counterSince June 16, 2000STUDIO KAMADAEnglish text only.
Factorizations
Factorizations of 299...992008-10-03(Fri) 22:15

Last update

Oct 3, 2008 22:15 JST

Sequence

2, 29, 299, 2999, 29999, ...

General term

3·10n-1
See also 899...99.

Room for prime numbers

upper limit of periods: 10000
upper limit of periodical factors: 4294967296
checked terms: 100000000
terms divided by periodical factors: 78530618
room for prime numbers: 21.47%

Prime numbers

  1. 3·101-1 = 29 is prime.
  2. 3·103-1 = 2999 is prime.
  3. 3·106-1 = 2999999 is prime.
  4. 3·107-1 = 29999999 is prime.
  5. 3·1019-1 = 2(9)19<20> is prime.
  6. 3·1027-1 = 2(9)27<28> is prime.
  7. 3·1043-1 = 2(9)43<44> is prime.
  8. 3·1055-1 = 2(9)55<56> is prime.
  9. 3·10207-1 = 2(9)207<208> is prime.
  10. 3·101311-1 = 2(9)1311<1312> is prime. (Chris Caldwell, Harvey Dubner / Dubner Cruncher / 1989)
  11. 3·103204-1 = 2(9)3204<3205> is prime. (Chris Caldwell, Harvey Dubner / Dubner Cruncher / 1989)
  12. 3·107050-1 = 2(9)7050<7051> is prime. (Harvey Dubner / Dubner Cruncher / 1993)
  13. 3·109439-1 = 2(9)9439<9440> is prime. (Harvey Dubner / Dubner Cruncher / 1993)
  14. 3·1026044-1 = 2(9)26044<26045> is prime. (Harvey Dubner / Dubner Cruncher / Sep 10, 2000)
  15. 3·1033058-1 = 2(9)33058<33059> is prime. (Harvey Dubner / Dubner Cruncher / Oct 9, 2000)
  16. 3·1034507-1 = 2(9)34507<34508> is prime. (Eric J. Sorensen / Yves Gallot's Proth.exe / Jan 4, 2002)
  17. 3·1049314-1 = 2(9)49314<49315> is prime. (Eric J. Sorensen / Yves Gallot's Proth.exe / Feb 8, 2002)
  18. 3·10119292-1 = 2(9)119292<119293> is prime. (Daniel Heuer / OpenPFGW / Aug 7, 2006)
Searched:
References:

Condition

n≤200

Status

Completed up to n=100. (Jun 14, 2003)
Completed up to n=110. (Jul 3, 2003)
Completed up to n=150. (May 14, 2005)
The following numbers are not factored yet. (n≤200)
n= 169, 171, 172, 174, 176, 177, 178, 180, 182, 191, 192, 195, 197, 198, 199 (15/200)

Factorization results

3·101-1 =
29
= definitely prime number
3·102-1 =
299
= 13 · 23
3·103-1 =
2999
= definitely prime number
3·104-1 =
29999
= 131 · 229
3·105-1 =
299999
= 7 · 17 · 2521
3·106-1 =
2999999
= definitely prime number
3·107-1 =
29999999
= definitely prime number
3·108-1 =
299999999
= 13 · 23076923
3·109-1 =
2999999999<10>
= 16937 · 177127
3·1010-1 =
29999999999<11>
= 2113 · 3767 · 3769
3·1011-1 =
299999999999<12>
= 7 · 683 · 953 · 65843
3·1012-1 =
2999999999999<13>
= 359 · 8356545961<10>
3·1013-1 =
29999999999999<14>
= 19 · 1578947368421<13>
3·1014-1 =
299999999999999<15>
= 13 · 107 · 33203 · 6495563
3·1015-1 =
2999999999999999<16>
= 83 · 103 · 227 · 1545895313<10>
3·1016-1 =
29999999999999999<17>
= 100126307 · 299621557
3·1017-1 =
299999999999999999<18>
= 7 · 157 · 3257 · 6961 · 12040213
3·1018-1 =
2999999999999999999<19>
= 61 · 3145189 · 15636684431<11>
3·1019-1 =
29999999999999999999<20>
= definitely prime number
3·1020-1 =
299999999999999999999<21>
= 13 · 23076923076923076923<20>
3·1021-1 =
2999999999999999999999<22>
= 17 · 191 · 757 · 11059 · 110363948159<12>
3·1022-1 =
29999999999999999999999<23>
= 167 · 311 · 337 · 1559 · 1099432012969<13>
3·1023-1 =
299999999999999999999999<24>
= 7 · 50367072601<11> · 850896044657<12>
3·1024-1 =
2999999999999999999999999<25>
= 23 · 130434782608695652173913<24>
3·1025-1 =
29999999999999999999999999<26>
= 23057 · 10833241 · 120104713180327<15>
3·1026-1 =
299999999999999999999999999<27>
= 13 · 59 · 71 · 5508933654075692748407<22>
3·1027-1 =
2999999999999999999999999999<28>
= definitely prime number
3·1028-1 =
29999999999999999999999999999<29>
= 47 · 638297872340425531914893617<27>
3·1029-1 =
299999999999999999999999999999<30>
= 74 · 29 · 4308549598586795731663531<25>
3·1030-1 =
2999999999999999999999999999999<31>
= 19441 · 45949 · 671304589 · 5002728961799<13>
3·1031-1 =
29999999999999999999999999999999<32>
= 19 · 16187 · 546924986987<12> · 178350167647709<15>
3·1032-1 =
299999999999999999999999999999999<33>
= 13 · 146437799 · 157588568214707166713677<24>
3·1033-1 =
2999999999999999999999999999999999<34>
= 113 · 149 · 34303 · 5194269029314101397578509<25>
3·1034-1 =
29999999999999999999999999999999999<35>
= 46811 · 51047 · 12554606696004419459257547<26>
3·1035-1 =
299999999999999999999999999999999999<36>
= 7 · 478631 · 3887236453<10> · 23034640168453340899<20>
3·1036-1 =
2999999999999999999999999999999999999<37>
= 193 · 2347451 · 6621668120347220058071014093<28>
3·1037-1 =
29999999999999999999999999999999999999<38>
= 173 · 6106248727864848361489924689599023<34>
3·1038-1 =
299999999999999999999999999999999999999<39>
= 13 · 2423 · 9524111876567510079685069367281501<34>
3·1039-1 =
2999999999999999999999999999999999999999<40>
= 20474512935513701<17> · 146523632061420300823699<24>
3·1040-1 =
29999999999999999999999999999999999999999<41>
= 1316507 · 13940701 · 24313333578409<14> · 67230905546473<14>
3·1041-1 =
299999999999999999999999999999999999999999<42>
= 7 · 42857142857142857142857142857142857142857<41>
3·1042-1 =
2999999999999999999999999999999999999999999<43>
= 9063097 · 331012677013166691253552731477992567<36>
3·1043-1 =
29999999999999999999999999999999999999999999<44>
= definitely prime number
3·1044-1 =
299999999999999999999999999999999999999999999<45>
= 13 · 594332567 · 10550048513531<14> · 3680390637464286032999<22>
3·1045-1 =
2999999999999999999999999999999999999999999999<46>
= 499 · 6012024048096192384769539078156312625250501<43>
3·1046-1 =
29999999999999999999999999999999999999999999999<47>
= 23 · 1304347826086956521739130434782608695652173913<46>
3·1047-1 =
299999999999999999999999999999999999999999999999<48>
= 7 · 1404819661871<13> · 30507220264887130087041437378722567<35>
3·1048-1 =
2999999999999999999999999999999999999999999999999<49>
= 443 · 757 · 334127 · 26773803868940651228170563387195934487<38>
3·1049-1 =
29999999999999999999999999999999999999999999999999<50>
= 19 · 103 · 1321 · 665293 · 17442737999925077569064711017059757319<38>
3·1050-1 =
299999999999999999999999999999999999999999999999999<51>
= 132 · 431 · 4118672689081398701245212042998942874009802441<46>
3·1051-1 =
2999999999999999999999999999999999999999999999999999<52>
= 1066480229<10> · 1356476046074293<16> · 2073749608604567097036502567<28>
3·1052-1 =
29999999999999999999999999999999999999999999999999999<53>
= 390621169 · 72645380763102632869<20> · 1057200780089282053600259<25>
3·1053-1 =
299999999999999999999999999999999999999999999999999999<54>
= 7 · 17 · 6132679193<10> · 679927496140561<15> · 604590671733065589907762577<27>
3·1054-1 =
2999999999999999999999999999999999999999999999999999999<55>
= 3217 · 1390016294869897<16> · 670888430310272971761577811789656151<36>
3·1055-1 =
29999999999999999999999999999999999999999999999999999999<56>
= definitely prime number
3·1056-1 =
299999999999999999999999999999999999999999999999999999999<57>
= 13 · 83 · 4331167543529607187088879<25> · 64194057375964295426367330839<29>
3·1057-1 =
2999999999999999999999999999999999999999999999999999999999<58>
= 29 · 1136834253520662461<19> · 90996797063160225886700832599613151271<38>
3·1058-1 =
29999999999999999999999999999999999999999999999999999999999<59>
= 6686869667<10> · 52776674411<11> · 626931419603<12> · 135592709679897593746997509<27>
3·1059-1 =
299999999999999999999999999999999999999999999999999999999999<60>
= 7 · 19531 · 641317 · 3421574356367246644163949706650392458891569799391<49>
3·1060-1 =
2999999999999999999999999999999999999999999999999999999999999<61>
= 743 · 808716498647<12> · 1057972676861663008729<22> · 4719127225971742808162711<25>
3·1061-1 =
29999999999999999999999999999999999999999999999999999999999999<62>
= 71 · 422535211267605633802816901408450704225352112676056338028169<60>
3·1062-1 =
299999999999999999999999999999999999999999999999999999999999999<63>
= 13 · 23076923076923076923076923076923076923076923076923076923076923<62>
3·1063-1 =
2999999999999999999999999999999999999999999999999999999999999999<64>
= 1728967 · 7703231 · 1605051241<10> · 140337174186780324552365181567296961903007<42>
3·1064-1 =
29999999999999999999999999999999999999999999999999999999999999999<65>
= 277 · 108303249097472924187725631768953068592057761732851985559566787<63>
3·1065-1 =
299999999999999999999999999999999999999999999999999999999999999999<66>
= 7 · 611704123343575338233723<24> · 70061883223682835822554541457490468968459<41>
3·1066-1 =
2999999999999999999999999999999999999999999999999999999999999999999<67>
= 503 · 15763439 · 50162659539371570232061<23> · 7542611608385988025064828485248227<34>
3·1067-1 =
29999999999999999999999999999999999999999999999999999999999999999999<68>
= 19 · 107 · 15920843 · 10644771958592162966987<23> · 87072588295411188803975078531858983<35>
3·1068-1 =
299999999999999999999999999999999999999999999999999999999999999999999<69>
= 13 · 23 · 1003344481605351170568561872909698996655518394648829431438127090301<67>
3·1069-1 =
2999999999999999999999999999999999999999999999999999999999999999999999<70>
= 17 · 36493 · 329860332209700670780056854383<30> · 14659956248770104285450993620607013<35>
3·1070-1 =
29999999999999999999999999999999999999999999999999999999999999999999999<71>
= 661 · 434132891 · 637935136493979035228233<24> · 163877972349517148682713565578488753<36>
3·1071-1 =
299999999999999999999999999999999999999999999999999999999999999999999999<72>
= 72 · 2371 · 2582222260477366821886915879806161182313498997237022181289217500581<67>
3·1072-1 =
2999999999999999999999999999999999999999999999999999999999999999999999999<73>
= 4188054211417<13> · 4267778689730745828517<22> · 167844482547367204773786131605885255691<39>
3·1073-1 =
29999999999999999999999999999999999999999999999999999999999999999999999999<74>
= 373 · 275676723385625913658191645377<30> · 291750980771364417216161647598876663509219<42>
3·1074-1 =
299999999999999999999999999999999999999999999999999999999999999999999999999<75>
= 13 · 47 · 1069 · 367823 · 90855262284385309<17> · 13744007092186107278415663200174774248999883123<47>
3·1075-1 =
2999999999999999999999999999999999999999999999999999999999999999999999999999<76>
= 757 · 51378297061009<14> · 1405847460733497973<19> · 54866526792220496038143451174747976388551<41>
3·1076-1 =
29999999999999999999999999999999999999999999999999999999999999999999999999999<77>
= 2402214527<10> · 135999956282039<15> · 91827063621559306927394843586328922240326571839259783<53>
3·1077-1 =
299999999999999999999999999999999999999999999999999999999999999999999999999999<78>
= 7 · 23677 · 4275127 · 4369427 · 3621327289<10> · 247502724582139745843<21> · 108112340743472502401674533227<30>
3·1078-1 =
2999999999999999999999999999999999999999999999999999999999999999999999999999999<79>
= 61 · 1427 · 2713 · 5410076687<10> · 4849502882804430492203<22> · 484191331287271863114267578513481652669<39>
3·1079-1 =
29999999999999999999999999999999999999999999999999999999999999999999999999999999<80>
= 293611531788139<15> · 102175823331241199704581398426177346644437517656619757456424151741<66>
3·1080-1 =
299999999999999999999999999999999999999999999999999999999999999999999999999999999<81>
= 13 · 109 · 502441 · 394460147 · 121000994263045222745790261071<30> · 8828242660013348139969025855696091<34>
3·1081-1 =
2999999999999999999999999999999999999999999999999999999999999999999999999999999999<82>
= 198347 · 580610829637<12> · 546035880317951<15> · 47707790680126762810965842706145250687293836957191<50>
3·1082-1 =
29999999999999999999999999999999999999999999999999999999999999999999999999999999999<83>
= 3623 · 1179592811783<13> · 81901814233106783<17> · 85709168379882713447112804288382078260973732635217<50>
3·1083-1 =
299999999999999999999999999999999999999999999999999999999999999999999999999999999999<84>
= 7 · 103 · 2917 · 2092564310751650241184817<25> · 55817750862408931155328183<26> · 1221232670144955999083128837<28>
3·1084-1 =
2999999999999999999999999999999999999999999999999999999999999999999999999999999999999<85>
= 59 · 3037200296737<13> · 16741555597023462687292691535071815284183972598585064174887691519199853<71>
3·1085-1 =
29999999999999999999999999999999999999999999999999999999999999999999999999999999999999<86>
= 17 · 19 · 29 · 223 · 977 · 6563 · 14653 · 152859471551123480004843160977546975097365506330010478081244364258113<69>
3·1086-1 =
299999999999999999999999999999999999999999999999999999999999999999999999999999999999999<87>
= 13 · 17309375399<11> · 1207510782643354586857133772644363<34> · 1104092571873395520541318241400785866473479<43>
3·1087-1 =
2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<88>
= 2741 · 964927 · 394211670918873961<18> · 2877320783415929720655717276789004987147764455948869723172437<61>
3·1088-1 =
29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<89>
= 1304488873<10> · 3300924483140581825965792499050421<34> · 6966991598609698357143166308824300493706869803<46> (Robert Backstrom / GMP-ECM 5.1-beta)
3·1089-1 =
299999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<90>
= 7 · 12594245972471028228269<23> · 186182086789309759054543090955981<33> · 18277346698490628671886518504139713<35>
3·1090-1 =
2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<91>
= 23 · 416998450980192814055629<24> · 312794405595744596969514780116162611260899355352176462266677835197<66>
3·1091-1 =
29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<92>
= 1597 · 184553 · 446028257 · 14076488831<11> · 16212071708719648632278491157629276678664053603353596806375780717<65>
3·1092-1 =
299999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<93>
= 13 · 2473 · 8354651 · 1116928758657913030746751251796032617863380560312387775178668625667297149218675001<82>
3·1093-1 =
2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<94>
= 503699641 · 48503123144589502741752878729057<32> · 122794781146491779173462117695893007175726748617613527<54>
3·1094-1 =
29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<95>
= 97 · 380774519116859555009563691113510103<36> · 812234892273730400146403072480506371926158526721772968889<57>
3·1095-1 =
299999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<96>
= 7 · 157 · 7544219843<10> · 14044244326009837<17> · 2576385525477167077559755888656850563188888467559516732456150855611<67>
3·1096-1 =
2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<97>
= 71 · 225175496540201364974370054300058530191<39> · 187647065404458407478575579255133377195945562460800825959<57>
3·1097-1 =
29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<98>
= 832 · 1129 · 6823 · 23264344193<11> · 18929164970412319489<20> · 1283729395505707376279023867054907059411215130486873257049<58>
3·1098-1 =
299999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<99>
= 13 · 1019 · 187379 · 376657 · 2065995084482425229722350759373801066391<40> · 155312880582011749094355956606205409844262829<45> (Robert Backstrom / PPSIQS Ver 1.1)
3·1099-1 =
2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999<100>
= 345221647 · 477752776081611404646500077456166023<36> · 18189468758616411279538180668857592713662364213329197479<56> (Robert Backstrom / PPSIQS Ver 1.1)
3·10100-1 =
2(9)100<101>
= 30908839729<11> · 52687875503<11> · 18421621929042446518945642871526259144172571872058046358421612697832167819925377<80>
3·10101-1 =
2(9)101<102>
= 7 · 17 · 461 · 42703 · 128060437587372995319339355138356780636701102819820530493717889157422282840645351747588735187<93>
3·10102-1 =
2(9)102<103>
= 757 · 341667013 · 11599047429948021078058597960005614850022606973185675972655317149495105361550724254328327239<92>
3·10103-1 =
2(9)103<104>
= 19 · 60083 · 23917741750007011930592110720920008759435096557<47> · 1098742369919843494185783706649927078558709517031491<52> (Makoto Kamada / SNFS / 5:47:41:70)
3·10104-1 =
2(9)104<105>
= 13 · 347 · 1321 · 133881109 · 2813505323<10> · 15058978723753<14> · 8380200882966911<16> · 32926128941294964210169<23> · 32165325017020156619259454561<29>
3·10105-1 =
2(9)105<106>
= 69233 · 43331937082027356896277786604653850042609738130660234281339823494576285875232909161815897043317493103<101>
3·10106-1 =
2(9)106<107>
= 218279 · 137438782475638975806192991538352292249827056198718154288777207152314240032252300954283279655853288681<102>
3·10107-1 =
2(9)107<108>
= 7 · 35491 · 132967 · 3286888271596093<16> · 2762969980683717258321223144209234268699368337958266176306842668501370570391151817<82>
3·10108-1 =
2(9)108<109>
= 479 · 1537022713<10> · 12042349012118749379843<23> · 5580815161537522052816552016371<31> · 60631261945090711190778038575214536541054929<44>
3·10109-1 =
2(9)109<110>
= 941 · 60259 · 78121 · 524086391 · 14770997282202389<17> · 26506062415929309987997152493<29> · 33005323977166274796073777418225748488133943<44>
3·10110-1 =
2(9)110<111>
= 13 · 23076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923<110>
3·10111-1 =
2(9)111<112>
= 966767341958861<15> · 3103125095145859264337050293405093023943285127966189415280642637135368146774978576169338417355259<97>
3·10112-1 =
2(9)112<113>
= 23 · 181 · 3407 · 127103 · 3483791461<10> · 954027040968047<15> · 5006959449134196242766265868072792925075855906976643628238419170429812879439<76>
3·10113-1 =
2(9)113<114>
= 72 · 29 · 8139497 · 183196997235114666313664862887412748867877758421<48> · 141583048280838478129901762617470802340141205501351431287<57> (Sander Hoogendoorn / SNFS)
3·10114-1 =
2(9)114<115>
= 171141301 · 5078181337<10> · 3451900116240059527310349962515641788338540306292431489892874508205404626512683628520178446569627<97>
3·10115-1 =
2(9)115<116>
= 66935581832507131<17> · 448192115145409256752005959887688729242511151091393953380282171310853902822633424231824418287457229<99>
3·10116-1 =
2(9)116<117>
= 13 · 191 · 419 · 342803 · 3080389672652381470662675187786673261869<40> · 273073929335371915922432805053316071687914686044309883829457031841<66> (Sander Hoogendoorn)
3·10117-1 =
2(9)117<118>
= 17 · 103 · 7717 · 1343893 · 698810987349616407838127758561787<33> · 236408012483724037920438356017353423704940485863994051049626928720839267<72> (Sander Hoogendoorn)
3·10118-1 =
2(9)118<119>
= 1801 · 2322347 · 269136729617782632743<21> · 525337354976588234359540934329<30> · 50730503927128935534261432720820845779278829698082773940411<59>
3·10119-1 =
2(9)119<120>
= 7 · 7141775796359<13> · 6000908468590146007802970302085578213299657647019234436854511092567500093029441038440754743913961970037423<106>
3·10120-1 =
2(9)120<121>
= 47 · 107 · 587 · 44209021499<11> · 11890818970927053203<20> · 2047296729179266187110579273833644931841<40> · 944274051192262206631103925845322418206838969<45>
3·10121-1 =
2(9)121<122>
= 19 · 695084724889<12> · 2271589796011125260933021182971065840770325771072812443357936760347860632353214061224348430869129003298879789<109>
3·10122-1 =
2(9)122<123>
= 13 · 2294796717664213509541276266917758467689777187014509<52> · 10056194912293669804719011098323636255061719884507348567986171070655047<71> (Makoto Kamada / GGNFS-0.70.0 / 3.39 hours)
3·10123-1 =
2(9)123<124>
= 2990366970937067399<19> · 1003221353484891513387954898308810381727983558088177158306275171844453418150696067538783658365482703827401<106>
3·10124-1 =
2(9)124<125>
= 2602864396977816164601828457<28> · 11525763706642949500110430345615582532053120160077139973457388941551304686760716557918497750074407<98>
3·10125-1 =
2(9)125<126>
= 7 · 3599650081<10> · 31612646761<11> · 3876544332029444008036492867365402990466431683<46> · 97153246083586305759374376504412500632762391535023918322219<59> (Sander Hoogendoorn / GGNFS)
3·10126-1 =
2(9)126<127>
= 179 · 2927 · 292983186719575321<18> · 5647443464815144203568297<25> · 3460596075084905650466669068797064557997911238583417117155774526018030889091019<79>
3·10127-1 =
2(9)127<128>
= 148738622029916094823<21> · 201696100115584238393124824460099143584753960141821190136295028657532443918821279751573958245772262039795113<108>
3·10128-1 =
2(9)128<129>
= 132 · 227 · 541 · 601 · 148983787999561869461523139665361324139<39> · 161435091255666683067612614137458155297916999164385294636452087869504653287195627<81> (Makoto Kamada / GGNFS-0.77.1 / 3.83 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 5, 2005)
3·10129-1 =
2(9)129<130>
= 757 · 3862845783794364415817<22> · 4154462659947867699343214598881767<34> · 246946653468267095788453656414425393826920686199248335419564218437793213<72> (Makoto Kamada / GMP-ECM 5.0.3 B1=400000, sigma=2577217194 for P34)
3·10130-1 =
2(9)130<131>
= 176410843726584853883407743387462128062837<42> · 170057573368314684049302929168844425493413216950195208787238174395441995530703625941928227<90> (Sander Hoogendoorn / GGNFS)
3·10131-1 =
2(9)131<132>
= 7 · 71 · 2281 · 151813 · 977057 · 18215699449<11> · 168678924343<12> · 85892292823905156190531<23> · 546893930756919181751220197647<30> · 12360804653411226627683395388566345189673<41>
3·10132-1 =
2(9)132<133>
= 1823 · 751446263 · 2189962393226079924195568697698785877427193914407518505622793919738599146505349576421961755644686047247091066773551414951<121>
3·10133-1 =
2(9)133<134>
= 17 · 277 · 947 · 63911747 · 284800447 · 1908595079<10> · 308272668350011<15> · 628163081468531196471678625762635108684284589253543477082381703073219111516811871677753<87>
3·10134-1 =
2(9)134<135>
= 13 · 23 · 131 · 50237491883<11> · 74611295693503631<17> · 6270336254236758322137851221<28> · 325878274972959912313450677639337986912758521683301002776370480401214035687<75>
3·10135-1 =
2(9)135<136>
= 9661029311<10> · 2737810280944238993239874575304072948881248252017519<52> · 113421269769628317461074177992926273808105712904085317777627767022874178511<75> (Makoto Kamada / GGNFS-0.77.1 / 5.63 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 6, 2005)
3·10136-1 =
2(9)136<137>
= 835817364193303896837129099287216945204282453961493<51> · 35893008790209509851297098644911189995904355230294598135551859369093208362424725320643<86> (Anton Korobeynikov / GGNFS-0.72.10 / 16.41 hours)
3·10137-1 =
2(9)137<138>
= 7 · 487 · 1050233 · 6621524008283<13> · 42100336899241<14> · 300583449314555435059595288664414400507392811785133653676322034725504693698971499976681413695127808189<102>
3·10138-1 =
2(9)138<139>
= 61 · 83 · 2617 · 58211 · 123215977 · 18301389014578223<17> · 1879512152331664267523<22> · 413385011612455959639469<24> · 1643961787701703715784696623<28> · 1350398306002428325645695676549<31>
3·10139-1 =
2(9)139<140>
= 19 · 233 · 18257 · 3189010880100257960332198816490123216053698925938885318275266097<64> · 116392853688224551320628030044644926368910927741779050815872100922653<69> (Makoto Kamada / GGNFS-0.77.1 / 11.04 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 6, 2005)
3·10140-1 =
2(9)140<141>
= 13 · 1043951 · 26883947 · 182071650990950202615387530626934743348640561028796729<54> · 4516088321889703271038563016128691273952825632884219310105789502309547671<73> (Makoto Kamada / GGNFS-0.77.1 / 8.19 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 10, 2005)
3·10141-1 =
2(9)141<142>
= 29 · 12049787588762983115267162180707134919286653<44> · 8585070491909711967989582026822386992430936673986287924871109410890430123873686351241585281361127<97> (Makoto Kamada / GGNFS-0.77.1 / 7.74 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 10, 2005)
3·10142-1 =
2(9)142<143>
= 59 · 1667 · 93717112244395171896790558091<29> · 3254728338396397350299417788498932335144337966986383779784082085195537945799463747173648638531505035959656813<109> (Tetsuya Kobayashi / GMP-ECM 5.0.3)
3·10143-1 =
2(9)143<144>
= 7 · 368161095989<12> · 2773039137463081<16> · 24566776282235900088908433900766498349491<41> · 1708760320079077756989239124726576953642075628982585485036155402183550090703<76> (Makoto Kamada / GGNFS-0.77.1 / 14.68 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 11, 2005)
3·10144-1 =
2(9)144<145>
= 114960971 · 2213287753<10> · 108090137887270909297090797793<30> · 109080439628348269202774046214310086366771298172396864071466868126105645656536199141927505676107861<99> (Tetsuya Kobayashi / GMP-ECM 5.0.3 B1=1000000)
3·10145-1 =
2(9)145<146>
= 113 · 1051 · 115336553 · 2287852509381529362215874023304871802874572090778188945277943<61> · 957293486672798203907184531262070219175708798167529171237812739812913587<72> (Makoto Kamada / GGNFS-0.77.1 / 11.34 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 12, 2005)
3·10146-1 =
2(9)146<147>
= 13 · 493573 · 18325201302275702459091151740961<32> · 2551395316378933371196249242159398075810419408174368073290161677105829014102810175513071204192402345218026591<109> (Makoto Kamada / GMP-ECM 5.0.3 B1=450000, sigma=3350150933 for P32)
3·10147-1 =
2(9)147<148>
= 2515313 · 4380884647177105247767<22> · 272249694675382115672371457148969342652091706433155665804841695191724637927901103092611354783625552190520929023861944169<120>
3·10148-1 =
2(9)148<149>
= 5698826293<10> · 120232877212186884433<21> · 123074961607917110161534951484159374642729<42> · 355748343355447265512908734948080985968709118990801171190063642693710339565499<78> (Makoto Kamada / GGNFS-0.77.1 / 28.55 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / May 14, 2005)
3·10149-1 =
2(9)149<150>
= 7 · 17 · 1249 · 3803 · 29983 · 47363 · 59021 · 25970585924786847027298660631<29> · 243827637273805306729808414600327800876310711471007497576365833251559647434564618561961895558734917<99> (Tetsuya Kobayashi / GMP-ECM 5.0.3)
3·10150-1 =
2(9)150<151>
= 383399 · 23802994718148901<17> · 328729499631075215103914984155771879133819146534222325019886723795831518647675685691088397349572871406691314755646056939225744501<129>
3·10151-1 =
2(9)151<152>
= 103 · 15607 · 35159 · 14094323 · 803919452098002873794823857201688324440053056001<48> · 46845872075351073831628759072931045137614880228706167557837224075618406020863534117667<86> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 / 32.36 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Jun 15, 2006)
3·10152-1 =
2(9)152<153>
= 13 · 263 · 87744954665106756361509213220239836209417958467388125182801988885639075753144194208832992102954080140391927464170810178414741152383737935068733547821<149>
3·10153-1 =
2(9)153<154>
= 72019 · 1472927109551<13> · 6437899768974245773<19> · 45425367911692522245626027985214885364243<41> · 96705293648696981037155654696825961344230797647139452351613239823428072265389<77> (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=4238945311 for P41 / Sep 7, 2005)
3·10154-1 =
2(9)154<155>
= 169973521 · 3541566709633<13> · 62282513633822346544465252554897044469175211<44> · 800162926125406274759982565017119197917086497848155175255046781462749015168218472947165613<90> (Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 / 63.81 hours on Pentium 4 3.20 GHz, 1 Gig RAM, Windows XP and Cygwin / Mar 17, 2007)
3·10155-1 =
2(9)155<156>
= 72 · 844643 · 159010443754010418818537<24> · 5423853441107577188852485479594908047413233<43> · 8404625993321570476494919510450078586561494231252473102406403901939727050282602317<82> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 27.74 hours on Cygwin on AMD XP 2700+ / Mar 16, 2007)
3·10156-1 =
2(9)156<157>
= 232 · 757 · 37958325803<11> · 34508927160252119290871470429799344288040408510935452205656946628557<68> · 5719146168209700929932117892283471025039070385347664045593119483067546173<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 29.42 hours on Cygwin on AMD XP 2700+ / Apr 14, 2007)
3·10157-1 =
2(9)157<158>
= 19 · 409 · 8669 · 1478382377561711<16> · 301223302549621999298659687439059017007707324952067882550054765883129452999327273835105189723866856348822058327855755819455471102120191<135>
3·10158-1 =
2(9)158<159>
= 13 · 8713 · 5289083 · 695325459814498871<18> · 8252373899553049676093269<25> · 998030902239641757418958240703001<33> · 87441739575224379973751656500118777910978931283986448286477478905281163<71> (Anton Korobeynikov / GGNFS-0.77.1 gnfs for P33 x P71 / 13.78 hours / May 27, 2005)
3·10159-1 =
2(9)159<160>
= 1321 · 6967 · 398760584767619777<18> · 1365996837467415111026906770750469<34> · 598426350404332450433128876484310209991358869759713755798077815328602741567697247226824883321819832989<102> (Jo Yeong Uk / GMP-ECM 6.1.2 B1=1000000, sigma=2625841172 for P34 / Jul 11, 2007)
3·10160-1 =
2(9)160<161>
= 3119 · 62171 · 716003 · 80479894854409<14> · 22773127470380768369771978355584433053642892841637684786821<59> · 117894381311324651726376382743763178993218466198694259251340381195966953253<75> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.28 / Nov 2, 2007)
3·10161-1 =
2(9)161<162>
= 7 · 445307 · 12654241 · 4753427389819<13> · 1600002742222315874207495930489789942851093204466890859980649901635579490615534553038031986322050491140769704228139579001336217079639569<136>
3·10162-1 =
2(9)162<163>
= 1586308304691323221318531843777<31> · 152512406662190891155427973892329217<36> · 12400194079641198397538641885769926694273799859212033454948583982801438301040530455353496340235711<98> (Makoto Kamada / GMP-ECM 6.0 B1=36000000, sigma=757237952 for P31 / Mar 19, 2005) (Wataru Sakai / GMP-ECM 6.0.1 B1=110000000, sigma=1534915970 for P38 / Jan 5, 2006)
3·10163-1 =
2(9)163<164>
= 997 · 2287 · 45747879641691574163746483574403221719068934066339<50> · 287600053136766851692762111657822054428122201049566171614253119368688303514147608918518033049860541686054719<108> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 63.42 hours on Cygwin on AMD 64 3200+ / Jul 24, 2007)
3·10164-1 =
2(9)164<165>
= 13 · 2591 · 20864331285956384714363476632186247632145067881<47> · 16745773198975668201316866017478902963614694091371<50> · 25491818321127692702503378138106307806982680946323585329451086103<65> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 / 125.82 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Jul 7, 2007)
3·10165-1 =
2(9)165<166>
= 17 · 563 · 10366352216620195513339<23> · 32537822232223537739373298666992795881162109492993066147359<59> · 929286216648341931114487283109312466413415118752186358498797622230367374713700369<81> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp snfs, Msieve 1.33 / Feb 6, 2008)
3·10166-1 =
2(9)166<167>
= 47 · 71 · 2667289 · 10991159 · 627960539 · 2137781721901653563<19> · 10345389693582740479529989859541374220406006881752101849<56> · 22080500640751102476087504432625828948573909939464280318314247588489<68> (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=3068145495 for P56 / Sep 14, 2005)
3·10167-1 =
2(9)167<168>
= 7 · 7643 · 5308447 · 22854213927330216399615920416772214007<38> · 39688758719895871031552328771144713882109670630545445702193<59> · 1164549798963657623144995222566231913164712125722393092919267<61> (Wataru Sakai / GMP-ECM 6.0.1 B1=110000000, sigma=2117868705 for P38 / Jan 5, 2006) (Sinkiti Sibata / GGNFS-0.77.1 gnfs for P59 x P61 / 127.93 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Mar 9, 2006)
3·10168-1 =
2(9)168<169>
= 1812361 · 130589868517<12> · 5316091494767<13> · 175320276174094299158123<24> · 14218271534104519162365193<26> · 7346438825607067443755539899769423966309<40> · 130202342717147930171665152085069493289786784935131<51> (Makoto Kamada / msieve 0.87 / 3.4 hours for P40 x P51)
3·10169-1 =
2(9)169<170>
= 29 · 257 · 1187 · 893281 · 162352619114966156197<21> · [23382557913863687360210358549889939699253493723541318867971867107182684122332981322256389039762608813026488643802138025103343450876035237<137>] SUBMIT/RESERVE
3·10170-1 =
2(9)170<171>
= 13 · 5783 · 173013747441272949252140271307882198468644836377812061<54> · 23064502808650629916626080541133445738284945384523360813873885767965239712427790623664167124028559969692067948321<113> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 83.81 hours on Cygwin on AMD 64 3200+ / May 26, 2007)
3·10171-1 =
2(9)171<172>
= 727 · 111443 · 75309234594877<14> · 1030775741943931673<19> · [477003566452786389911877468453776625956725654131330694818959918237745129415207167148176672507358290335561961809131023352008434233079<132>] SUBMIT/RESERVE
3·10172-1 =
2(9)172<173>
= 38122987748499595028686163894145203<35> · [786926780186075758268741106446345233058414651262593009833784935602647827417065446546566009104898212188196236218414523309890529326286496133<138>] (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=111443754 for P35 / Sep 1, 2005) SUBMIT/RESERVE
3·10173-1 =
2(9)173<174>
= 7 · 107 · 157 · 3013176114760906824959<22> · 3438554741560059188437<22> · 30644010457996651884427900089832310981<38> · 1965123061305630337817335362597030221689<40> · 4088876295547466384808084321913583821345407444169<49> (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=1547437923 for P38, Msieve 1.01 for P40 x P49 / Aug 31, 2005)
3·10174-1 =
2(9)174<175>
= 166087909788096950834522423<27> · [18062723553012053659512862987893876280483835577393700324705380850483733185155234049468881141228481012368229092117049920534892184452140953606048539513<149>] SUBMIT/RESERVE
3·10175-1 =
2(9)175<176>
= 19 · 1358197 · 127908438358629022538945818383105074917390387700273693347951544125819<69> · 9088782074048181389749646028623925455114377328452874707792183747630337777668429784177679834126974147<100> (matsui / GGNFS-0.77.1-20060513-prescott snfs / 170.28 hours / May 27, 2008)
3·10176-1 =
2(9)176<177>
= 13 · 58742557 · [392848460391723787629417001321938997702754462610864503618337946659745794230185163320743373889511195042515376425934660571944066430014666827034392171197502977663654019639<168>] SUBMIT/RESERVE
3·10177-1 =
2(9)177<178>
= 311 · 116471 · 1402627451282133493<19> · [59047392893160869043607199325076222570768127309080308034366074617573380127309180479637247193714433698078123225234200167427666412839137529216792714585203<152>] SUBMIT/RESERVE
3·10178-1 =
2(9)178<179>
= 23 · 28871 · 950809 · 3670957 · 6486841 · 20123971618573<14> · [99154416116749536613833960946915313870286305565293496539549511674257280995516346625540083524497935293003719656030483300925526737113890395767<140>] SUBMIT/RESERVE
3·10179-1 =
2(9)179<180>
= 7 · 83 · 269 · 8731 · 81853 · 116981 · 341557 · 12603850771<11> · 40741126949<11> · 135924365039<12> · 65229101266939367735801851025243606155752420471073669310383<59> · 14765247618055126790247356701740302955486828755600519733418471207<65> (matsui / GGNFS-0.77.1-20060513-pentium4 gnfs for P59 x P65 / Feb 16, 2008)
3·10180-1 =
2(9)180<181>
= 572624573272440906246891681503<30> · [5239034683502261512217266544200832044977356842743189184376130950310853527047649101007537456670565558710101254243540624698650299081238828416459698436833<151>] (Makoto Kamada / GMP-ECM 6.0 B1=16000000, sigma=2663771591 for P30 / Mar 20, 2005) SUBMIT/RESERVE
3·10181-1 =
2(9)181<182>
= 17 · 149 · 67651 · 175070045379264539259437251461445348065890039216448801818566940450735222120090896600987641321136218833541784373309607529547899173169269046904608994971714020303094918024122353<174>
3·10182-1 =
2(9)182<183>
= 13 · 1307 · 3253 · 15313 · 30483181 · 712236001 · 217790685050910667548997<24> · [74960842897132103681852428080646416843208943146159715909272551474037174009562269180153698832515915719138940829286706658162043208493<131>] SUBMIT/RESERVE
3·10183-1 =
2(9)183<184>
= 757 · 705259 · 94685971491169408238495197<26> · 59345951695499727131645089060192058135909213873136735226382733194452511684809704681156559640467203767085254024562482893630526915384657525961066917309<149> (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=517744189 for P26 / Jul 22, 2005)
3·10184-1 =
2(9)184<185>
= 10073641022189321360228001328707180659381468877455557544719139<62> · 2978069194040036330503581914737461793403041082476154833888528931755723356899703483852214198475678536123147506448805613562741<124> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 343.63 hours on Core 2 Quad Q6600 / Sep 12, 2007)
3·10185-1 =
2(9)185<186>
= 7 · 103 · 5419 · 40859069 · 34405086211<11> · 54620506344778751196212174083932539853598979159171505198079512296438983419526842906298190446596589467895874271186208542033563390832223006082042424056219876319739<161>
3·10186-1 =
2(9)186<187>
= 1000926126622857454738657<25> · 169578631674993232722608070359<30> · 5038740629385387262999058978219<31> · 3507729531114303162480919388024654186192017726789378826407554907313223454226891369837005953138455530667<103> (Makoto Kamada / GMP-ECM 5.0.3 B1=400000, sigma=2779326909 for P31) (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=1358866576 for P30 / Jul 30, 2005)
3·10187-1 =
2(9)187<188>
= 337638313967807182936900258849<30> · 99433004049017708218656527004744377<35> · 47527930809248160978423930812756482163<38> · 18801394593718690635972065355070083787495002798358052698294076860191499763907183853901<86> (Makoto Kamada / GMP-ECM 6.0 B1=11000000, sigma=588872100 for P35 / Mar 21, 2005) (Makoto Kamada / GMP-ECM 6.0 B1=13000000, sigma=2468554643 for P30 / Mar 21, 2005) (anonymous / GMP-ECM B1=1000000, sigma=2711386167 for P38 / Jan 27, 2007)
3·10188-1 =
2(9)188<189>
= 13 · 109 · 167 · 769 · 25375234751<11> · 5153248863097<13> · 3749089470469489319<19> · 3362726945702192537278270379287745910169270402907379473520095703855904159132288646009078852590438801004689733992343446479621750210601907473<139>
3·10189-1 =
2(9)189<190>
= 467 · 53231 · 120681235922282410424252068989278960590214915983533769445820098792073350698826821501228716003542718361734522440414343737249273167086349073612617335851494820140105283114760171990070187<183>
3·10190-1 =
2(9)190<191>
= 97 · 29924824213<11> · 247984694771318430568948981693<30> · 7668447060104434870881489582121<31> · 512358733922895524489343752888689<33> · 10607461577425281731753905244766737614406396259890391295260540539167282031764330723127<86> (Makoto Kamada / GMP-ECM 6.0 B1=4000000, sigma=2904675407 for P33 / Mar 28, 2005) (Makoto Kamada / GMP-ECM 6.0 B1=4000000, sigma=3586049989 for P31 / Mar 28, 2005) (Wataru Sakai / GMP-ECM 6.0.1 B1=44000000, sigma=2685518144 for P30 / Sep 13, 2005)
3·10191-1 =
2(9)191<192>
= 7 · 359 · 1301 · 281993 · 2790288133<10> · 23268995217971929<17> · 13515484787040813847<20> · [370812897556704338509590133832163695071597917566000336371183993274408395233490200784926313895161253111564845043776594915089730392839809<135>] SUBMIT/RESERVE
3·10192-1 =
2(9)192<193>
= 179209 · 592154051319954517820401873<27> · 294029254151558642128613500432031<33> · [96147100344714093985880165790142508713790938454554091728820058311092885918809960853895469472773862773301432799536380961132175497<128>] (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=53705871 for P33) SUBMIT/RESERVE
3·10193-1 =
2(9)193<194>
= 19 · 1882472591<10> · 838762474401972650861798055481516772627977863833371814325102897830745962547163252918274564975563762894145974622026976657878272172382120181983904157118943370077801881231942155301549131<183>
3·10194-1 =
2(9)194<195>
= 13 · 1744151 · 2118866528953<13> · 6244392889110125089580580780440747420845559279279194303632447024695108721938978055392965370236240048699212656733908110604978637693204515295186661381098719191277421837118682341<175>
3·10195-1 =
2(9)195<196>
= 12377 · 26641 · 4242465959<10> · [2144553944128461259777982403156803246875030233764787788772260756804252498292781255804248305688539873567816220314997405530013908251499707524258561767735217712828686152785412015873<178>] SUBMIT/RESERVE
3·10196-1 =
2(9)196<197>
= 122344767534061284667205826233542620221024729103782351<54> · 349916959335497159053279727421119255555113601555011417<54> · 700762515289784210874039143325825539548489780330736974377987653994531387998577206825482297<90> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 516.20 hours on Core 2 Quad Q6700 / Oct 3, 2008)
3·10197-1 =
2(9)197<198>
= 72 · 17 · 29 · 310459974207253356569798917<27> · [40001164850322949267202116877001435748940914164768609280109508184346779185483073822845813110708992902199245808876061101423961725002568546450350599960157751339884241871<167>] SUBMIT/RESERVE
3·10198-1 =
2(9)198<199>
= 61 · 7304109398819<13> · [6733240862575855788126000455131138398562461563032705077407339199594400440823080129940917996693737402843780633456155832655094181124192730043729226838332273140405257637543355501673585561<184>] SUBMIT/RESERVE
3·10199-1 =
2(9)199<200>
= 112403 · 277334011 · 1601852971<10> · 252830208606500054458883<24> · [2376230715420405644099040790825456071766775286180604701904756892104926933239051489210649996039224207690221146377023330989100613796750537016047758744439071<154>] SUBMIT/RESERVE
3·10200-1 =
2(9)200<201>
= 13 · 23 · 59 · 17005838671277138484212913100164389773822345672014058159968255767813616008162802562213026472422198288078907091434725922566747916784762768550535683918145229862252706762655178277875403888668442832039<197>

Factorizations
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