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Factorizations of 722...221

Table of contents

  1. About 722...221
  2. Prime numbers of the form 722...221
  3. Factorizations of 722...221
  4. References

1. About 722...221

First ten terms

71, 721, 7221, 72221, 722221, 7222221, 72222221, 722222221, 7222222221, 72222222221

General term

(65·10n-11)/9

2. Prime numbers of the form 722...221

Last update

Sep 15, 2010

Searched up to

n≤30000

Difficulty of search

19.31%

Results

  1. (65·101-11)/9 = 71 is prime. (Makoto Kamada / Dec 6, 2004)
  2. (65·104-11)/9 = 72221 is prime. (Makoto Kamada / Dec 6, 2004)
  3. (65·1016-11)/9 = 7(2)151<17> is prime. (Makoto Kamada / PPSIQS / Dec 6, 2004)
  4. (65·1025-11)/9 = 7(2)241<26> is prime. (Makoto Kamada / PPSIQS / Dec 6, 2004)
  5. (65·1029-11)/9 = 7(2)281<30> is prime. (Makoto Kamada / PPSIQS / Dec 6, 2004)
  6. (65·1041-11)/9 = 7(2)401<42> is prime. (Makoto Kamada / PPSIQS / Dec 6, 2004)
  7. (65·1047-11)/9 = 7(2)461<48> is prime. (Makoto Kamada / PPSIQS / Dec 6, 2004)
  8. (65·1088-11)/9 = 7(2)871<89> is prime. (Makoto Kamada / PPSIQS / Dec 6, 2004)
  9. (65·101132-11)/9 = 7(2)11311<1133> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Sep 13, 2006)
  10. (65·101570-11)/9 = 7(2)15691<1571> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Sep 5, 2006)
  11. (65·103985-11)/9 = 7(2)39841<3986> is PRP. (Makoto Kamada / PFGW / Dec 18, 2004)
  12. (65·1010609-11)/9 = 7(2)106081<10610> is PRP. (Ray Chandler / srsieve, PFGW / Sep 9, 2010)
  13. (65·1012175-11)/9 = 7(2)121741<12176> is PRP. (Serge Batalov / PFGW / Feb 22, 2009)
  14. (65·1029369-11)/9 = 7(2)293681<29370> is PRP. (Ray Chandler / srsieve, PFGW / Sep 14, 2010)

3. Factorizations of 722...221

Last update

Dec 8, 2011

Completed up to

Range

n≤200

Terms which have not been factored yet

n=180, 182, 183, 186, 189, 191, 192, 195, 197 (9/200)

Results

(65·101-11)/9 =
71
= definitely prime number
(65·102-11)/9 =
721
= 7 · 103
(65·103-11)/9 =
7221
= 3 · 29 · 83
(65·104-11)/9 =
72221
= definitely prime number
(65·105-11)/9 =
722221
= 487 · 1483
(65·106-11)/9 =
7222221
= 32 · 277 · 2897
(65·107-11)/9 =
72222221
= 47 · 1536643
(65·108-11)/9 =
722222221
= 72 · 31 · 149 · 3191
(65·109-11)/9 =
7222222221<10>
= 3 · 19 · 126705653
(65·1010-11)/9 =
72222222221<11>
= 17 · 443 · 9589991
(65·1011-11)/9 =
722222222221<12>
= 61 · 67247 · 176063
(65·1012-11)/9 =
7222222222221<13>
= 3 · 216901 · 11099107
(65·1013-11)/9 =
72222222222221<14>
= 73673 · 980307877
(65·1014-11)/9 =
722222222222221<15>
= 7 · 103174603174603<15>
(65·1015-11)/9 =
7222222222222221<16>
= 32 · 113 · 210499 · 33736487
(65·1016-11)/9 =
72222222222222221<17>
= definitely prime number
(65·1017-11)/9 =
722222222222222221<18>
= 263 · 439 · 2801 · 2233250653<10>
(65·1018-11)/9 =
7222222222222222221<19>
= 3 · 2407407407407407407<19>
(65·1019-11)/9 =
72222222222222222221<20>
= 317 · 1783 · 4493 · 142421 · 199687
(65·1020-11)/9 =
722222222222222222221<21>
= 7 · 23 · 241 · 120907 · 153948862103<12>
(65·1021-11)/9 =
7222222222222222222221<22>
= 3 · 2999 · 802736714707371593<18>
(65·1022-11)/9 =
72222222222222222222221<23>
= 5537700659<10> · 13041915168319<14>
(65·1023-11)/9 =
722222222222222222222221<24>
= 31 · 27361 · 4157717 · 204796373543<12>
(65·1024-11)/9 =
7222222222222222222222221<25>
= 33 · 191302777 · 1398253157266799<16>
(65·1025-11)/9 =
72222222222222222222222221<26>
= definitely prime number
(65·1026-11)/9 =
722222222222222222222222221<27>
= 7 · 17 · 62539247 · 97044569538683797<17>
(65·1027-11)/9 =
7222222222222222222222222221<28>
= 3 · 19 · 126705653021442495126705653<27>
(65·1028-11)/9 =
72222222222222222222222222221<29>
= 1158541 · 226506425867<12> · 275219316643<12>
(65·1029-11)/9 =
722222222222222222222222222221<30>
= definitely prime number
(65·1030-11)/9 =
7222222222222222222222222222221<31>
= 3 · 9497 · 253491355944762283606129031<27>
(65·1031-11)/9 =
72222222222222222222222222222221<32>
= 29 · 3319 · 393581 · 1906476568955052604691<22>
(65·1032-11)/9 =
722222222222222222222222222222221<33>
= 7 · 1479375996529<13> · 69741974600559674107<20>
(65·1033-11)/9 =
7222222222222222222222222222222221<34>
= 32 · 631 · 1271741895091076284948445540099<31>
(65·1034-11)/9 =
72222222222222222222222222222222221<35>
= 227 · 622477 · 10066407341<11> · 50774678298321239<17>
(65·1035-11)/9 =
722222222222222222222222222222222221<36>
= 320237 · 2255274132040402021697125011233<31>
(65·1036-11)/9 =
7222222222222222222222222222222222221<37>
= 3 · 712 · 103 · 2131 · 5697179 · 381902372036845973641<21>
(65·1037-11)/9 =
72222222222222222222222222222222222221<38>
= 3191 · 229119257 · 98783054443573764275904083<26>
(65·1038-11)/9 =
722222222222222222222222222222222222221<39>
= 7 · 31 · 829 · 4014732214273052437961578395058297<34>
(65·1039-11)/9 =
7222222222222222222222222222222222222221<40>
= 3 · 2407407407407407407407407407407407407407<40>
(65·1040-11)/9 =
72222222222222222222222222222222222222221<41>
= 8408399 · 48309973 · 177795490076006914159784023<27>
(65·1041-11)/9 =
722222222222222222222222222222222222222221<42>
= definitely prime number
(65·1042-11)/9 =
7222222222222222222222222222222222222222221<43>
= 32 · 17 · 23 · 5995631 · 603795837599<12> · 566926253724673770211<21>
(65·1043-11)/9 =
72222222222222222222222222222222222222222221<44>
= 2225739283<10> · 15031585161284987<17> · 2158697430611409901<19>
(65·1044-11)/9 =
722222222222222222222222222222222222222222221<45>
= 7 · 83 · 1243067508127749091604513291260279212086441<43>
(65·1045-11)/9 =
7222222222222222222222222222222222222222222221<46>
= 3 · 192 · 99497 · 201434737965431137<18> · 332734655392009052383<21>
(65·1046-11)/9 =
72222222222222222222222222222222222222222222221<47>
= 59 · 454176617 · 2695219030603675897337809886361119807<37>
(65·1047-11)/9 =
722222222222222222222222222222222222222222222221<48>
= definitely prime number
(65·1048-11)/9 =
7222222222222222222222222222222222222222222222221<49>
= 3 · 77309611 · 31139820473387292136386605378306811133837<41>
(65·1049-11)/9 =
72222222222222222222222222222222222222222222222221<50>
= 111869 · 645596387043973059759381260422657056219526609<45>
(65·1050-11)/9 =
722222222222222222222222222222222222222222222222221<51>
= 72 · 241 · 27529 · 29917 · 74259025787777112980414710295398724233<38>
(65·1051-11)/9 =
7(2)501<52>
= 33 · 419 · 638400267145957944154708938585894300558845772317<48>
(65·1052-11)/9 =
7(2)511<53>
= 269 · 997 · 48497 · 50647 · 66089 · 80764129227461<14> · 20540315658923159927<20>
(65·1053-11)/9 =
7(2)521<54>
= 31 · 47 · 28723 · 47046061 · 143279325471468713<18> · 2560204765231578647827<22>
(65·1054-11)/9 =
7(2)531<55>
= 3 · 15107 · 103619 · 4211410757<10> · 5848090033777<13> · 62443942382192361494011<23>
(65·1055-11)/9 =
7(2)541<56>
= 34472671 · 17924329768127<14> · 116883440648229711039022931685655213<36>
(65·1056-11)/9 =
7(2)551<57>
= 7 · 17130232137839670819624173<26> · 6022954175074870775198687061911<31>
(65·1057-11)/9 =
7(2)561<58>
= 3 · 336996378787509569<18> · 7143718920865257486475606503874588232303<40>
(65·1058-11)/9 =
7(2)571<59>
= 17 · 541 · 21786637 · 944191210993187<15> · 381746012891132425264322519557847<33>
(65·1059-11)/9 =
7(2)581<60>
= 29 · 373 · 66767331258410115764280504966462255914044764927634484813<56>
(65·1060-11)/9 =
7(2)591<61>
= 32 · 367 · 389 · 2776061 · 4296916943629<13> · 304165652999683<15> · 1549232278703336969069<22>
(65·1061-11)/9 =
7(2)601<62>
= 25471 · 45952268083<11> · 2940958892867<13> · 389567574130127<15> · 53857494316204252133<20>
(65·1062-11)/9 =
7(2)611<63>
= 7 · 55949 · 72200603 · 43754772233<11> · 583732973921790068111118295883675489453<39>
(65·1063-11)/9 =
7(2)621<64>
= 3 · 19 · 6139663 · 37718449 · 547138948784355368429280652588918733032996235819<48>
(65·1064-11)/9 =
7(2)631<65>
= 23 · 1373 · 56530087 · 91947590731<11> · 439999786792882219195629936916479982639667<42>
(65·1065-11)/9 =
7(2)641<66>
= 2096951629<10> · 344415298967405138090680403683370906321569815391398435649<57>
(65·1066-11)/9 =
7(2)651<67>
= 3 · 181 · 3191 · 4783 · 262971763 · 3279450847806970253<19> · 1010493649441067384209022380141<31>
(65·1067-11)/9 =
7(2)661<68>
= 193 · 374208405296488198042602187679907887161773172135866436384571099597<66>
(65·1068-11)/9 =
7(2)671<69>
= 7 · 31 · 5360841817366811841641<22> · 620837756273723274892727123596066606358231693<45>
(65·1069-11)/9 =
7(2)681<70>
= 32 · 6822864637<10> · 162425316606158888031955653593<30> · 724115528032316556315797973809<30>
(65·1070-11)/9 =
7(2)691<71>
= 103 · 2399 · 292282877664327054647455137950773268077808400030037686504580072693<66>
(65·1071-11)/9 =
7(2)701<72>
= 61 · 71 · 33462973 · 2239749769714592718465525191<28> · 2224941721440958177130223465330037<34>
(65·1072-11)/9 =
7(2)711<73>
= 3 · 25343471 · 367563554957616339638431<24> · 258434835950275911043154903894608862069407<42>
(65·1073-11)/9 =
7(2)721<74>
= 156445349 · 2213223452753<13> · 3171022230936320599<19> · 65778450732710171210179085024981807<35>
(65·1074-11)/9 =
7(2)731<75>
= 7 · 17 · 4051 · 15803 · 21545448742591<14> · 4400140647547731167648846648642832536056767985238533<52>
(65·1075-11)/9 =
7(2)741<76>
= 3 · 277 · 8691001470784864286669340820965369701831795694611579088113384142265008691<73>
(65·1076-11)/9 =
7(2)751<77>
= 3491 · 20688118654317451223781788090009230083707310862853687259301696425729654031<74>
(65·1077-11)/9 =
7(2)761<78>
= 859553 · 160328849367497<15> · 5240666350249511157949920187787338109115144869617693602181<58>
(65·1078-11)/9 =
7(2)771<79>
= 34 · 30893 · 134590619 · 72277746700309677686716691<26> · 296692350128696808549364797970239518353<39>
(65·1079-11)/9 =
7(2)781<80>
= 919 · 78587837020916455084028533430056825051384354975214605247249425704267924072059<77>
(65·1080-11)/9 =
7(2)791<81>
= 7 · 241 · 9161 · 1451538691<10> · 17742932839<11> · 69035633723274307157<20> · 26283641833224676621969843607551771<35>
(65·1081-11)/9 =
7(2)801<82>
= 3 · 19 · 90037059198676974557919029083<29> · 1407261122798914531804477799076925150623460426647791<52>
(65·1082-11)/9 =
7(2)811<83>
= 571 · 3253 · 1955013077<10> · 2305524692960601841<19> · 8626432550229109686922190833455259835062885176031<49>
(65·1083-11)/9 =
7(2)821<84>
= 31 · 176937353309294599849<21> · 131670846227147082967192184904665026077738594118101125910053659<63>
(65·1084-11)/9 =
7(2)831<85>
= 3 · 97 · 109 · 81977933 · 60214032212863<14> · 89446016452402271<17> · 10051529474241962039<20> · 51305453615268102644609<23>
(65·1085-11)/9 =
7(2)841<86>
= 83 · 11071 · 78596988139230816016905365719645510654910008262357230082525628361759445574427297<80>
(65·1086-11)/9 =
7(2)851<87>
= 7 · 23 · 10039 · 202243 · 10657253591<11> · 10838106398549<14> · 4046911042570673009<19> · 4726706650428439071488891211694003<34>
(65·1087-11)/9 =
7(2)861<88>
= 32 · 29 · 223 · 71052283 · 629937719439514597<18> · 2772361288880238625768262288265512478893877055281446229457<58>
(65·1088-11)/9 =
7(2)871<89>
= definitely prime number
(65·1089-11)/9 =
7(2)881<90>
= 152801611244267<15> · 88690392231153644909539<23> · 5561494596026800051798711<25> · 9582411530356031921352463547<28>
(65·1090-11)/9 =
7(2)891<91>
= 3 · 17 · 3221 · 5479 · 8024327508267708139245297512084501739767471168323682334522036347156590121039969669<82>
(65·1091-11)/9 =
7(2)901<92>
= 8647 · 50287 · 7378009143200958178605149301007931<34> · 22511812956715159275034011448551192579590320351519<50> (Makoto Kamada / GGNFS-0.71.1 / 0.24 hours)
(65·1092-11)/9 =
7(2)911<93>
= 72 · 133393030873<12> · 110494745703590342451640861009032451992193176435413318935740721726391791377913573<81>
(65·1093-11)/9 =
7(2)921<94>
= 3 · 3761789443<10> · 5733189271<10> · 11718722323882657553<20> · 31358263388293457486167747<26> · 303757187071990773317178413009<30>
(65·1094-11)/9 =
7(2)931<95>
= 461 · 1207811081<10> · 129709239227733751550500368335429504399875657569625628180512742649240394160476562681<84>
(65·1095-11)/9 =
7(2)941<96>
= 307 · 3191 · 1473187 · 40958984291<11> · 12217957534657150697163033585596897739805576512645473623399022370094833649<74>
(65·1096-11)/9 =
7(2)951<97>
= 32 · 802469135802469135802469135802469135802469135802469135802469135802469135802469135802469135802469<96>
(65·1097-11)/9 =
7(2)961<98>
= 50408981030119<14> · 383742524772473017528891<24> · 1436543154422221620366307<25> · 2598988291501142351007449122472653307<37>
(65·1098-11)/9 =
7(2)971<99>
= 7 · 31 · 317 · 57223 · 92603117 · 1602529320829632653<19> · 1236373360543613441493676253927476441921041228322507710408502343<64>
(65·1099-11)/9 =
7(2)981<100>
= 3 · 19 · 47 · 2572373 · 393967625075515217<18> · 2660134873223942676835468087016543670470499366597696127726752832150749439<73>
(65·10100-11)/9 =
7(2)991<101>
= 2857 · 4481 · 290803 · 176431903 · 368266891 · 27400598682539737070856151<26> · 10896497777327398748757599577000520213166962477<47>
(65·10101-11)/9 =
7(2)1001<102>
= 36245308983223656829629931<26> · 19925950212109015292883041187356166587929364102984386844289172673856306943591<77>
(65·10102-11)/9 =
7(2)1011<103>
= 3 · 45293 · 194174684095620472963<21> · 843178827205421297027061729613<30> · 324643121356409471495914294387495680281341221821<48> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=316146510 for P30 / Oct 25, 2009)
(65·10103-11)/9 =
7(2)1021<104>
= 6257 · 34562401 · 45544388587<11> · 9268918316065523293<19> · 26273619006171758906208372083<29> · 30110430063001277429797073802758801<35>
(65·10104-11)/9 =
7(2)1031<105>
= 7 · 59 · 103 · 32579 · 50583268403<11> · 254093718716411119413770305538977<33> · 40545718826709883506943613462934918716086071233370911<53> (Lionel Debroux / msieve 1.44 SVN for P33*P53 / Oct. 25, 2009)
(65·10105-11)/9 =
7(2)1041<106>
= 33 · 568163 · 9836159 · 11666526653<11> · 203914426528769155691551711<27> · 20119587140604673420208325923735881216263695480472475393<56>
(65·10106-11)/9 =
7(2)1051<107>
= 17 · 71 · 941 · 33289 · 14106348317938464479<20> · 49816029539572413590189<23> · 2718250589640920936254174796549236874737846859877625237<55>
(65·10107-11)/9 =
7(2)1061<108>
= 36749656866201527263<20> · 174577584931942788813973330285134439<36> · 112571661871895252862906862024566402469110010962824053<54> (Dmitry Domanov / msieve/SIQS for P36 x P54 / 0.84 hours / Oct 27, 2009)
(65·10108-11)/9 =
7(2)1071<109>
= 3 · 23 · 9033556013789<13> · 135554491375990857956197246460694492102127861<45> · 85476966858717394152054163418298515138093927220521<50> (Erik Branger / GGNFS, Msieve snfs / 0.59 hours / Oct 27, 2009)
(65·10109-11)/9 =
7(2)1081<110>
= 52391597 · 2542076848723<13> · 137580139588561846772155174238321<33> · 3941529571374024940821143658563287380985182879516137168171<58> (Sinkiti Sibata / Msieve 1.42 for P33 x P58 / 1.24 hours / Oct 27, 2009)
(65·10110-11)/9 =
7(2)1091<111>
= 7 · 241 · 11688923 · 136800951105172457528839267681<30> · 267726986734980001505148507344895954470265087738188776900038050613946241<72> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=3593170758 for P30 / Oct 25, 2009)
(65·10111-11)/9 =
7(2)1101<112>
= 3 · 661 · 1873 · 7691 · 14042547361<11> · 18004524120768035455263753672367453928843226843039861132007789577867406537674496211893061769<92>
(65·10112-11)/9 =
7(2)1111<113>
= 349 · 1609 · 70607932059021754016721120546462990586001<41> · 1821528136121762022116250471027322875569923541409150218970043515481<67> (Serge Batalov / Msieve 1.44 snfs / 0.72 hours / Oct 28, 2009)
(65·10113-11)/9 =
7(2)1121<114>
= 31 · 433 · 1140421 · 2283571 · 268640172103<12> · 665437126115828664121719211862052196062517<42> · 115574905654581117954367725646096133674508047<45> (Lionel Debroux / msieve 1.44 SVN for P42*P45 / Oct. 25, 2009)
(65·10114-11)/9 =
7(2)1131<115>
= 32 · 233 · 409 · 558040613659747<15> · 160981721112651612109794172448162077483<39> · 93736068617683451547390765327106178850798232594071318277<56> (Sinkiti Sibata / Msieve 1.42 for P39 x P56 / 4.92 hours / Oct 28, 2009)
(65·10115-11)/9 =
7(2)1141<116>
= 292 · 2069 · 1179403 · 1293491 · 27207505229564357185374503544568735317801566843002828109393489528423254265434259768642706896449313<98>
(65·10116-11)/9 =
7(2)1151<117>
= 7 · 131 · 1109 · 4478083 · 10910022265230896815348697<26> · 257003941307123936731048016743<30> · 56560391395329397038261288537270234427729359475049<50> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=2799717756 for P30 / Oct 25, 2009)
(65·10117-11)/9 =
7(2)1161<118>
= 3 · 19 · 480449 · 27896501 · 9453637901744292931814330745472718949801429572470615709728076636490931650393379561480609523605335642497<103>
(65·10118-11)/9 =
7(2)1171<119>
= 33749 · 160903 · 2607083 · 331664699 · 21680954101<11> · 709436125268781511031348681112661866146907940530933259792242954349642175386938963979<84>
(65·10119-11)/9 =
7(2)1181<120>
= 20369 · 45841 · 3326471 · 3191030608347436943531<22> · 22562190230629062843875180557417<32> · 3229617486163457345402032865206564186148256744671897<52> (Lionel Debroux / msieve 1.44 SVN for P32*P52 / Oct. 25, 2009)
(65·10120-11)/9 =
7(2)1191<121>
= 3 · 9221 · 294887 · 243954764641450571<18> · 3629164370805557831196327089178640473969423651749841689140412788789190865658305504046190819471<94>
(65·10121-11)/9 =
7(2)1201<122>
= 7963 · 534570376243<12> · 73739065922107105379<20> · 947352483431407184943321232710242057202163<42> · 242873434001740665351347420833894420438989397<45> (Erik Branger / YAFU, Msieve 1.38 for P42 x P45 / Oct 27, 2009)
(65·10122-11)/9 =
7(2)1211<123>
= 7 · 17 · 337 · 2341 · 429083189 · 1070422681903<13> · 16749265563776643054522967806993042830725255427983320541338857269849647431469009956490420529981<95>
(65·10123-11)/9 =
7(2)1221<124>
= 32 · 769 · 941747 · 1201969709349506345505143<25> · 921879652291185505889055485965285802486807701294267560880108956538072818458269386968672881<90>
(65·10124-11)/9 =
7(2)1231<125>
= 3191 · 22633100038302169295588286500226331000383021692955882865002263310003830216929558828650022633100038302169295588286500226331<122>
(65·10125-11)/9 =
7(2)1241<126>
= 91555041401965548538648038653167603029653<41> · 7888393813851928434485152622480874620149146146332238895830736022441467295327701644057<85> (Dmitry Domanov / Msieve 1.40 snfs / 1.50 hours / Oct 27, 2009)
(65·10126-11)/9 =
7(2)1251<127>
= 3 · 83 · 76943 · 1489283 · 253119236947592748421874848152025240321195694868720042212710563125940868983793534207846492153028501753356342073641<114>
(65·10127-11)/9 =
7(2)1261<128>
= 113 · 16931 · 39750651883367<14> · 64893015152296778849911<23> · 14634152801766667439187443032434376048662504560030521846104266261105375344365668191711<86>
(65·10128-11)/9 =
7(2)1271<129>
= 7 · 312 · 19590479 · 5480300397918213347033803264599535929286861927346590556350890141193332761221656358203208588786046405554651632742271237<118>
(65·10129-11)/9 =
7(2)1281<130>
= 3 · 47772103 · 497906247822126535549567<24> · 101210986180825513135350272030243765074733802033944791241618155386022551023563534166445405182061607<99>
(65·10130-11)/9 =
7(2)1291<131>
= 23 · 5339081861<10> · 499612399907<12> · 126572059583857<15> · 821375128603147487<18> · 159369281928039688919101133<27> · 71049203209099903539034237893557690074748219347783<50>
(65·10131-11)/9 =
7(2)1301<132>
= 61 · 67537 · 18384757 · 1738600657950757<16> · 104926812229665807978137<24> · 2585275154096954616576397<25> · 20218468793432177734163055500154308523685991169918667973<56>
(65·10132-11)/9 =
7(2)1311<133>
= 33 · 234885793535699<15> · 2009909228753029<16> · 566596501162504883443096281968195196539848368614669350949366766383882013598518767459758237533500950313<102>
(65·10133-11)/9 =
7(2)1321<134>
= 3374743 · 930079638576089<15> · 12124751083772558653<20> · 1956008027289071692987626397027<31> · 970211774512288584777603488856185473243272911240495962296960133<63> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=463105062 for P30 / Oct 25, 2009)
(65·10134-11)/9 =
7(2)1331<135>
= 73 · 174943 · 41632857953318896692018011<26> · 289097231475692230907052556795922292203690834891909097670848469398324780605860541674059365053583149439<102>
(65·10135-11)/9 =
7(2)1341<136>
= 3 · 19 · 8053 · 180391 · 10080019 · 47143046448625917952027767536030904815495237561<47> · 183545791821273701961220689454604108763314382917801245535477001041814229<72> (Erik Branger / GGNFS, Msieve snfs / 6.58 hours / Oct 28, 2009)
(65·10136-11)/9 =
7(2)1351<137>
= 123427 · 1375629339975159871097<22> · 62806303538900550603721255401770903<35> · 6772609105223622686935968347184377631672554842728485633440352400986340351953<76> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=6175954588 for P35 / Oct 27, 2009)
(65·10137-11)/9 =
7(2)1361<138>
= 3856127651773716445077580043028022865033<40> · 187292093893732785337096962993710590056537036033026265546665061444636987452833698017865574966552037<99> (Dmitry Domanov / Msieve 1.40 snfs / 4.39 hours / Oct 28, 2009)
(65·10138-11)/9 =
7(2)1371<139>
= 3 · 17 · 103 · 773 · 5441 · 112083887363024514430569516904031<33> · 2916500408302875083987535970330480585387768895593985589434940784587907313673484732150584806331979<97> (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=2474648913 for P33 / Oct 27, 2009)
(65·10139-11)/9 =
7(2)1381<140>
= 1607 · 6229 · 11177622899<11> · 11441463551237<14> · 7607869544039245259<19> · 2195567796210923571947<22> · 3377502626866662855970439385689378352253232031522406181418167759157193<70>
(65·10140-11)/9 =
7(2)1391<141>
= 7 · 241 · 1977175504445211461870746854270739911051029758911560186271011<61> · 216526244460396024191855897937745004522218028630947175795677723021683328286153<78> (Erik Branger / GGNFS, Msieve snfs / 5.60 hours / Oct 27, 2009)
(65·10141-11)/9 =
7(2)1401<142>
= 32 · 71 · 145991 · 3380926859<10> · 12718567937<11> · 6088571724331250328637<22> · 6943388399896641031086000361099687<34> · 42587586623151738614250628439153952183704337824580960958877<59> (Sinkiti Sibata / Msieve 1.42 for P34 x P59 / 2.4 hours / Oct 27, 2009)
(65·10142-11)/9 =
7(2)1411<143>
= 14182188136387<14> · 2301042251793941<16> · 49683938243911040863561670600066704163687710361<47> · 44543772791552787387347470419203004445531100088375155605652133154283<68> (Sinkiti Sibata / Msieve 1.40 snfs / 10.58 hours / Nov 2, 2009)
(65·10143-11)/9 =
7(2)1421<144>
= 29 · 31 · 179 · 544122550207<12> · 8248242097891005439670575673961808479386202722453971748763599281003838028230619518250683642910027852607871174338889670013555243<127>
(65·10144-11)/9 =
7(2)1431<145>
= 3 · 277 · 540159107444178312222571<24> · 733012834913677092865758737462221<33> · 88725536638157740998348475984873035913<38> · 247393284518799506736103973363549350223610371477<48> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=685820606 for P33 / Oct 25, 2009) (Lionel Debroux / msieve 1.44 SVN for P38*P48 / Oct. 25, 2009)
(65·10145-11)/9 =
7(2)1441<146>
= 47 · 607 · 351457 · 10203519393642125535430984893281<32> · 70454049702556330053008041614724445605807<41> · 10019732907879640889882400544847060911821000275230632388769933171<65> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=2948961324 for P32 / Oct 25, 2009) (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=1037193634 for P41 / Oct 28, 2009)
(65·10146-11)/9 =
7(2)1451<147>
= 7 · 42602801 · 228010369498745966470246714367913773<36> · 10621358195754820181708181688331386998838914009256762910359610187203730566466660828760503361669159883911<104> (Robert Backstrom / GMP-ECM 6.2.1 B1=1532000, sigma=4260663187 for P36 / Nov 3, 2009)
(65·10147-11)/9 =
7(2)1461<148>
= 3 · 227 · 11184883 · 1054504601<10> · 2662674431<10> · 159164693352747801448663667857<30> · 2121675718095529931539651978543648474065642777242525093936507377683034299794559188305104881<91> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=554021633 for P30 / Oct 25, 2009)
(65·10148-11)/9 =
7(2)1471<149>
= 821 · 15121 · 434867 · 2659663 · 4831786039<10> · 5683466138107710514513519<25> · 939723580029040882857358260430399230301<39> · 194913992192781453472395092670134360915528563343150609321<57> (Sinkiti Sibata / Msieve 1.42 for P39 x P57 / 7.88 hours / Oct 28, 2009)
(65·10149-11)/9 =
7(2)1481<150>
= 229 · 10309737107<11> · 1760809446734728886340349673660727500140667053250604025945597<61> · 173730237829917538457626291929595253008299451778851719371130464180604004301231<78> (Dmitry Domanov / GGNFS/msieve snfs / 11.49 hours / Nov 4, 2009)
(65·10150-11)/9 =
7(2)1491<151>
= 32 · 5483 · 37957 · 1120753070347<13> · 3440394737677175849640997609181109072328298376898417140492042179462004170782465745842684213618458192931443437812403487810497465417<130>
(65·10151-11)/9 =
7(2)1501<152>
= 2632819547<10> · 359828389017095641457<21> · 4707966628617424628297466037653799757180336867<46> · 16192762768567533085113383462849628534669727951104188819800098462441995657197<77> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 7.84 hours on Core 2 Quad Q6700 / Nov 8, 2009)
(65·10152-11)/9 =
7(2)1511<153>
= 7 · 23 · 167 · 1459910748169<13> · 9358321928237<13> · 1376221109049077<16> · 1428617606697552076727783455616869301947246428392018038050395498843640449548667168979694421359431356530397443<109>
(65·10153-11)/9 =
7(2)1521<154>
= 3 · 19 · 3191 · 30851 · 1993529 · 8594630348195199186618987496491138043989264641<46> · 75119066309768402960586373080898748135184106551828886169635340771025166138551902760422135897<92> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 9.93 hours on Core 2 Quad Q6700 / Nov 9, 2009)
(65·10154-11)/9 =
7(2)1531<155>
= 17 · 491 · 15641 · 32401 · 696107 · 3960053 · 552586313 · 49006952297<11> · 228708700081375949518358892095039631405319715311566809992202679367231259088151664695569077723226794539314364633<111>
(65·10155-11)/9 =
7(2)1541<156>
= 5009 · 29179 · 140681 · 33419257 · 1051034990647471390387314439730823692406620878635072579513660788633211183709773880171221031052879465835094749341883755304840879585185383<136>
(65·10156-11)/9 =
7(2)1551<157>
= 3 · 149 · 2909 · 484061 · 1869071 · 924547593040272577001488578136091171063098712873<48> · 6639944322588482605733024627603148158770302262895769428985277259280354195849327659562685229<91> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 12.28 hours on Core 2 Quad Q6700 / Nov 13, 2009)
(65·10157-11)/9 =
7(2)1561<158>
= 467 · 881 · 34893421 · 76139466457<11> · 45062034422087<14> · 16026975876783402520793945195297<32> · 2781337945606846567176996666297459217<37> · 32893382824650786898544395629261720525621863468742293<53> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=4061380540 for P32 / Oct 25, 2009) (Sinkiti Sibata / Msieve 1.42 for P37 x P53 / 2.12 hours / Oct 27, 2009)
(65·10158-11)/9 =
7(2)1571<159>
= 7 · 31 · 3607 · 83363948032550770439971746177796233984623<41> · 63165174686566479174510487178756948267564308740641<50> · 175230215598453693379399967411213917661767959640494153861891613<63> (Dmitry Domanov / GGNFS/msieve snfs / 19.63 hours / Nov 12, 2009)
(65·10159-11)/9 =
7(2)1581<160>
= 34 · 1627537 · 54784153792746622370863262559210576458816067591873087015838393010247258813127452764000595569492711707081118128699933690018799081234004770703566582338093<152>
(65·10160-11)/9 =
7(2)1591<161>
= 799427 · 1595513 · 7102157 · 18255534834763987<17> · 471751366330868587<18> · 165075270855299030459<21> · 5608047366998422034274240784803206323876607056271977059725656674258725391289638454441193<88>
(65·10161-11)/9 =
7(2)1601<162>
= 20084017 · 191866891 · 311840341079435138195582161480994283224403261766637618030009178235597<69> · 601018626647427049816918876130796226415550083819651184343799035882306940635219<78> (Sinkiti Sibata / Msieve 1.40 snfs / 29.98 hours / Nov 23, 2009)
(65·10162-11)/9 =
7(2)1611<163>
= 3 · 59 · 1999 · 4773779 · 70720939585198509430447494622061780717823615546513973846559159308700434243<74> · 60460878757510508486907856776275737477095178737018964166774638595681693266091<77> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 24.47 hours on Core 2 Quad Q6700 / Nov 22, 2009)
(65·10163-11)/9 =
7(2)1621<164>
= 382159282100879841810432048201209139152111<42> · 12134760941028933954849302273360311799514764407<47> · 15573822111719989074008727773441965485234326451554657360445839721618992013973<77> (Dmitry Domanov / GGNFS/msieve snfs / 30.58 hours / Oct 28, 2009)
(65·10164-11)/9 =
7(2)1631<165>
= 7 · 642113 · 1373173 · 4123318093<10> · 4443565537<10> · 4462792390541<13> · 1551622602733807349047209724184123573558714451797777<52> · 922284432714733061874653609820085576890214786673481956403908905108631<69> (Sinkiti Sibata / Msieve 1.42 snfs / 2.07 hours, 38 hours / Nov 28, 2009)
(65·10165-11)/9 =
7(2)1641<166>
= 3 · 1627 · 1117427261<10> · 113006746106565909443027295307940874726468067<45> · 11717592946789296253681058279544472082801984835493741742797532427363964872859069731881552804947725855354637643<110> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 24.57 hours on Core 2 Quad Q6700 / Nov 30, 2009)
(65·10166-11)/9 =
7(2)1651<167>
= 82700799104208379<17> · 55453638863452050299801690813<29> · 7006480171196645346248326347718850587339<40> · 2247662988012906180974676225729465654983752806424867683142296040326087299267616457<82> (juno1369 / GGNFS, Msieve snfs / 61.47 hours / Dec 28, 2009)
(65·10167-11)/9 =
7(2)1661<168>
= 83 · 479951 · 186194310489180847831<21> · 1205454286248948897370580333<28> · 80775322797797116536878474414203332807128234937282452137646928658325398870716282230779143024128932303444387722419<113>
(65·10168-11)/9 =
7(2)1671<169>
= 32 · 883 · 356663 · 1750972928149<13> · 19066300121646209<17> · 76324456342783727235694040876895245044105397613783298144010596987729503060155770532911048621119758337098604247226240081132726355821<131>
(65·10169-11)/9 =
7(2)1681<170>
= 7283 · 4542588659828027852927753185791967431732095768199561187<55> · 2183017035769276937291582142435683590937076880103696235615273791181575193188745388390184796157340731360291701301<112> (Ignacio Santos / GGNFS, Msieve snfs / 55.07 hours / Nov 4, 2009)
(65·10170-11)/9 =
7(2)1691<171>
= 7 · 17 · 241 · 4561 · 137318191 · 2432092757<10> · 16532501209010326328520525611886349321305200481174185359356861653992011916137513923036477752127969316841589222143132245878806112584469177647313857<146>
(65·10171-11)/9 =
7(2)1701<172>
= 3 · 19 · 29 · 4057 · 9527262744286699<16> · 113038098552808152333300693660266407762509330260576038174778795482943749243352536319570074259994155309361453570779507295979881755900620285036710227299<150>
(65·10172-11)/9 =
7(2)1711<173>
= 103 · 5979393746891<13> · 663739544597610103788635722670085967343540439502149443<54> · 176676495664991616221649990076759866757755288109911870665022125840998503243417393462806753502719263724939<105> (Dmitry Domanov / Msieve 1.40 snfs / May 5, 2010)
(65·10173-11)/9 =
7(2)1721<174>
= 31 · 23297491039426523297491039426523297491039426523297491039426523297491039426523297491039426523297491039426523297491039426523297491039426523297491039426523297491039426523297491<173>
(65·10174-11)/9 =
7(2)1731<175>
= 3 · 23 · 827078701561385359<18> · 126553721043697296995128325231919441623995058867075734690182197831579733767304657689007634209657153421361465669449370654078160933407196372992688822601850951<156>
(65·10175-11)/9 =
7(2)1741<176>
= 1033 · 1063 · 1069 · 31193 · 23130988929735880776501196872889855809350456144945578855817695577767<68> · 85272345721153945645916966734694939433866935390429349973433032857169622505106349698492527897041<95> (matsui / Msieve 1.47 snfs / Aug 23, 2010)
(65·10176-11)/9 =
7(2)1751<177>
= 72 · 71 · 5081 · 190683595955278199<18> · 214266309871754149760892399791793520905701058158946731932111827582831846703716088798817353317704250172252189515211591211747762114477380195769005507317221<153>
(65·10177-11)/9 =
7(2)1761<178>
= 32 · 317 · 184489 · 2951159 · 8241774017<10> · 641128651117<12> · 2348723219984939568761<22> · 84446013705880654515662053<26> · 4436383768335229913835451829319795344080644065909948012322515923010106594231142135982879378911<94>
(65·10178-11)/9 =
7(2)1771<179>
= 4255673 · 234266889100618179920977<24> · 72442209309158127987739588954659741610014546174151794042633293565691185752529448690819720103027285064238366983976032343902085653549697251985980905701<149>
(65·10179-11)/9 =
7(2)1781<180>
= 2671 · 7908167 · 598908397 · 57090089666091053647927140207479846769968307180533171610247232039165399608116102641666202279912360565667107730436463649705100179944678981987604621839339419850649<161>
(65·10180-11)/9 =
7(2)1791<181>
= 3 · 97 · 151027 · 357083 · [460207919282161412691332926397305096124322642044162414952187626236971298701471345434469399191203996811686802844967524107915409768510601917220275598087343980664891297391<168>] SUBMIT/RESERVE
(65·10181-11)/9 =
7(2)1801<182>
= 761 · 2559857 · 21594553 · 1716825939774977570562455072884974086947675934997632043580300020347095505461302371402936929383168816588205242595483797700393093738122438549478251467080984303689140141<166>
(65·10182-11)/9 =
7(2)1811<183>
= 7 · 3191 · 3277279 · 79914138638654348716331969466047<32> · [123455079967625126063601605724659725324415469636604976125161982026594698677760137137053398542435440384884193974430798105548337904952096280941<141>] (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=3580476653 for P32 / Oct 25, 2009) SUBMIT/RESERVE
(65·10183-11)/9 =
7(2)1821<184>
= 3 · 6369793 · 1218592889<10> · [310145606769777636643220644301777324310575746693680702607206795982293929699920478901879824980546954932915006336813087174869254981387593793713741265305737745853462607591<168>] SUBMIT/RESERVE
(65·10184-11)/9 =
7(2)1831<185>
= 691 · 219621875269<12> · 2157276602733659502141754392473<31> · 4503477033199215094729890033147187<34> · 1366875469678489414121668461325082477<37> · 35837232906713279419812768310828169169378234147431171772663813102526637<71> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=2649173361 for P37 / Oct 25, 2009) (Jo Yeong Uk / GMP-ECM 6.2.3 B1=1000000, sigma=4945725169 for P34 / Oct 28, 2009)
(65·10185-11)/9 =
7(2)1841<186>
= 3673 · 145459 · 51028247 · 523181223872965338269<21> · 1045359163418150399691709<25> · 61950651458183075429960343799297<32> · 781871016839220677109463407665525311825701689960463807826403466950410272126295951203562513177<93> (Wataru Sakai / GMP-ECM 6.2.1 B1=3000000, sigma=2064621114 for P32 / Oct 28, 2009)
(65·10186-11)/9 =
7(2)1851<187>
= 33 · 172 · 1049 · 20626961 · 854419049725243<15> · [50064234729386384844850264376526375206219808282529066648644309012416554505539891354552710477385413915276264309275363263995936749331694895008623376635605614541<158>] SUBMIT/RESERVE
(65·10187-11)/9 =
7(2)1861<188>
= 29715085646469174857<20> · 2430490124830040927874133162125994448560062580707268172650779871100969239496835288600530650940346090764323702786118553200613398240086551180813835804225455863091381916453<169>
(65·10188-11)/9 =
7(2)1871<189>
= 7 · 31 · 2017 · 6142674119<10> · 1504447232279<13> · 178554491687377290963711739724672232423915534676023840475591758148961902428988106218048031824591723980832462399583966685403008304835081288934898128026486230970389<162>
(65·10189-11)/9 =
7(2)1881<190>
= 3 · 19 · 1878673818397<13> · [67444200148355475547383462406421453919126441892825323706754292729415703664811290123867800103407911750856983605237761678415589512609401780110698609843353697781018263323978878649<176>] SUBMIT/RESERVE
(65·10190-11)/9 =
7(2)1891<191>
= 7537 · 14431 · 23344241149563613682333430859514417<35> · 28444358544940857253460828223626676832099701367436350921395203348863608393282485204870853410621446990712688012260075968530494323385016381562269843379<149> (Ignacio Santos / GMP-ECM 6.2.3 B1=3000000, sigma=2852687881 for P35 / Jun 21, 2010)
(65·10191-11)/9 =
7(2)1901<192>
= 47 · 61 · 254363797 · 255431651 · [3877154830687554251378820331115979979505486630261509005732169800575359132443621186566294411681478948830070029424814954516165075006344413213571783880324515579111516162248929<172>] SUBMIT/RESERVE
(65·10192-11)/9 =
7(2)1911<193>
= 3 · 109 · 138311 · 9328219865407<13> · [17118574585827733954844815151896649812966409137196426793073463318498055402144027227848627940044688861532903780379719132582272001194962968446984773642028704399247001920408099<173>] SUBMIT/RESERVE
(65·10193-11)/9 =
7(2)1921<194>
= 383 · 10119847691<11> · 18633657004828692989575391020667056032167584580146150196869555033890779265962503040321253283625926001921540634072680011651627434829079830971107233340526248580885651003455964127760057<182>
(65·10194-11)/9 =
7(2)1931<195>
= 7 · 103174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603174603<195>
(65·10195-11)/9 =
7(2)1941<196>
= 32 · 472543 · 3485641 · [487196711545104196715807584096094877103433274039437416016151570761483589589178851760650391245115485955490625449445689457325836841124762748602116340247970366247086740384521141372654563<183>] SUBMIT/RESERVE
(65·10196-11)/9 =
7(2)1951<197>
= 23 · 3547097268239611347671<22> · 226659362713426290036496337<27> · 4001519194703733032330492599<28> · 241773531235173452056941639607<30> · 4037035717973795540380000717740600791104637017568173701425365648273643288713769844015518557<91> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=3381242514 for P30 / Oct 25, 2009)
(65·10197-11)/9 =
7(2)1961<198>
= 28229 · 3744133 · 14173418461594230755660934797<29> · [482113704024717995573432236096562156807368640495270349626344808807036266612615099637469070684376291687005726123103261186593648405369600898740302808291405587049<159>] SUBMIT/RESERVE
(65·10198-11)/9 =
7(2)1971<199>
= 3 · 1543 · 3801682540095071<16> · 5577434579407067171<19> · 73582295694250211936997454617863231921187218354254070649094470069261558214941974689388781157487145498669853587953476967931545146735160680969039150249746573770189<161>
(65·10199-11)/9 =
7(2)1981<200>
= 29 · 677 · 2459 · 178141009 · 701666683 · 164842371458509<15> · 100682426438506217502581151517<30> · 721121362426889777091682228610183469620476049265075407476162930349381617520906257626423210451154016172746458044032134707938443745373<132> (Lionel Debroux / GMP-ECM 6.2.3 B1=1e6, sigma=1812186586 for P30 / Oct 25, 2009)
(65·10200-11)/9 =
7(2)1991<201>
= 7 · 241 · 182106629 · 1543119435673<13> · 1523457938520887953156641845252838962509878368131028291546152849562739526033146972230870523564150843372126520915289765459824158428176203984598283772499992018681286169288483510999<178>

4. References