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Factorizations
Factorizations of 900...0012008-11-28(Fri) 00:37

Last update

Nov 28, 2008 00:37 JST

Sequence

91, 901, 9001, 90001, 900001, ...

General term

9·10n+1

Room for prime numbers

upper limit of periods: 10000
upper limit of periodical factors: 4294967296
checked terms: 100000000
terms divided by periodical factors: 70854596
room for prime numbers: 29.15%

Prime numbers

  1. 9·103+1 = 9001 is prime.
  2. 9·104+1 = 90001 is prime.
  3. 9·105+1 = 900001 is prime.
  4. 9·109+1 = 9000000001<10> is prime.
  5. 9·1022+1 = 9(0)211<23> is prime.
  6. 9·1027+1 = 9(0)261<28> is prime.
  7. 9·1036+1 = 9(0)351<37> is prime.
  8. 9·1057+1 = 9(0)561<58> is prime.
  9. 9·1062+1 = 9(0)611<63> is prime.
  10. 9·1078+1 = 9(0)771<79> is prime.
  11. 9·10201+1 = 9(0)2001<202> is prime.
  12. 9·10537+1 = 9(0)5361<538> is prime.
  13. 9·10696+1 = 9(0)6951<697> is prime.
  14. 9·10790+1 = 9(0)7891<791> is prime.
  15. 9·10905+1 = 9(0)9041<906> is prime.
  16. 9·101038+1 = 9(0)10371<1039> is prime.
  17. 9·1066886+1 = 9(0)668851<66887> is prime. (Peter Benson / OpenPFGW, Paul Jobling's NewPGen, Yves Gallot's Proth.exe / Dec 31, 2004)
Searched:
References:

Condition

n≤200

Status

Completed up to n=100. (Dec 7, 2004)
Completed up to n=150. (Apr 7, 2007)
The following numbers are not factored yet. (n≤200)
n= 168, 175, 176, 178, 179, 181, 182, 185, 187, 188, 191, 195, 196, 198, 199, 200 (16/200)

Factorization results

9·101+1 =
91
= 7 · 13
9·102+1 =
901
= 17 · 53
9·103+1 =
9001
= definitely prime number
9·104+1 =
90001
= definitely prime number
9·105+1 =
900001
= definitely prime number
9·106+1 =
9000001
= 61 · 147541
9·107+1 =
90000001
= 7 · 13 · 989011
9·108+1 =
900000001
= 409 · 2200489
9·109+1 =
9000000001<10>
= definitely prime number
9·1010+1 =
90000000001<11>
= 113 · 796460177
9·1011+1 =
900000000001<12>
= 634939 · 1417459
9·1012+1 =
9000000000001<13>
= 1072157 · 8394293
9·1013+1 =
90000000000001<14>
= 7 · 13 · 103 · 9602048437<10>
9·1014+1 =
900000000000001<15>
= 1097 · 820419325433<12>
9·1015+1 =
9000000000000001<16>
= 23 · 53 · 7383100902379<13>
9·1016+1 =
90000000000000001<17>
= 29 · 12553 · 286469 · 863017
9·1017+1 =
900000000000000001<18>
= 19 · 47368421052631579<17>
9·1018+1 =
9000000000000000001<19>
= 17 · 173 · 264601 · 11565276061<11>
9·1019+1 =
90000000000000000001<20>
= 7 · 13 · 9642641 · 102566401571<12>
9·1020+1 =
900000000000000000001<21>
= 1669850621<10> · 538970365781<12>
9·1021+1 =
9000000000000000000001<22>
= 101477 · 88690047991170413<17>
9·1022+1 =
90000000000000000000001<23>
= definitely prime number
9·1023+1 =
900000000000000000000001<24>
= 59 · 89 · 419 · 409059485884947929<18>
9·1024+1 =
9000000000000000000000001<25>
= 1277 · 34781 · 202632707706349273<18>
9·1025+1 =
90000000000000000000000001<26>
= 7 · 13 · 989010989010989010989011<24>
9·1026+1 =
900000000000000000000000001<27>
= 876653 · 2462224309<10> · 416953065713<12>
9·1027+1 =
9000000000000000000000000001<28>
= definitely prime number
9·1028+1 =
90000000000000000000000000001<29>
= 53 · 7672134296041<13> · 221335177673237<15>
9·1029+1 =
900000000000000000000000000001<30>
= 169148534693<12> · 5320767345892032557<19>
9·1030+1 =
9000000000000000000000000000001<31>
= 661 · 9338569 · 1458010722709494472789<22>
9·1031+1 =
90000000000000000000000000000001<32>
= 7 · 13 · 487 · 1493 · 28195807 · 48242279334679103<17>
9·1032+1 =
900000000000000000000000000000001<33>
= 16901 · 48817 · 1090834891658648232287453<25>
9·1033+1 =
9000000000000000000000000000000001<34>
= 47 · 909983219 · 1065587651<10> · 197479531885607<15>
9·1034+1 =
90000000000000000000000000000000001<35>
= 17 · 41043601 · 128987650159127692753171553<27>
9·1035+1 =
900000000000000000000000000000000001<36>
= 19 · 1289 · 36477404545339<14> · 1007423463151225049<19>
9·1036+1 =
9000000000000000000000000000000000001<37>
= definitely prime number
9·1037+1 =
90000000000000000000000000000000000001<38>
= 72 · 13 · 23 · 87407 · 197339 · 356136186044107373212487<24>
9·1038+1 =
900000000000000000000000000000000000001<39>
= 272429779957429<15> · 3303603593339310073120669<25>
9·1039+1 =
9000000000000000000000000000000000000001<40>
= 38201 · 235595926808198738252925316091201801<36>
9·1040+1 =
90000000000000000000000000000000000000001<41>
= 4129 · 51103721909<11> · 426525592954465283837529341<27>
9·1041+1 =
900000000000000000000000000000000000000001<42>
= 53 · 31081 · 546350892039242563405538662520875157<36>
9·1042+1 =
9000000000000000000000000000000000000000001<43>
= 1032841 · 200569872671203969<18> · 43445354086585722169<20>
9·1043+1 =
90000000000000000000000000000000000000000001<44>
= 7 · 13 · 1652393935719810859<19> · 598532206897841844839929<24>
9·1044+1 =
900000000000000000000000000000000000000000001<45>
= 29 · 97 · 313 · 8641 · 11813 · 16493429 · 607146191816885557369397<24>
9·1045+1 =
9000000000000000000000000000000000000000000001<46>
= 1303 · 5532177317<10> · 10909587209<11> · 114444172630926939804739<24>
9·1046+1 =
90000000000000000000000000000000000000000000001<47>
= 40697 · 2211465218566479101653684546772489372681033<43>
9·1047+1 =
900000000000000000000000000000000000000000000001<48>
= 103 · 8737864077669902912621359223300970873786407767<46>
9·1048+1 =
9000000000000000000000000000000000000000000000001<49>
= 2098659371971387633<19> · 4288452009029840199691181281297<31>
9·1049+1 =
90000000000000000000000000000000000000000000000001<50>
= 7 · 13 · 87339225260767<14> · 11323789351899085812386611845621133<35>
9·1050+1 =
900000000000000000000000000000000000000000000000001<51>
= 17 · 185177 · 285894989499712357874453344955494091662380889<45>
9·1051+1 =
9000000000000000000000000000000000000000000000000001<52>
= 5303 · 1697152555157458042617386385065057514614369224967<49>
9·1052+1 =
90000000000000000000000000000000000000000000000000001<53>
= 535637 · 28064609683944217<17> · 5987050673047259348191289748869<31>
9·1053+1 =
900000000000000000000000000000000000000000000000000001<54>
= 19 · 317 · 373 · 621654619 · 644423915856720982631763433468126261601<39>
9·1054+1 =
9000000000000000000000000000000000000000000000000000001<55>
= 53 · 8788913350268140529281<22> · 19321082594304586677823683769757<32>
9·1055+1 =
90000000000000000000000000000000000000000000000000000001<56>
= 7 · 13 · 20325049727<11> · 48659708207118277767203565032192406157797293<44>
9·1056+1 =
900000000000000000000000000000000000000000000000000000001<57>
= 22349 · 40270258177099646516622667680880576312139245603830149<53>
9·1057+1 =
9000000000000000000000000000000000000000000000000000000001<58>
= definitely prime number
9·1058+1 =
90000000000000000000000000000000000000000000000000000000001<59>
= 2836549 · 19745953963988218120980173<26> · 1606845419421940062477406913<28>
9·1059+1 =
900000000000000000000000000000000000000000000000000000000001<60>
= 232 · 223 · 433241 · 17609718952061731403087007685427467197151800957383<50>
9·1060+1 =
9000000000000000000000000000000000000000000000000000000000001<61>
= 52069729 · 165220125649<12> · 2903138521729<13> · 360351625548496622538364964689<30>
9·1061+1 =
90000000000000000000000000000000000000000000000000000000000001<62>
= 7 · 132 · 173 · 3889314411127<13> · 113067713261508411500006922947650419833838557<45>
9·1062+1 =
900000000000000000000000000000000000000000000000000000000000001<63>
= definitely prime number
9·1063+1 =
9000000000000000000000000000000000000000000000000000000000000001<64>
= 1846367 · 6443011 · 756546466489705346851565812353711496009046424433973<51>
9·1064+1 =
90000000000000000000000000000000000000000000000000000000000000001<65>
= 509 · 16715162760707934917<20> · 10578257079088291910027606345457172703854417<44>
9·1065+1 =
900000000000000000000000000000000000000000000000000000000000000001<66>
= 4721 · 7459 · 25558060971253457331200579406921787420600688835179728118459<59>
9·1066+1 =
9000000000000000000000000000000000000000000000000000000000000000001<67>
= 17 · 61 · 537684018665889709<18> · 16141229955383838954779796325035290472200075897<47>
9·1067+1 =
90000000000000000000000000000000000000000000000000000000000000000001<68>
= 7 · 13 · 53 · 89 · 967 · 216824706300274768218062939196360764018857398893392710120649<60>
9·1068+1 =
900000000000000000000000000000000000000000000000000000000000000000001<69>
= 1937018929<10> · 464631494574310378357691309892201884620818798410410371369169<60>
9·1069+1 =
9000000000000000000000000000000000000000000000000000000000000000000001<70>
= 223849 · 8854438717133<13> · 56519161534037<14> · 80339773672359894075979909433788068169<38>
9·1070+1 =
90000000000000000000000000000000000000000000000000000000000000000000001<71>
= 177481 · 507096534276908514150810509293952592108451045464021500893053340921<66>
9·1071+1 =
900000000000000000000000000000000000000000000000000000000000000000000001<72>
= 19 · 1021624687<10> · 1127992566528760154341995397<28> · 41104681929792392767439545550068561<35>
9·1072+1 =
9000000000000000000000000000000000000000000000000000000000000000000000001<73>
= 29 · 1193737 · 369568350763637<15> · 3803265121978231417<19> · 184962839464472374696671097901953<33>
9·1073+1 =
90000000000000000000000000000000000000000000000000000000000000000000000001<74>
= 7 · 13 · 131 · 157 · 3434714219<10> · 40505281728310780921<20> · 345643109794933143493746424616869980967<39>
9·1074+1 =
900000000000000000000000000000000000000000000000000000000000000000000000001<75>
= 26513 · 33945611586768754950401689737110096933579753328555802813714027081054577<71>
9·1075+1 =
9000000000000000000000000000000000000000000000000000000000000000000000000001<76>
= 761 · 27259 · 770146331600773683360157<24> · 563345308535846414525123654230410396421566407<45>
9·1076+1 =
90000000000000000000000000000000000000000000000000000000000000000000000000001<77>
= 39191309 · 2296427506414751290904827904574455525330883946744417238015703940891589<70>
9·1077+1 =
900000000000000000000000000000000000000000000000000000000000000000000000000001<78>
= 797 · 997 · 1347545921<10> · 840514975997107693570604695977849746413871622498980856073069009<63>
9·1078+1 =
9000000000000000000000000000000000000000000000000000000000000000000000000000001<79>
= definitely prime number
9·1079+1 =
90000000000000000000000000000000000000000000000000000000000000000000000000000001<80>
= 72 · 13 · 47 · 1361 · 939179 · 362132527 · 6494282636470574357798239086613389616047164558265238476143<58>
9·1080+1 =
900000000000000000000000000000000000000000000000000000000000000000000000000000001<81>
= 53 · 7228517 · 8649300328437453436924860432196733<34> · 271604183953600044068617132843666403597<39> (Makoto Kamada / msieve 0.83 / 3.2 minutes)
9·1081+1 =
9000000000000000000000000000000000000000000000000000000000000000000000000000000001<82>
= 23 · 59 · 103 · 9539 · 15569 · 433572640799482999983753283405797953951283348120523679061716819187841<69>
9·1082+1 =
90000000000000000000000000000000000000000000000000000000000000000000000000000000001<83>
= 17 · 197 · 4373989 · 444342046542949<15> · 3671809354584061<16> · 3765755685692309199255513351359290351036969<43>
9·1083+1 =
900000000000000000000000000000000000000000000000000000000000000000000000000000000001<84>
= 73235077 · 82599773 · 43082588561<11> · 3453366913153286556653523424034883035479542624501723609121<58>
9·1084+1 =
9000000000000000000000000000000000000000000000000000000000000000000000000000000000001<85>
= 1229 · 166349 · 7272783344894506752237530908390190689<37> · 6052987567340882018702428727084789529529<40> (Makoto Kamada / GGNFS-0.70.1 / 0.13 hours)
9·1085+1 =
90000000000000000000000000000000000000000000000000000000000000000000000000000000000001<86>
= 7 · 13 · 52301303 · 18909872838368654237715855549736284982976638058347972917405346268543042053637<77>
9·1086+1 =
900000000000000000000000000000000000000000000000000000000000000000000000000000000000001<87>
= 2684897 · 16342553 · 54480808381<11> · 8406226122100292597<19> · 44786834372208198144524113843511052885709673<44>
9·1087+1 =
9000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<88>
= 887 · 386371357 · 236255147171<12> · 111155942984264837424265452151937913841984420295647335851780876209<66>
9·1088+1 =
90000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<89>
= 769 · 14660735954786333<17> · 62196933420067104176339596580486953<35> · 128348685461100483103749562395167021<36>
9·1089+1 =
900000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<90>
= 19 · 1013 · 1637 · 28564773432627871239776865954944655910167469236294439209861550034422138918173953059<83>
9·1090+1 =
9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<91>
= 1913 · 6353 · 132840597418340897<18> · 12859187943990900293<20> · 433515190810669877226290663075470944758601165829<48>
9·1091+1 =
90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<92>
= 7 · 13 · 823 · 288931 · 399389392454346926675860819<27> · 10413833149628141442784411438682714753267783316927489613<56>
9·1092+1 =
900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<93>
= 1645448113<10> · 9480123974237142790153<22> · 157953409519630929548571869<27> · 365271086023415027274232621052946461<36>
9·1093+1 =
9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<94>
= 53 · 3253 · 7083946094974808924944084339<28> · 2230909539925799570887029026531<31> · 3303127731542927100919793136721<31> (Makoto Kamada / GGNFS-0.71.4)
9·1094+1 =
90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<95>
= 6113 · 13693948969<11> · 5497124074493<13> · 1171170382948606419965693035937581<34> · 166995122940312683736314427080836801<36>
9·1095+1 =
900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<96>
= 18374716688349200481047<23> · 48980347031454379028995841919619369493502916547701926929456719936658697383<74>
9·1096+1 =
9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<97>
= 821 · 353920196149253<15> · 12320837891262052071437478413<29> · 2513933370128468437396549479896274014744538673329629<52>
9·1097+1 =
90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<98>
= 7 · 13 · 11251 · 371135635889864816448450317<27> · 1216658351270915809990980393779<31> · 194674332501533702073581470782453127<36> (Makoto Kamada / GGNFS-0.71.4)
9·1098+1 =
900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<99>
= 17 · 665117 · 1302994037<10> · 61087606833217334930936140025570390625015013586542691774287192644976828132114177457<83>
9·1099+1 =
9000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<100>
= 647 · 1159303 · 11998895445679379799918978391750473540741698203219135396897417073903734149720758838785348561<92>
9·10100+1 =
90000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001<101>
= 29 · 44497 · 852673 · 6267889 · 13049983777688172742896635745449048831681908684773511663795549758829314812199285941<83>
9·10101+1 =
9(0)1001<102>
= 929 · 1087 · 62687801663<11> · 14217204524644415207780393657951435545559485039852289925018458324888753728301649466849<86>
9·10102+1 =
9(0)1011<103>
= 857 · 4729 · 27724157 · 146688169 · 7824928201<10> · 1082959301461<13> · 64438650881125819456903404728709964010133394499896709654209<59>
9·10103+1 =
9(0)1021<104>
= 7 · 13 · 23 · 6817147193929<13> · 6307693901839245662279188002838915868613967313464590717271270615162436918251411823620733<88>
9·10104+1 =
9(0)1031<105>
= 173 · 401017 · 12972797010421811792073566252600451214059928931270279995193146281071704670643674584536446143483661<98>
9·10105+1 =
9(0)1041<106>
= 146173 · 324660412100191757<18> · 189647015921930560555613778008392694518228331817885356768303090522447538729954849641<84>
9·10106+1 =
9(0)1051<107>
= 53 · 109 · 601 · 273608402981042587412878642296398297<36> · 94740623536944631063360702956769539501899999853290343142238204929<65> (Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 / 1.31 hours on Pentium 4 2.80GHz / Apr 5, 2007)
9·10107+1 =
9(0)1061<108>
= 19 · 140725352693<12> · 3209015382997<13> · 14021490200609<14> · 101043252088451<15> · 24713519911140033558724499<26> · 2995771394891056123697829969739<31>
9·10108+1 =
9(0)1071<109>
= 373777 · 4126417 · 516866967797<12> · 56849295635453<14> · 318262207989327241<18> · 1969570745833601789<19> · 316808116066994770590704313455437421<36>
9·10109+1 =
9(0)1081<110>
= 7 · 13 · 18480611 · 36737531 · 1456715783890529448958356929556268261049304839622936526296628689514369386951968743985378548771<94>
9·10110+1 =
9(0)1091<111>
= 535741 · 13711467855528170180393<23> · 1270514145578868772995123173<28> · 96432665403955779086149730071450484314220266525570368649<56>
9·10111+1 =
9(0)1101<112>
= 89 · 76439746214259187150670786361768507023<38> · 1322919037723783381478589398425519069856963653988055358561452629090981383<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 1.17 hours on Cygwin on AMD 64 3200+ / Apr 5, 2007)
9·10112+1 =
9(0)1111<113>
= 179604761533489094411512153<27> · 501100300635507398407031482924168213889400921792034725619610165043624629901632661507817<87>
9·10113+1 =
9(0)1121<114>
= 22699 · 1184459 · 184673635431641860805463910676143935673766213<45> · 181263705428764681773841097459967268253297158583781910475797<60> (Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 / 2.33 hours on Pentium 4 2.80GHz / Apr 5, 2007)
9·10114+1 =
9(0)1131<115>
= 17 · 4029232093952705808639019244540988181<37> · 131392720091863853149542807291473246596308272142652439543027874153558812956013<78> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 1.42 hours on Core 2 Duo E6300@2.33GHz / Apr 4, 2007)
9·10115+1 =
9(0)1141<116>
= 7 · 13 · 103 · 3391343 · 4528368424529<13> · 40963716780981360581121590745000013<35> · 15263392336091573406619034605037192244798168990720053726167<59> (Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 / 1.71 hours on Pentium 4 2.80GHz / Apr 5, 2007)
9·10116+1 =
9(0)1151<117>
= 3917 · 719189 · 1814814873154884385579882421783353<34> · 176040896601909387016192468843434263374254628094985647651842242628087932409<75> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 2.15 hours on Cygwin on AMD 64 3400+ / Apr 5, 2007)
9·10117+1 =
9(0)1161<118>
= 12527 · 12134790579207611427656536951386453899<38> · 59205649022301612078526981553969233951090001376598142943906491679184248013837<77> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 1.19 hours on Core 2 Duo E6300@2.33GHz / Apr 5, 2007)
9·10118+1 =
9(0)1171<119>
= 196073 · 186381179361616798004946995918881<33> · 1741085366837536144261031347273683656221<40> · 1414498837021419722168181729011819304044237<43> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 1.71 hours on Core 2 Duo E6300@2.33GHz / Apr 5, 2007)
9·10119+1 =
9(0)1181<120>
= 53 · 141413 · 8157992210918944356031188001<28> · 21390846892616080268751387717062038727<38> · 688122943822261605646355479136296441670952499967<48> (Makoto Kamada / Msieve 1.17 for P38 x P48 / 53 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Apr 4, 2007)
9·10120+1 =
9(0)1191<121>
= 261066330188528555113<21> · 177543491136813067537023060576498121<36> · 194172127768048952704457311156481550648638322505777201579412750737<66> (Shaopu Lin / GGNFS-0.77.1-20060722-pentium4 / 2.19 hours on Pentium 4 2.80GHz / Apr 5, 2007)
9·10121+1 =
9(0)1201<122>
= 72 · 13 · 8329 · 13099 · 45779 · 398459 · 7782345244798188203154573931<28> · 9122453056596871193844391369874307223847672767541887333118289467395936693<73>
9·10122+1 =
9(0)1211<123>
= 113 · 229 · 2618281 · 2053239600061821515593493<25> · 6469529502156373506385505019204630074610658399452446570031177365503040875278827264072161<88>
9·10123+1 =
9(0)1221<124>
= 2383 · 5569 · 35081 · 28502281 · 678249788730965343155876794263068283826182488644313608841077587266701477227270380314651873177483730318783<105>
9·10124+1 =
9(0)1231<125>
= 168745086793<12> · 360847422557<12> · 1478045369332241890902656097128029833077561869578361464994129936119444146965960462980286762223022100301<103>
9·10125+1 =
9(0)1241<126>
= 19 · 23 · 47 · 1091 · 2340179 · 17162849181227637954686586305558908249546272559153601351238220969425254370779811594520448516673293863019660069131<113>
9·10126+1 =
9(0)1251<127>
= 61 · 1609 · 4480517 · 489006813651285661577821<24> · 41851746914137401114783396877147747465402212469861187936155145864696669256526001874056468957<92>
9·10127+1 =
9(0)1261<128>
= 7 · 13 · 167 · 401 · 1289 · 112974047 · 101416511916384986434377207218778382110001626648805153438789813840049798877618436058332277078236972412647025251<111>
9·10128+1 =
9(0)1271<129>
= 29 · 2833 · 6121 · 19705421 · 90821744521678073858476364997021996717514800118315880931365217585390573943501211754500252286470470063005559638673<113>
9·10129+1 =
9(0)1281<130>
= 32801 · 2379277 · 4721270754216020253013<22> · 24425952708110930637045019522319838870076516710636340358528847569412668324375792540254249902835601<98>
9·10130+1 =
9(0)1291<131>
= 17 · 24593 · 216594009296418960195645951195437<33> · 993883859583954448735204608842181266122491024424875540660278630042828155798346154067493353733<93> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 2.48 hours on Core 2 Duo E6300@2.33GHz / Apr 5, 2007)
9·10131+1 =
9(0)1301<132>
= 8299284248153821291347886062343<31> · 108443086546915815961290212547662608185723634371339940135709867135880497559893063530678305973289665207<102> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3271453043 / Apr 1, 2007)
9·10132+1 =
9(0)1311<133>
= 53 · 317 · 66451101285889<14> · 46727238867176438789<20> · 172518262538517256211201296934178206279773673815078420298703678317899978288552723100833170379181<96>
9·10133+1 =
9(0)1321<134>
= 7 · 13 · 4968920397271493729905247<25> · 199039410966227048395930800201621775495118194835533213227230187549388956000123172044967043230129417917126413<108>
9·10134+1 =
9(0)1331<135>
= 181 · 2753 · 16531089961<11> · 109258751591334591151303372851647591688655864712545289987012012810113495421933518921235388716934090390154756359979711637<120>
9·10135+1 =
9(0)1341<136>
= 5927 · 3426823 · 4329778969<10> · 259922171552969<15> · 1684172380678722094703<22> · 233786976732721857354891289970301694664296598730453186421784242313375317460159807<81>
9·10136+1 =
9(0)1351<137>
= 10037 · 17333 · 25821394384510406269905557<26> · 20034806731811563556317515354285137946810212466345951716652047292947478596158891683089943960150394732133<104>
9·10137+1 =
9(0)1361<138>
= 12487 · 499844315469822755436751497077<30> · 22694932497912076567821810183311352533<38> · 6353612804509099688291593709903803564908420180194675150217717604303<67> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 6.82 hours on Core 2 Duo E6300@2.33GHz / Apr 5, 2007)
9·10138+1 =
9(0)1371<139>
= 2477 · 16193 · 95401 · 297051702914765761<18> · 7917794276392453813733352128005820521294962763082702780279765673387190228554203906926288871175245862306839581<109>
9·10139+1 =
9(0)1381<140>
= 7 · 132 · 59 · 4424608127<10> · 78922087410589632675170017604509175183<38> · 80446991336116621276555908785459354423609<41> · 45901044757666544367296133139543971866289750757<47> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 7.37 hours on Core 2 Duo E6300@2.33GHz / Apr 6, 2007)
9·10140+1 =
9(0)1391<141>
= 97 · 149 · 293 · 4733 · 15127035346844083517<20> · 2968428278701030960390847160398665805832820067222560940788494279870037016639555085825216568275848011788840672529<112>
9·10141+1 =
9(0)1401<142>
= 66031908616111316843093170997<29> · 10183815601095370522960916473439173<35> · 13383759748561580248834032773181350478449614572726727955728581327175944905132921<80> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 11.33 hours on Athlon XP 2100+ / Apr 6, 2007)
9·10142+1 =
9(0)1411<143>
= 229133 · 310418237090102149002920451352517921093<39> · 1265341173550541325953165241360932050982648906067589633583866154278345401523423025383948873896217729<100> (Jo Yeong Uk / GGNFS-0.77.1-20050930-k8 / 9.89 hours on Core 2 Duo E6300@2.33GHz / Apr 6, 2007)
9·10143+1 =
9(0)1421<144>
= 19 · 77489 · 611292196990948120989668482657300764590695725233666442299789919248300777495753217264793440970568997569094696632662972197751667299467292811<138>
9·10144+1 =
9(0)1431<145>
= 2237 · 13037 · 4866859180076729377<19> · 51314734681449885673<20> · 1235685617145325558299524025805769976067100096210061984084437289336349768789543780996327483772010049<100>
9·10145+1 =
9(0)1441<146>
= 7 · 13 · 53 · 1171 · 223087 · 71432210402443879563413543498850639433397418526784449272113902643251546615538700296073783136343533299157202720662883596987399818198131<134>
9·10146+1 =
9(0)1451<147>
= 17 · 593 · 4969 · 43311462465413<14> · 414827032242983066169768755751739547509414478568984740154577785626904744946199325072271275054311681358974385543488309046005093<126>
9·10147+1 =
9(0)1461<148>
= 23 · 173 · 619 · 34179008207<11> · 2232476256742247<16> · 11256217824559833795361777689647<32> · 4254407909962889924194452125012698010158754770741473106917463514453834819046073932527<85> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1756400291 for P32 / Apr 1, 2007)
9·10148+1 =
9(0)1471<149>
= 653 · 2281 · 84913 · 31698046485101<14> · 261951712169089<15> · 2095543670347181<16> · 12564731965918073741<20> · 258782207455264963620629<24> · 12577425718924187164902411359943135119916884967529589<53>
9·10149+1 =
9(0)1481<150>
= 103 · 58339727 · 1166377014449061208501451129<28> · 128410914744380971148367297133654714694280189508284997411663239770422292780242256394289470851646562594123742518849<114>
9·10150+1 =
9(0)1491<151>
= 4253 · 3566992060520775519655367333427319075823880194840139594754009<61> · 593259886101759296204495700498020412031125484426971874909743168024374007473423673233213<87> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 20.35 hours on Cygwin on AMD XP 2700+ / Apr 7, 2007)
9·10151+1 =
9(0)1501<152>
= 7 · 13 · 157 · 1740270742464737399801648274260382251<37> · 6819290242424764524862346427986183895917940998262231863<55> · 530817791290284114816038893859259470090732398434626858971<57> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 18.56 hours on Cygwin on AMD 64 3400+ / Apr 5, 2007)
9·10152+1 =
9(0)1511<153>
= 2453694145358638423681793453<28> · 366793881667127514159991244654759652553502341108307784162958825376075982241849183509637602652073381767430229080916195981422117<126>
9·10153+1 =
9(0)1521<154>
= 773 · 21663953434896401<17> · 12334939976056907489717<23> · 389973351927832109532862973<27> · 50855108656179945301710095305209161<35> · 2196942769126627989787668260704574508308842635667637<52> (Makoto Kamada / Msieve 1.17 for P35 x P52 / 45 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Apr 4, 2007)
9·10154+1 =
9(0)1531<155>
= 10853 · 26821 · 28549 · 16267258734889<14> · 1901411797254127264433<22> · 350135609181819555812464717434349042876917394195532215257435914615091264169694418641882756172089510266656829<108>
9·10155+1 =
9(0)1541<156>
= 89 · 38348003093<11> · 10408775320664023<17> · 25334370346380999588577332444700636857837271323408124361236405327634077592313937181311311768555333005844781154521489990877494531<128>
9·10156+1 =
9(0)1551<157>
= 29 · 706993936910368903640116661982625450877<39> · 8380009192709174113059633311180980138633<40> · 52382271492126465895543889093087824425922340013871527868319133952371915809809<77> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 33.66 hours on Cygwin on AMD 64 3200+ / Apr 8, 2007)
9·10157+1 =
9(0)1561<158>
= 7 · 13 · 2130403278394440947268336034474352786160213379<46> · 464236512889873201316103265893901452919829671364175589843047024998926643175420109046920841497010559322144023409<111> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 28.69 hours on Cygwin on AMD 64 3200+ / Apr 16, 2007)
9·10158+1 =
9(0)1571<159>
= 53 · 297169 · 1147441 · 3134536849<10> · 4239692077429<13> · 975984724665859590593<21> · 14045487519807987354189692281<29> · 731065838605280441298711208972441<33> · 373928656032028718755230220853513167273321<42> (Makoto Kamada / Msieve 1.17 for P33 x P42 / 3.4 minutes on Pentium 4 3.06GHz, Windows XP and Cygwin / Apr 4, 2007)
9·10159+1 =
9(0)1581<160>
= 2617259 · 242181437 · 14198908344034847336575319741350686708681220266239586986186954292521964542514964603560170769429429159052564755825042072402510102485892918360726847<146>
9·10160+1 =
9(0)1591<161>
= 196668336511615844317373683402996797341833<42> · 1739150909232723432175836807853304310816643860207313<52> · 263130261241924464291801141224892605010946153371020043305094966475369<69> (Jo Yeong Uk / GMP-ECM 5.0.3 B1=3000000, sigma=510691330 for P42 / Apr 6, 2007) (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 27.70 hours on Core 2 Quad Q6600 / Nov 4, 2007)
9·10161+1 =
9(0)1601<162>
= 192 · 268115868282277<15> · 1452612416148001223786387377375980929408933<43> · 6401224184307784221531476143753944364302696193784598490179821129689892756268275790197304471135782300801<103> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 50.93 hours on Cygwin on AMD 64 3200+ / Jul 27, 2007)
9·10162+1 =
9(0)1611<163>
= 17 · 233 · 5693 · 199673 · 3207278521<10> · 118788802665563673626749<24> · 152599297155465124131657187052166911440245078117469<51> · 34380518818628962059427663768446076926280486458367419362075072569669<68> (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 / 87.52 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / Jun 30, 2007)
9·10163+1 =
9(0)1621<164>
= 72 · 13 · 179 · 470008183 · 259481291797001816650176355670832013<36> · 580459551785892461725007555092462668798367841<45> · 11149788091046450752175493549254706615173820321550790352125382027235333<71> (Robert Backstrom / GGNFS-0.77.1-20060513-athlon-xp / 66.05 hours on Cygwin on AMD 64 3200+ / Aug 2, 2007)
9·10164+1 =
9(0)1631<165>
= 206021 · 987313 · 288154417 · 941596665917777874062834896326197<33> · 16307446785923947920819586784374506111817003364273287474816055749579556455124440591984263685499136336546651516313<113> (Wataru Sakai / GMP-ECM 6.1.2 B1=11000000, sigma=2433879795 for P33 / Apr 25, 2007)
9·10165+1 =
9(0)1641<166>
= 8543 · 59663 · 3954007 · 395828143 · 308476461133<12> · 177394921202126672010300241<27> · 206167261153879385980988085801694230252224190918900189043640628173950040223577792748169151113262087142413<105>
9·10166+1 =
9(0)1651<167>
= 31044228049<11> · 3156962265562069<16> · 918316216270703869309355611043163454536041928282487371533968756152838364897784813275043801939717925018733579383644373085052186912082380439021<141>
9·10167+1 =
9(0)1661<168>
= 65011 · 331853765402124003677<21> · 7113900758268929663283411570479354669535798745893423331<55> · 5864096533496964606518020454924687639490103035820928855353490102504942263905443892896093<88> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.38 snfs / 31.92 hours, 2.63 hours / Nov 27, 2008)
9·10168+1 =
9(0)1671<169>
= 193 · 183122333 · 1365503329<10> · 70195540469<11> · [2656694412039548462553232526428776317534088841928298827414634961259564708940735214813108191929447902768879073075808499186281445628188276129<139>] SUBMIT/RESERVE
9·10169+1 =
9(0)1681<170>
= 7 · 13 · 23 · 26680727 · 2783029903<10> · 11273267512862863753557060067341695659241008487576093151619<59> · 51369807273759613054098903544267959129913929401519425473243091409904983605073403539507467663<92> (matsui / GGNFS-0.77.1-20060513-pentium-m / Oct 25, 2008)
9·10170+1 =
9(0)1691<171>
= 10159789 · 88584516863489979959229468249783533890319966290638516213279626181213015349039236936908827535689963639992917175740559178935704274960828418779169528028584058192547109<164>
9·10171+1 =
9(0)1701<172>
= 47 · 53 · 3036861280810645404931<22> · 51385746424530178231491293825778690117107805206225197788441809802689717<71> · 23152674067043755161598533865974421832973091656998852143841113795270050798893<77> (Serge Batalov / Msieve-1.38 snfs / 57.00 hours on Opteron-2.6GHz; Linux x86_64 / Nov 8, 2008)
9·10172+1 =
9(0)1711<173>
= 160373 · 9302113 · 96610277 · 39310818573473761<17> · 4325644542490474479111141763201<31> · 3672344386838070849076190962119037504153608805562136202004095912497329465957985573008491906892452695341017<106> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=3869421807 for P31 / Apr 3, 2007)
9·10173+1 =
9(0)1721<174>
= 263 · 659 · 719503 · 119042288029767638893284897945328190576465889847<48> · 17758729179548142956399209216703776600136321973088783<53> · 3413937667616485389431567664007791715409001756176675366899769851<64> (Serge Batalov / Msieve-1.38 snfs / 50.00 hours on Opteron-2.6GHz; Linux x86_64 / Oct 11, 2008)
9·10174+1 =
9(0)1731<175>
= 6701858154129508946109631584557125937056799890919240999671909373<64> · 1342911143897373658594292493986198100072281134132513257099614367422167831910468286290583725850693432647730948437<112> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona / 173.62 hours on Core 2 Quad Q6600 / Jun 5, 2007)
9·10175+1 =
9(0)1741<176>
= 7 · 13 · 93455747615903<14> · 781769166175247748256859<24> · [13536817181273073003693400687887924526607703152525801239445965870724371117220030478103125284496228788782993959108776273823788324466266743<137>] SUBMIT/RESERVE
9·10176+1 =
9(0)1751<177>
= 382561419661867013<18> · 4153302760261926665697975045884449<34> · [566431958152526346806249739676161934366904899317226070390042476342664318676795495580542611504898377157441268210176302406249773<126>] (Wataru Sakai / GMP-ECM 6.1.2 B1=11000000, sigma=2985295769 for P34 / Apr 26, 2007) SUBMIT/RESERVE
9·10177+1 =
9(0)1761<178>
= 3167 · 387077 · 2076611 · 308752979 · 54988062023<11> · 212417999009<12> · 60289087720622533<17> · 479166086119340027893509641<27> · 54841284613190781418275599643521<32> · 618783381714794412883445208544663378606596249013437821041<57> (Jo Yeong Uk / Msieve 1.17 for P32 x P57 / 01:04:40 on Core 2 Duo E6300@2.33GHz / Apr 4, 2007)
9·10178+1 =
9(0)1771<179>
= 17 · 5948821 · 11127937531757<14> · 93538933098093421<17> · [854979291506345519628166634586895248107835034057612689204135409051812377264630845811700927262664210543325726446234062428676191570742682692069<141>] SUBMIT/RESERVE
9·10179+1 =
9(0)1781<180>
= 19 · 5534131 · [8559324138266979756599260308914187059787421196323610508563751210918494511128923592996186564316677912509042331554569462239252910234401941810119591922999483140456730671612409<172>] SUBMIT/RESERVE
9·10180+1 =
9(0)1791<181>
= 197 · 677 · 8540277647845249<16> · 7901610622200460470784299047274434117414932293996553516196916846809334887302400903200935211332411879702681245947054177548931208164691085896512718667263943128521<160>
9·10181+1 =
9(0)1801<182>
= 7 · 13 · 1634877253<10> · [604945103490891258359817052889773744371138417821627744544202175043039155300432202545905145692923154892649919931946712950558748149033662658091317262343113052652529008556087<171>] SUBMIT/RESERVE
9·10182+1 =
9(0)1811<183>
= 96497 · 6693857016013088704017026959632722629<37> · [1393324476133628308508018984618709804986257885467422408615899381022222419474636732587515795416876689048777120508243524120001407382238214675677<142>] (Wataru Sakai / GMP-ECM 6.1.2 B1=11000000, sigma=2126479012 for P37 / Apr 16, 2007) SUBMIT/RESERVE
9·10183+1 =
9(0)1821<184>
= 103 · 3233244966365310870649684607<28> · 298693157390062566861005989423<30> · 90477668522699163072144221687303949991107197335419536336160629162770149946285624825258787157424462314629011259798775595755047<125> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=1982672773 for P30 / Apr 3, 2007)
9·10184+1 =
9(0)1831<185>
= 29 · 53 · 433 · 17907001038501948144357766109<29> · 56385136584339210524733082811161<32> · 13545949246627659985095780182634249171497673616306498864681<59> · 9887438744319177885322438170306294338262729295517657911743749<61> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2641429563 for P32 / Apr 3, 2007) (Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4 gnfs for P59 x P61 / 104.60 hours on Pentium 4 2.4GHz, Windows XP and Cygwin / May 23, 2007)
9·10185+1 =
9(0)1841<186>
= 14221071273845475492291671003825582287<38> · [63286371516555504143607328750089379622990817116008869593801609303856339184629344856413421757600029944178214967248795969528509796283408631275118450223<149>] (Jo Yeong Uk / GMP-ECM 6.1.2 B1=3000000, sigma=668692240 for P38 / May 15, 2007) SUBMIT/RESERVE
9·10186+1 =
9(0)1851<187>
= 61 · 161271954417042232580477<24> · 71338953778563773721289257398483341<35> · 12824105714440400124634673307313813672129762979860127394144076399375268657498186011572935151644208597728853041885465975326330013<128> (Wataru Sakai / GMP-ECM 6.1.2 B1=11000000, sigma=127397403 for P35 / May 15, 2007)
9·10187+1 =
9(0)1861<188>
= 7 · 13 · 4373 · 5717 · 20183 · 24068660737760877432355395211891<32> · [81435881553600072016173523292608504397039692207307496066394773089520233394402320905105063604429647318463867320494190178646753385161893694575807<143>] (Wataru Sakai / GMP-ECM 6.1.2 B1=11000000, sigma=339987454 for P32 / Apr 26, 2007) SUBMIT/RESERVE
9·10188+1 =
9(0)1871<189>
= 4141301 · 70442857268715121<17> · [3085096470467553716571243018296201390389844915921257662957676179654699793002475367590978985379736811297391370822375481960768001760038496868559597961057134463224215981<166>] SUBMIT/RESERVE
9·10189+1 =
9(0)1881<190>
= 292491769289<12> · 30770096614607442434998740550149853895569595410325501933751612480916630488207323840651677996626513818154443541121889883389415391379642385394042834145946927251212111970233595327609<179>
9·10190+1 =
9(0)1891<191>
= 173 · 42037512353<11> · 7960021585261<13> · 12612461717629<14> · 170152793363537<15> · 724446316717717134607037007499933077187253954289961463613214636811007979491931912187393728040640579565260686886805540303793806234663736093<138>
9·10191+1 =
9(0)1901<192>
= 23 · 10939 · 867042811 · [4125689211319745148634875587195033206071389358078471912403470848886756520895730611538619729654483625649557218575022770064156124696869372420089262021995804506989196994259462677503<178>] SUBMIT/RESERVE
9·10192+1 =
9(0)1911<193>
= 1109 · 14734116298400713270539985713991888026642775154005017603856013<62> · 550791043881235942395862556041076669468450897765276463896412425335034457457595786628772946981138862497150863003489314800842696753<129> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.36 / 151.51 hours / Aug 18, 2008)
9·10193+1 =
9(0)1921<194>
= 7 · 13 · 989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989010989011<192>
9·10194+1 =
9(0)1931<195>
= 17 · 1249 · 8089 · 1037297 · 106869415441<12> · 6800424794926771388308831050471833<34> · 6950942827174514887338020534901240077527602856760093566826256645756923667399042440819259600295410278353642353978340831657491455631029153<136> (Wataru Sakai / GMP-ECM 6.1.2 B1=11000000, sigma=1421895638 for P34 / Apr 23, 2007)
9·10195+1 =
9(0)1941<196>
= 67173650371<11> · 15472533389903<14> · 29762810324360176001<20> · [290943188952943929416223017734743387603196817752925324130758252314472136364971113186136347634916042572255336895287042231079084595756856358700011595255077<153>] SUBMIT/RESERVE
9·10196+1 =
9(0)1951<197>
= 937 · 815382640321<12> · 251608683962632814402459881<27> · [468183206158271709437041067192679905095516353142302832825335469438037025341058753341105551468789888005112961200277229858369247536549356131933117963185455473<156>] SUBMIT/RESERVE
9·10197+1 =
9(0)1961<198>
= 19 · 53 · 59 · 83383 · 5391689 · 245839937164230974479691215063<30> · 137058584136541446774168911670541604476144697821768163614455130433232887280296804832661364194002488967472974602034234806509032799755754187638460748172517<153> (Makoto Kamada / GMP-ECM 6.1.2 B1=250000, sigma=2973887166 for P30 / Apr 1, 2007)
9·10198+1 =
9(0)1971<199>
= 206641 · [43553796197269660909500050812762230147937727750059281555935172594015708402495148591034693018326469577673356207141854714214507285582241665497166583591833179281943080027680857138709162266926698961<194>] SUBMIT/RESERVE
9·10199+1 =
9(0)1981<200>
= 7 · 13 · 89 · 167198846303<12> · [66462677633894619242012436296497628451883448584116333347217796555802090712745601850045829303919789161741956247894874681805211744721204318793550086988640266010799811885330760352828421333<185>] SUBMIT/RESERVE
9·10200+1 =
9(0)1991<201>
= 15173 · 2624002403996012093<19> · [22605120322128290234994542913326329088540242367431696402672044446973941361940320722688629269158445660264295657818619045719941047926923330869272561595953477974249006496562263505809<179>] SUBMIT/RESERVE

Factorizations

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