488414430953673552639897<33> · 107136670558984692997845953645695662813997409001629<51> · 113072457467357463380646477639339817944564509365675623543253<60> (Dmitry Domanov / GGNFS/msieve snfs / 6.00 hours / Nov 1, 2009)
(62·10142+1)/9 =
6(8)1419<143>
= 32 · 114727531 · 3575800165071310752931<22> · 53527759688163829497674421563<29> · 348567359058999619931597659950935233388714981082615696133237086287734048862496093347<84>
(62·10143+1)/9 =
6(8)1429<144>
= 43 · 99581 · 138917 · 11273287 · 281762389 · 2919397037<10> · 5280147761759531<16> · 121282972867437013<18> · 1183524895479531318516657280516253<34> · 164777834200755466127443978877428258379671<42> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3962379111 for P34 / Oct 27, 2009)
(62·10144+1)/9 =
6(8)1439<145>
= 7 · 6947 · 4257496835970046328258574077329808655160261495634343872354609<61> · 33273578231402606240782600493794607850183398235273622964448002794566112533642949<80> (Dmitry Domanov / GGNFS/msieve snfs / 6.07 hours / Nov 1, 2009)
(62·10145+1)/9 =
6(8)1449<146>
= 3 · 53 · 3037 · 6329 · 20233 · 24151 · 289021 · 912403 · 5929006956554283372161105073815933362297298798067922111<55> · 29503850915816027505202414387618333019676491925964734615718733<62> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 4.05 hours on Core 2 Quad Q6700 / Nov 3, 2009)
(62·10146+1)/9 =
6(8)1459<147>
= 132 · 6211201993<10> · 37581034560382870644756808555485568620305131<44> · 17462969313698974114395124223099743671734245518631937018327064999870014820154330993298790107<92> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 5.79 hours on Core 2 Quad Q6700 / Nov 4, 2009)
(62·10147+1)/9 =
6(8)1469<148>
= 14609058570850068072790171345251209857<38> · 54119127478220719186968454440445122879267586001<47> · 8713169520734770932259156884452356918743245463266750664655868777<64> (Dmitry Domanov / GGNFS/msieve snfs / 14.47 hours / Oct 30, 2009)
(62·10148+1)/9 =
6(8)1479<149>
= 3 · 968893963 · 1010325931287078378105743<25> · 26271799596027579924616943<26> · 1154296887283017820556565817700236598461<40> · 773540093204736296456243349622971513303636130557709<51> (Sinkiti Sibata / Msieve 1.42 for P40 x P51 / 1.1 hours / Oct 30, 2009)
(62·10149+1)/9 =
6(8)1489<150>
= 20483 · 1451521 · 2159958576333471630827291022074668095705599543<46> · 10727212141443721091591595069382603712040863221467467516173427204992746524141860104161935808261<95> (Dmitry Domanov / GGNFS/msieve snfs / 11.72 hours / Nov 4, 2009)
(62·10150+1)/9 =
6(8)1499<151>
= 7 · 61 · 335899951 · 631812782018320361<18> · 12191688122843586596710384365301<32> · 6235325251854743704987134113434328800026549545253723826064948248579721224281529557691548137<91> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=5303952899 for P32 / Nov 3, 2009)
(62·10151+1)/9 =
6(8)1509<152>
= 33 · 19 · 8209 · 6997873 · 602312530483<12> · 385804537726962521<18> · 5493701927661664353508380996233<31> · 1831138445587014365066380042150258971520737748665221421217743758160394976207491<79> (Serge Batalov / GMP-ECM B1=2000000, sigma=932480872 for P31 / Dec 31, 2009)
(62·10152+1)/9 =
6(8)1519<153>
= 13 · 170389 · 17112287 · 61904591240871231337602021900587<32> · 2047286436358399332746767528784913403<37> · 143401848245111395152462431599114639891263907588462914138515107713364511<72> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=108486840 for P32 / Dec 27, 2009) (Sinkiti Sibata / Msieve 1.42 gnfs for P37 x P72 / 9 hours / Jan 1, 2010)
(62·10153+1)/9 =
6(8)1529<154>
= 1753 · 32684360309<11> · 57313000691<11> · 141538472279167<15> · 1590493408689164431945838016669293<34> · 18005674193602941951875933406071629901<38> · 517557209533412051293341030536534190408042217<45> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2225071728 for P34 / Dec 27, 2009) (Lionel Debroux / msieve 1.44 SVN for P38 x P45 / 0.41 hours on Core 2 Duo T7200, 2 GB RAM / Dec 31, 2009)
(62·10154+1)/9 =
6(8)1539<155>
= 3 · 139 · 37936115637691489223436383<26> · 4354720287474058280946883255618085620204303167233828045457246437603310089190259962104798376091326426030033350341984625758094599<127>
(62·10155+1)/9 =
6(8)1549<156>
= 172 · 23 · 433 · 307751512093900182523103591179516105887904485683<48> · 777741743749371700205770435793158260169789376483035661599247350889095620550394856646401246531737334533<102> (Dmitry Domanov / GGNFS/msieve snfs / 18.09 hours / Jan 1, 2010)
(62·10156+1)/9 =
6(8)1559<157>
= 7 · 347 · 9699161 · 40974536749<11> · 7136305681408538334160672270641270769017006451761389856205581367445514507027666374784734677010890308448142939820780137025132161975932969<136>
(62·10157+1)/9 =
6(8)1569<158>
= 3 · 71 · 2711 · 1161739689442675091020903<25> · 102690727902958995563124478016140964888563257175380873839387631011049167743447454146217171210116669438999994776655523371206712341<129>
(62·10158+1)/9 =
6(8)1579<159>
= 13 · 53 · 233 · 3126199 · 7801756927813<13> · 3591192411773887177750066177591277<34> · 48992130663808788824021380783744673823751813871645838891644996896011597575479103140844753977049090503<101> (Serge Batalov / GMP-ECM B1=2000000, sigma=2890323597 for P34 / Dec 31, 2009)
(62·10159+1)/9 =
6(8)1589<160>
= 587 · 154684043 · 18710416164771881999377883947<29> · 3319788860369352872404102738800668772432910172315087<52> · 1221438636218331585834875340346720758794325326050050023941628269694861<70> (Sinkiti Sibata / Msieve 1.40 snfs / 36.50 hours / Jan 2, 2010)
(62·10160+1)/9 =
6(8)1599<161>
= 32 · 29 · 277 · 62301097 · 16556159061948455796618403686337<32> · 49863314046997116438075933006463<32> · 18526461581725696646250632430189163201851631153233661011208358341151186188524227730391<86> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2825776746 for P32(4986...) / Dec 27, 2009) (Sinkiti Sibata / Msieve 1.42 snfs / 1.03 hours / Jan 2, 2010)
(62·10161+1)/9 =
6(8)1609<162>
= 5869 · 7096942015658167<16> · 229277065428152667545393143151558398679295264580138699<54> · 72136189770841945401903354365295300858708682566494112260440581982604466005105846653154657<89> (Sinkiti Sibata / Msieve 1.42 snfs / 24 hours / Jan 3, 2010)
(62·10162+1)/9 =
6(8)1619<163>
= 7 · 1069 · 2512409 · 4574932102448503776738276586531<31> · 80093715606321353511254833907906321101627948022995314816785837005521295579182426767932811900706911611508850538489919996177<122> (Serge Batalov / GMP-ECM B1=3000000, sigma=258849838 for P31 / Dec 31, 2009)
(62·10163+1)/9 =
6(8)1629<164>
= 3 · 1468007911603<13> · 162472477444654241<18> · 96276374230400885885182531034195486354127956785612315383939639974866586760747039227242561373698359338295514296378842095649774561815681<134>
(62·10164+1)/9 =
6(8)1639<165>
= 13 · 43 · 193 · 844900827765026587<18> · 2696285677671288548611387213<28> · 2802905287043159341788711013948568251724706661354238768576567129696000031071383341425552388540974373558194899838537<115>
(62·10165+1)/9 =
6(8)1649<166>
= 757412903047<12> · 521483570100224510383352162072882440892494875084805613<54> · 17441179455317004161955466957426397054551514294451788913467649233897745421755225210506617140729284699<101> (Dmitry Domanov / GGNFS/msieve snfs / 30.42 hours / Jan 1, 2010)
(62·10166+1)/9 =
6(8)1659<167>
= 3 · 24781 · 85213357 · 67193814930516706987933988837<29> · 161834877717331928617574569181743331586512186067094126233241172797345120186897744758474935900131070727674383980562569115350047<126>
(62·10167+1)/9 =
6(8)1669<168>
= 83 · 541 · 66307387 · 29717167063<11> · 30308264898066505497321836782433<32> · 256887769913150024201321311600349830234761549203321768639263596611961882059969351105361960829823504911592936350331<114> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2227692396 for P32 / Dec 28, 2009)
(62·10168+1)/9 =
6(8)1679<169>
= 7 · 34359289 · 6852669169<10> · 1047030289873<13> · 1515116683634143<16> · 376086460207166299103907106949428103083327376659<48> · 7005742679143560472394984002006753697421168708337655022037043987570498747347<76> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 56.26 hours on Core 2 Quad Q6700 / Jan 3, 2010)
(62·10169+1)/9 =
6(8)1689<170>
= 32 · 19 · 62248757 · 1132246658442052086249310300011175812648265977323<49> · 5715856779672020785607712412512635373068953262320874474059217265128852249119318167249014571590732236340019928669<112> (Wataru Sakai / Msieve / 81.71 hours / Jan 13, 2010)
(62·10170+1)/9 =
6(8)1699<171>
= 13 · 39863909 · 383296237894535365487<21> · 2277059144940033129476351<25> · 1523060226866909075654992949807018073573771976629917241151403087745079662274751409483084205279443061249287230392440841<118>
(62·10171+1)/9 =
6(8)1709<172>
= 17 · 53 · 59 · 1801568534798807<16> · 3492695044055543<16> · 53216027439132375430995215492636147<35> · 387006687681412470632539132793733289263031398892586524902106088059519115017667158339741992322196507893<102> (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=406518593 for P35 / Jan 5, 2010)
(62·10172+1)/9 =
6(8)1719<173>
= 3 · 47 · 11621 · 4343587 · 9679168304291887873286160687744980087700712492606809369302810577537418625236734738991738454521350985445223633498178475968593028423062434386416046271488582167827<160>
(62·10173+1)/9 =
6(8)1729<174>
= 4073 · 4547 · 455201 · 1950953623<10> · 51731867207590248363764618349610394268656931225806836823599340188387<68> · 809657808216972881450973750171735866842379212534385190588465448602888403011520279519<84> (Robert Backstrom / Msieve 1.42 snfs / Jun 16, 2010)
(62·10174+1)/9 =
6(8)1739<175>
= 7 · 1032373 · 936901439791<12> · 794801393114227<15> · 4851564966728101<16> · 263863989763758947200189069218892503677449721546951549560744692777316768139336346907735306446963120060996159412737683674361107<126>
(62·10175+1)/9 =
6(8)1749<176>
= 3 · 131 · 743 · 22943 · 56656753 · 390057029 · 357032212319<12> · 153200967741473<15> · 162215110648549389956882405770800727596818702289519241<54> · 52441801712007636051659829247711284124133796479273577819813583068954163<71> (Warut Roonguthai / Msieve 1.48 gnfs for P54 x P71 / Sep 17, 2011)
(62·10176+1)/9 =
6(8)1759<177>
= 13 · 140539126890670831<18> · 377058362065081483265994212944068911947742144530567715429143916751025315909257289450606664973938156161415864804050471680361137833618176742316941953994714866163<159>
(62·10177+1)/9 =
6(8)1769<178>
= 23 · 167 · 1289 · 2908698503555321<16> · 164021530706799001<18> · 992406222413648305174340403977<30> · 2938751804720088266217488864767251391489762075217540818048669967383822092013634121211026480988278875386033433<109> (Serge Batalov / GMP-ECM B1=2000000, sigma=2119590681 for P30 / Dec 31, 2009)
(62·10178+1)/9 =
6(8)1779<179>
= 34 · 8528110711<10> · 5782535061466773471299<22> · 17246185647358790329071631699191379287026073550490142779625945067695168087272434729439319427853455250860486157927119740178720743824709551574956021<146>
(62·10179+1)/9 =
6(8)1789<180>
= 1011331 · 33219128218033<14> · 4312717682524591753110449217010003193750937828460470478222807<61> · 4754628617059391869221750537857342485532262540840535818285605373163075979429605631989516981154301749<100> (matsui / Msieve 1.47 snfs / Sep 4, 2010)
(62·10180+1)/9 =
6(8)1799<181>
= 72 · 8287 · 4955719 · 1169326727087214881821997197<28> · [2927609931950584916702830006912517286735722035384881939027028727223087579830910534731775555298686768547604661150105448501137142486782871664821<142>] SUBMIT/RESERVE
(62·10181+1)/9 =
6(8)1809<182>
= 3 · 223 · 1483 · 4447663862006358848389<22> · [15611691253616364848780951704788592703228927208774297633269385491247051574841263527032988314254882845171845471693377444452676582307835077309170215569961563<155>] SUBMIT/RESERVE
(62·10182+1)/9 =
6(8)1819<183>
= 13 · 169471 · 440009294827667063<18> · 70652607976977098005433<23> · [10058202790687866343208722284566699982743146914873165476464462409692378139959275838581442394280532140782549907454921959731108198978935517<137>] SUBMIT/RESERVE
(62·10183+1)/9 =
6(8)1829<184>
= 10113258741133<14> · 247251143777525117<18> · 2754988258221747327551570788844918542558912214535497272169598959287250108752510703417080056401953873958661698826598618120678205714026425323622220616484449<154>
(62·10184+1)/9 =
6(8)1839<185>
= 3 · 53 · 400951333 · 933004087 · 762564853827856022999096033<27> · 2364802067766686006835964048686807187<37> · 642251705823719648362007474811269274631423424957850035191810206850583469985495109810743277682304105231<102> (Dmitry Domanov / GMP-ECM B1=3000000, sigma=4006625762 for P37 / May 9, 2011)
(62·10185+1)/9 =
6(8)1849<186>
= 43 · 521 · 468696803 · 3255346740117809<16> · [20153652045725763265772398519588981197973816584824163419019766884909383457328310655688725519825538483465352726046104173916460241938964064624033837841944047969<158>] SUBMIT/RESERVE
(62·10186+1)/9 =
6(8)1859<187>
= 7 · 907332384157<12> · 565065758305350737<18> · [1919489484964800766157402571167927480827154213127576347725188837876179464649665402838955174313454204956427538818079187965640057443985987928175206845172207003<157>] SUBMIT/RESERVE
(62·10187+1)/9 =
6(8)1869<188>
= 32 · 17 · 19 · 421 · 10789 · 23856470228954949409243403461<29> · 218692894593556699079474568613923532199339868634431903081767136554015085798527902461165734848033895545939399436036739330076401771227634065292515228503<150>
(62·10188+1)/9 =
6(8)1879<189>
= 13 · 29 · 63601 · 497017 · 922453578973249487663<21> · 1849190057369076140141407201103<31> · 3006746979172029135860649135821173<34> · 1177667319927559790709272878782439111818259<43> · 9570333351896616991124445351088249914236626668727<49> (Serge Batalov / GMP-ECM B1=3000000, sigma=2304118069 for P31 / Dec 31, 2009) (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=2629018177 for P34 / Jan 17, 2010) (Erik Branger / GGNFS, Msieve gnfs for P43 x P49 / 1.27 hours / Jan 18, 2010)
(62·10189+1)/9 =
6(8)1889<190>
= 3997811 · 4062948800033<13> · 159797119339533337<18> · 2654095990387660713717958288976466444545367802169269394550056102711834329511388432741579609525076595044119580567874105265326881952301706881795430171199419<154>
(62·10190+1)/9 =
6(8)1899<191>
= 3 · 46854808139<11> · 130448795210477<15> · [3756935067359240500961455618659191449330832223845963500727016846486372047178710602889418476076859267783358873492810648281262721931343390973838800599531501468534328221<166>] SUBMIT/RESERVE
(62·10191+1)/9 =
6(8)1909<192>
= 439 · 3944925421262293064917534217<28> · [397782673676387672909984107165608470457721099421561796218861542328748601772187644024325809270355330198218071744990341342901681615455201118431165141901946910207703<162>] SUBMIT/RESERVE
(62·10192+1)/9 =
6(8)1919<193>
= 7 · 71 · 1096591313<10> · 1455383600819124071<19> · 8685013806144526198404896817926059214704735091446412224064996616213840649851429205423547491686000570434177301284586978051050211186882214937515216862908008007065119<163>
(62·10193+1)/9 =
6(8)1929<194>
= 3 · 367 · 41471503 · 1508731944691546113663146416715432403696421602373711078463100382360312509303696676733082404073710321454657038618626766719503328837383705582353944248129323031208642684114235290844982163<184>
(62·10194+1)/9 =
6(8)1939<195>
= 13 · 8849 · 408347 · 54315538547<11> · 111847463603<12> · 2413970916554344090699312372671384896989163268442106720280022316727360512803125743227491057175255835005768382510984525897418106331268440467470442165318927519871711<163>
(62·10195+1)/9 =
6(8)1949<196>
= 11900107 · 19982593 · 376506017 · 41371145179894991<17> · 27709219442314269517733553661<29> · 25282667868355140733212912540868075985105142265695600452749<59> · 2654787814352433936618556409145199621494963919444041855456438115069933<70> (Serge Batalov / GMP-ECM B1=2000000, sigma=809520046 for P29 / Dec 31, 2009) (ruffenach timothee / Msieve 1.44 gnfs for P59 x P70 / May 11, 2010)
(62·10196+1)/9 =
6(8)1959<197>
= 32 · 25367 · 89531588268845862199637813684159136194493359744125099143364201653532024332803<77> · 3370243446485131770113347484910600373057261501134355778377433073145208681591570225369931387074948824171964384746621<115> (Robert Backstrom / Msieve 1.42 for P77 x P115 / Mar 17, 2010)
(62·10197+1)/9 =
6(8)1969<198>
= 53 · 502537759 · 918684274727294587178667856012189<33> · [28153884795426993298483778284244471883800094553639205956249429198695026754574463533805155344427554984976566485681239912057444589830272994200869730194689063<155>] (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1831825089 for P33 / Dec 28, 2009) SUBMIT/RESERVE
(62·10198+1)/9 =
6(8)1979<199>
= 7 · 113 · 4287908645681<13> · 5002697224194967163381<22> · 140914941419544596631669553<27> · 967551883484650368439527991<27> · 389335045641826884043776271524628176938144933<45> · 7648356946798376318897104196293214401401437074839678930464373121<64> (Serge Batalov / GMP-ECM B1=2000000, sigma=108283914 for P27 / Dec 31, 2009) (Jo Yeong Uk / GGNFS/Msieve v1.39 gnfs for P45 x P64 / 7.85 hours on Core 2 Quad Q6700 / Jan 1, 2010)
(62·10199+1)/9 =
6(8)1989<200>
= 3 · 23 · 5075003952872869487<19> · 11166159982842974251<20> · 72720307681375854069523<23> · 391009372282598562511570190167212961362072351157<48> · 619607952985904633144967216064295218654410415308394696166882666826776905948061927555883983<90> (Wataru Sakai / GMP-ECM 6.2.3 B1=11000000, sigma=2783007953 for P48 / Jul 25, 2010)
(62·10200+1)/9 =
6(8)1999<201>
= 13 · 139 · 2971 · 8623 · 14880927115842592459636109099147421165025834545867378981565196331108353727207778421392348439664825984867174660721139769923364754656689745836847829484493152574688519751847125715562736297396219<191>

4. References

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