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Factorizations of near-repdigit-related numbers

Table of contents

  1. Introduction
  2. How to contribute your factors ▶
  3. Graphs ▶
  4. Wanted list ▶
  5. Records ▶
  6. Reserved numbers and submitted numbers
  7. News and updates
  8. Contributors
  9. Factor tables
  10. List of near-repdigit-related prime numbers
  11. Expression generator of near-repdigit-related numbers
  12. Implementations
  13. Related links

1. Introduction

We are collecting prime factorizations of near-repdigit-related numbers such as repunit numbers, near-repdigit numbers, plateau and depression numbers, quasi-repdigit numbers, and so on.

2. How to contribute your factors ▶

3. Graphs ▶

4. Wanted list ▶

5. Records ▶

6. Reserved numbers and submitted numbers

Reserved Numbers

plain text version
namereserved numbers (c-digits / elapsed days)
Alexander Mkrtychyan(64·10224+53)/9 (c222 / 463)
Justin Card(58·10197+41)/9 (c122 / 99)
Michael Dressner(43·10226-7)/9 (c226 / 92), (5·10171-11)/3 (c135 / 33)
Markus Tervooren6·10242+1 (c243 / 62)
Dmitry Domanov(16·10235-7)/9 (c236 / 61), (26·10200-11)/3 (c201 / 28), (22·10197-7)/3 (c198 / 24), (67·10192-13)/9 (c191 / 4), (67·10190-13)/9 (c189 / 4)
juno1369(59·10158+13)/9 (c115 / 25), (67·10166-31)/9 (c164 / 12), (35·10190-71)/9 (c124 / 9), (44·10196+1)/9 (c125 / 1)
Lionel Debroux(16·10227-7)/9 (c205 / 17), (2·10190-17)/3 (c185 / 0)
Sinkiti Sibata(10207-7)/3 (c202 / 13), (10216+17)/9 (c208 / 12), (10219+17)/9 (c212 / 7), (59·10184+31)/9 (c182 / 3), (64·10161+17)/9 (c135 / 1), (65·10161-11)/9 (c147 / 0)
Robert Backstrom(16·10241-7)/9 (c241 / 8)
Wataru Sakai(61·10194-43)/9 (c131 / 4), (47·10200+61)/9 (c198 / 1)
Jo Yeong Uk2·10195-1 (c173 / 4), (59·10161+13)/9 (c133 / 0)
Erik Branger(64·10205-1)/9 (c137 / 3), (65·10168+61)/9 (c152 / 2)

Submitted Numbers

Please wait until the tables are manually updated for the following numbers.

plain text version
namesubmitted numbers (c-digits = factors)
Jo Yeong Uk(59·10161+31)/9 (c148 = 16143737774649079582774376407801783420888231<44> · ......)
Dmitry Domanov(19·10188+11)/3 (c186 = 5821078419106027523809386387218682764306133231192700907154676066616935391<73> · ......)
Sinkiti Sibata(67·10160+41)/9 (c130 = 6458162601207874684709389465413979594157825818758560151613079<61> · ......)

7. News and updates

Nov 19, 2009 (5th)
By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 19, 2009
(67·10160-13)/9 = 7(4)1593<161> = 223 · 2790386777<10> · 1084302893662699352989<22> · C129
C129 = P51 · P78
P51 = 363065558163129755586591876057933957697079245966993<51>
P78 = 303897660134854542414694170874725162056604936336714237480477623856561460344929<78>
Nov 19, 2009 (4th)
By Dmitry Domanov / GGNFS/msieve / Nov 19, 2009
(65·10167+61)/9 = 7(2)1669<168> = 3 · 3163 · 1283549 · 1810364976295258400527<22> · 6731034634722746219253576990142331<34> · C103
C103 = P41 · P63
P41 = 43887433213139645955484994448382146047239<41>
P63 = 110879128047013805011879885468739184560992940355555347685320723<63>
Nov 19, 2009 (3rd)
By Wataru Sakai / GMP-ECM 6.2.1 / Nov 19, 2009
(59·10170+13)/9 = 6(5)1697<171> = 3 · 31 · 73 · 229 · 2371 · 136027 · C157
C157 = P33 · C124
P33 = 233155008560892980603136314014073<33>
C124 = [5607467793672916357063206022743587336819544589797022881608229298842144002627748832647796629860992889557912488547520943964517<124>]
(59·10171+31)/9 = 6(5)1709<172> = 7 · 1319207906438579<16> · C156
C156 = P37 · P120
P37 = 2356463302077488153069650734241665823<37>
P120 = 301257269819596050498849046453150412524164514988049351771398639204280300958087733288868202951958003834996085783952664261<120>
(22·10172+17)/3 = 7(3)1719<173> = 7 · 241 · 3371 · 14678148955213<14> · C153
C153 = P34 · C120
P34 = 4675036528889963296972072581793651<34>
C120 = [187919259193893023850805073342750434538681070849906401604520432741490252970095903458623817348949668880171189653291036289<120>]
Nov 19, 2009 (2nd)
By Sinkiti Sibata / Msieve / Nov 19, 2009
(65·10160+7)/9 = 7(2)1593<161> = 89 · 691 · 1063 · 30689 · 80147 · 345231714617358424861<21> · C124
C124 = P47 · P77
P47 = 20357986503829909242696372348001111417687352381<47>
P77 = 63907821471927606482939461715126003027541213468536152840468146898123845327793<77>
Nov 19, 2009
By Robert Backstrom / Msieve / Nov 19, 2009
(10229-7)/3 = (3)2281<229> = 3814997 · C222
C222 = P101 · P122
P101 = 32956293259679429768656597360038775832848835783382963927693572571464416807016576796602091743934862861<101>
P122 = 26512225547078900430922693339363341417936176675074791272188321866779709375923927312831198488509643069134973196513414342243<122>
C222 is the fourth largest composite number factored by snfs in our tables so far, and P101 is the third largest prime factor found by nfs in our tables so far. Congratulations!
Nov 18, 2009 (4th)
By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM / Nov 18, 2009
(67·10160-31)/9 = 7(4)1591<161> = 61982719611999597353<20> · 143698186760416432999<21> · C121
C121 = P58 · P64
P58 = 5184273162643458694917399313243984064834873060204015700713<58>
P64 = 1612213304015942235676505728696547693838364040958693307596122831<64>
(65·10162+61)/9 = 7(2)1619<163> = 7 · 433 · 40118289197111849803<20> · C140
C140 = P35 · P106
P35 = 13579168028242955813092310115106577<35>
P106 = 4373904977664475284540946690165627879231370447085692210555464579063477417774709742461792175457447644986089<106>
Nov 18, 2009 (3rd)
By Sinkiti Sibata / Msieve / Nov 18, 2009
(67·10158-13)/9 = 7(4)1573<159> = 137 · 367 · 27749 · 723919956530258273<18> · C132
C132 = P63 · P70
P63 = 323406167861964574204330095340435316519039701961176025430412333<63>
P70 = 2279079514444156964263123471753688115851723190657786980680661703364237<70>
Nov 18, 2009 (2nd)
By Wataru Sakai / GMP-ECM 6.2.1 / Nov 18, 2009
(65·10167+61)/9 = 7(2)1669<168> = 3 · 3163 · 1283549 · 1810364976295258400527<22> · C137
C137 = P34 · C103
P34 = 6731034634722746219253576990142331<34>
C103 = [4866200326894477313327351434330702713602820686731038277709376544750901688090575230106979546318423633797<103>]
Nov 18, 2009
By Erik Branger / GGNFS, Msieve / Nov 18, 2009
(59·10172-41)/9 = 6(5)1711<173> = 42787 · 31693768213<11> · 2536830201015107<16> · 139446318301636885367<21> · C123
C123 = P58 · P65
P58 = 6709643923662083287600130339490360747447730333693040348921<58>
P65 = 20366943698391295213823441988462062034872745975969857861877209429<65>
Nov 17, 2009 (4th)
By Sinkiti Sibata / Msieve / Nov 17, 2009
(67·10176+41)/9 = 7(4)1759<177> = 7 · C177
C177 = P36 · P42 · P43 · P57
P36 = 381496638149806557062385644326745051<36>
P42 = 803770627877673149683896774769690484334047<42>
P43 = 2540492572298568949029546317256747678065197<43>
P57 = 136519118946285151795581433335283513926057235634807181623<57>
(62·10159-71)/9 = 6(8)1581<160> = 7 · 367 · 397 · 1427 · 1295003 · 27044153094400533691<20> · C126
C126 = P48 · P78
P48 = 637642494412674002793864923763006295921649455939<48>
P78 = 211957692852734056509800472053686387750176129582452776229614596712235602760093<78>
Nov 17, 2009 (3rd)
By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 17, 2009
(59·10159+31)/9 = 6(5)1589<160> = 7 · 41 · 118759055073185934621037<24> · C135
C135 = P55 · P80
P55 = 2549878433376721403304445956812713905944758972355130839<55>
P80 = 75429529077254560793474090742639833438562153315193101308443515089992511037341899<80>
Nov 17, 2009 (2nd)
By Ignacio Santos / GGNFS, Msieve / Nov 17, 2009
(64·10178+71)/9 = 7(1)1779<179> = 229 · C177
C177 = P38 · P139
P38 = 33350205132654546757222414370710831411<38>
P139 = 9311153207174220903648886531701264110925845510393319781488890048252156953150920948299831365494816188137632384373019136801433203324125922001<139>
Nov 17, 2009
By Dmitry Domanov / GGNFS/msieve, ECMNET, GMP-ECM / Nov 17, 2009
(59·10164+13)/9 = 6(5)1637<165> = 32 · 89 · 967 · C159
C159 = P48 · P112
P48 = 172494834689383932407753106094143525376103225653<48>
P112 = 4906529533010920434450031087476390453047270898213110900861533572593100963811674429717024242278907331943447184807<112>
(62·10190-71)/9 = 6(8)1891<191> = 17 · C190
C190 = P39 · C152
P39 = 159056495352762286480580492048359527989<39>
C152 = [25477033004606382089474543221740888076315860678491961319226765661507788975891994600263548413995024764740782104709424866797319890147044298005667883592637<152>]

2009: November October September August July June May April March February January
2008: December November October September August July June May April March February January
2007: December November October September August July June May April March February January
2006: December November October September August July June May April March February January
2005: December November October September August July June May April March February January
2004: December November October September August

8. Contributors

I am thankful to contributors 10metreh, Alexander Mkrtychyan, Andreas Tete, Anton Korobeynikov, Bryan Koen, Cedric Vonck, Chris Monico, Dmitry Domanov, Erik Branger, Greg Childers, honeycrack7, Hugo Platzer, Ignacio Santos, Jeff Gilchrist, JMB, Jo Yeong Uk, JPascoa, Julien Peter Benney, Justin Card, Kenichiro Yamaguchi, Kenji Ibusuki, Lionel Debroux, Luigi Morelli, Maksym Voznyy, Markus Tervooren, matsui, Max Dettweiler, Michael Peterson, Nechaev Sergey, Naoki Yamamoto, Norbert Schneider, Patrick Keller, Phil Carmody, Philippe Strohl, Robert Backstrom, Samuel Chong, Sander Hoogendoorn, Serge Batalov, Shaopu Lin, Shusuke Kubota, Sinkiti Sibata, suberi, Takahiro Nohara, Tetsuya Kobayashi, Thomas Womack, Tomoya Adachi, Tyler Cadigan, Wataru Sakai, Wojciech Florek, Yang Hae Hun and Yoichi Hanatani.

9. Factor tables

Last update

Nov 20, 2009

Repunit numbers

Recent changes
2009: September August July June May April March February January
2008: December November October September

Near-repdigit numbers of the form AA...AAB

formgeneral termrangeterms which have not been factored yetlast update
11...113(10n+17)/9n≤250n=184, 189, 192, 193, 201, 202, 203, 206, 208, 209, 210, 211, 214, 216, 217, 218, 219, 220, 223, 224, 225, 226, 227, 230, 231, 232, 234, 235, 236, 237, 238, 239, 240, 243, 244, 246, 250 (37/250)Nov 8, 2009
11...117(10n+53)/9n≤250n=201, 202, 203, 205, 208, 209, 210, 212, 216, 217, 218, 219, 221, 222, 227, 228, 229, 231, 232, 233, 234, 235, 237, 238, 240, 243, 245, 246, 247, 248, 249 (31/250)Nov 8, 2009
11...119(10n+71)/9n≤200n=176, 177, 178, 179, 183, 188, 189, 190, 191, 193, 195, 199, 200 (13/200)Nov 8, 2009
22...221(2·10n-11)/9n≤200n=175, 176, 179, 183, 185, 186, 187, 188, 189, 191, 196, 199, 200 (13/200)Nov 6, 2009
22...223(2·10n+7)/9n≤200n=173, 174, 176, 179, 182, 184, 193, 195, 196, 198, 199, 200 (12/200)Nov 6, 2009
22...227(2·10n+43)/9n≤200n=179, 183, 184, 185, 186, 189, 190, 192, 194, 197, 199, 200 (12/200)Nov 7, 2009
22...229(2·10n+61)/9n≤200n=180, 181, 182, 183, 184, 186, 189, 191, 194, 195, 196, 199 (12/200)Nov 6, 2009
33...331(10n-7)/3n≤250n=182, 183, 189, 190, 196, 199, 200, 205, 206, 207, 208, 209, 211, 215, 217, 218, 219, 221, 226, 227, 230, 231, 232, 233, 235, 237, 242, 243, 247, 248, 250 (31/250)Nov 20, 2009
33...337(10n+11)/3n≤200n=173, 178, 179, 180, 184, 185, 186, 187, 191, 192, 193, 194, 196, 197, 198, 199 (16/200)Nov 5, 2009
44...441(4·10n-31)/9n≤200n=174, 175, 176, 180, 181, 185, 195, 196, 197, 198 (10/200)Nov 5, 2009
44...443(4·10n-13)/9n≤200n=172, 175, 176, 178, 179, 180, 184, 185, 188, 189, 191, 193, 195, 196, 197, 198, 200 (17/200)Nov 5, 2009
44...447(4·10n+23)/9n≤200n=178, 181, 183, 184, 185, 188, 192, 193, 195, 196, 197, 200 (12/200)Nov 5, 2009
44...449(4·10n+41)/9n≤200n=178, 179, 180, 183, 184, 186, 188, 189, 193, 199, 200 (11/200)Nov 5, 2009
55...551(5·10n-41)/9n≤200n=180, 181, 183, 184, 187, 189, 190, 192, 196, 198, 199, 200 (12/200)Nov 4, 2009
55...553(5·10n-23)/9n≤200n=176, 178, 179, 182, 187, 188, 193, 196, 200 (9/200)Nov 4, 2009
55...557(5·10n+13)/9n≤200n=174, 175, 176, 179, 180, 181, 182, 183, 185, 187, 188, 191, 192, 193, 194, 198 (16/200)Nov 4, 2009
55...559(5·10n+31)/9n≤200n=173, 174, 179, 180, 181, 182, 183, 184, 191, 194, 196 (11/200)Nov 4, 2009
66...661(2·10n-17)/3n≤200n=172, 175, 176, 183, 186, 190, 193, 194, 195, 197, 200 (11/200)Nov 4, 2009
66...667(2·10n+1)/3n≤250n=198, 200, 201, 203, 207, 208, 210, 211, 212, 214, 215, 217, 218, 219, 220, 221, 222, 224, 225, 226, 227, 228, 230, 231, 232, 236, 237, 239, 241, 242, 243, 244, 246, 247, 248, 249 (36/250)Nov 4, 2009
77...771(7·10n-61)/9n≤200n=178, 179, 181, 182, 187, 189, 190, 191, 193, 194, 195, 197, 198 (13/200)Oct 21, 2009
77...773(7·10n-43)/9n≤250n=186, 195, 197, 199, 200, 203, 206, 208, 209, 210, 211, 212, 213, 215, 217, 218, 220, 225, 226, 227, 230, 232, 235, 236, 237, 238, 239, 240, 242, 245, 248, 249, 250 (33/250)Oct 21, 2009
77...779(7·10n+11)/9n≤200n=177, 178, 180, 181, 183, 185, 187, 191, 192, 193, 194, 196, 199 (13/200)Oct 24, 2009
88...881(8·10n-71)/9n≤200n=171, 176, 179, 180, 182, 184, 187, 188, 191, 193, 196, 197, 198, 199 (14/200)Oct 22, 2009
88...883(8·10n-53)/9n≤200n=172, 174, 176, 179, 184, 185, 186, 194, 195, 196, 197, 199 (12/200)Oct 22, 2009
88...887(8·10n-17)/9n≤200n=180, 181, 182, 183, 184, 187, 188, 189, 196, 198, 200 (11/200)Oct 22, 2009
88...889(8·10n+1)/9n≤250n=202, 203, 205, 206, 208, 214, 218, 220, 221, 224, 227, 229, 232, 235, 236, 238, 239, 242, 244, 248 (20/250)Oct 22, 2009
99...99110n-9n≤250n=201, 211, 215, 221, 229, 231, 235, 241, 243, 245, 247 (11/250)Oct 23, 2009
99...99710n-3n≤200n=181, 183, 186, 189, 192, 193, 195, 196, 198, 199 (10/200)Oct 23, 2009

Near-repdigit numbers of the form ABB...BB

formgeneral termrangeterms which have not been factored yetlast update
133...33(4·10n-1)/3n≤250n=209, 211, 213, 215, 219, 221, 229, 231, 237, 239, 247, 249 (12/250)Nov 8, 2009
177...77(16·10n-7)/9n≤250n=194, 205, 206, 209, 212, 213, 215, 220, 221, 223, 227, 228, 231, 234, 235, 237, 238, 240, 241, 242, 245, 246, 248 (23/250)Nov 11, 2009
199...992·10n-1n≤250n=195, 196, 197, 200, 202, 203, 205, 206, 208, 209, 214, 215, 218, 221, 223, 224, 226, 227, 228, 229, 230, 233, 234, 235, 237, 238, 239, 240, 241, 244, 246 (31/250)Nov 8, 2009
211...11(19·10n-1)/9n≤200n=176, 178, 179, 183, 184, 185, 188, 189, 192, 194, 195, 196, 197, 200 (14/200)Nov 7, 2009
233...33(7·10n-1)/3n≤200n=173, 175, 177, 179, 182, 183, 185, 186, 187, 189, 191, 193, 194, 197, 199, 200 (16/200)Nov 7, 2009
277...77(25·10n-7)/9n≤200n=175, 177, 179, 181, 183, 184, 187, 192, 193, 195, 196, 197, 198, 199 (14/200)Nov 7, 2009
299...993·10n-1n≤200n=171, 172, 174, 176, 177, 178, 180, 182, 191, 192, 195, 197, 198, 199 (14/200)Nov 7, 2009
311...11(28·10n-1)/9n≤200n=175, 176, 177, 178, 180, 181, 182, 184, 187, 188, 194, 196, 197, 198, 199, 200 (16/200)Nov 6, 2009
377...77(34·10n-7)/9n≤200n=173, 174, 175, 177, 178, 179, 180, 184, 185, 186, 189, 191, 192, 197, 198 (15/200)Nov 6, 2009
411...11(37·10n-1)/9n≤200n=173, 174, 177, 178, 183, 184, 185, 187, 189, 190, 191, 198, 199 (13/200)Nov 6, 2009
433...33(13·10n-1)/3n≤200n=173, 176, 177, 179, 180, 181, 182, 184, 187, 189, 190, 192, 193, 194, 196, 198, 200 (17/200)Nov 6, 2009
477...77(43·10n-7)/9n≤250n=207, 210, 215, 218, 221, 223, 225, 226, 227, 230, 232, 233, 235, 239, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250 (24/250)Nov 5, 2009
499...995·10n-1n≤200n=177, 182, 185, 186, 187, 189, 191, 193, 197, 198, 199 (11/200)Nov 5, 2009
511...11(46·10n-1)/9n≤200n=175, 176, 179, 180, 183, 184, 187, 188, 190, 192, 196, 197 (12/200)Nov 4, 2009
533...33(16·10n-1)/3n≤250n=181, 183, 185, 187, 189, 191, 193, 195, 197, 199, 213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 235, 237 (22/250)Nov 4, 2009
577...77(52·10n-7)/9n≤200n=173, 176, 178, 182, 185, 188, 190, 191, 192, 195, 198, 200 (12/200)Nov 4, 2009
599...996·10n-1n≤200n=172, 180, 190, 191, 193, 195, 196, 199 (8/200)Nov 4, 2009
611...11(55·10n-1)/9n≤200n=177, 179, 183, 185, 186, 188, 194, 196, 197, 198 (10/200)Nov 4, 2009
677...77(61·10n-7)/9n≤200n=176, 183, 184, 185, 189, 190, 191, 194, 196, 197, 200 (11/200)Nov 4, 2009
711...11(64·10n-1)/9n≤350n=205, 233, 245, 259, 263, 265, 271, 275, 277, 281, 283, 289, 293, 295, 299, 303, 305, 307, 311, 313, 315, 325, 329, 335, 337, 339, 341, 345, 347, 349 (30/350)Oct 29, 2009
733...33(22·10n-1)/3n≤200n=172, 173, 179, 180, 183, 185, 186, 188, 190, 192, 194, 197, 199 (13/200)Oct 21, 2009
799...998·10n-1n≤250n=205, 217, 220, 223, 224, 226, 227, 235, 236, 239, 241, 244, 245, 248 (14/250)Oct 22, 2009
811...11(73·10n-1)/9n≤250n=188, 195, 199, 200, 201, 203, 204, 205, 206, 207, 210, 211, 212, 213, 214, 215, 218, 219, 220, 221, 222, 224, 225, 227, 229, 231, 233, 234, 235, 237, 239, 240, 241, 242, 243, 244, 246, 248, 249 (39/250)Oct 28, 2009
833...33(25·10n-1)/3n≤250n=203, 205, 207, 211, 213, 217, 221, 225, 227, 229, 233, 235, 239, 243, 245, 247, 249 (17/250)Oct 22, 2009
877...77(79·10n-7)/9n≤200n=177, 184, 185, 186, 188, 189, 190, 192, 193, 194, 195, 197, 198, 199 (14/200)Oct 22, 2009
899...999·10n-1n≤250n=181, 185, 187, 189, 191, 197, 201, 203, 205, 207, 209, 211, 215, 217, 219, 221, 225, 231, 235, 237, 241, 243, 245, 247 (24/250)Nov 12, 2009
911...11(82·10n-1)/9n≤200n=172, 176, 177, 178, 180, 181, 182, 183, 188, 189, 191, 194 (12/200)Oct 23, 2009
977...77(88·10n-7)/9n≤200n=173, 175, 177, 179, 181, 182, 185, 187, 188, 189, 191, 193, 197, 198, 200 (15/200)Oct 23, 2009

Near-repdigit palindrome numbers of the form AA...AABAA...AA

formgeneral termrangeterms which have not been factored yetlast update
11...11311...11(102n+1+18·10n-1)/9n≤75Completed / Jun 29, 2005Jan 18, 2009
11...11411...11(102n+1+27·10n-1)/9n≤75Completed / Oct 13, 2005Jan 18, 2009
11...11511...11(102n+1+36·10n-1)/9n≤75Completed / Oct 9, 2005Jan 18, 2009
11...11611...11(102n+1+45·10n-1)/9n≤75Completed / Oct 14, 2005Jan 18, 2009
11...11711...11(102n+1+54·10n-1)/9n≤75Completed / Oct 15, 2005Jan 18, 2009
11...11811...11(102n+1+63·10n-1)/9n≤75Completed / Sep 29, 2005Jan 18, 2009
11...11911...11(102n+1+72·10n-1)/9n≤75Completed / Oct 15, 2005Jan 18, 2009
33...33133...33(102n+1-6·10n-1)/3n≤75Completed / Aug 19, 2005Jan 18, 2009
33...33533...33(102n+1+6·10n-1)/3n≤75Completed / Oct 11, 2005Jan 18, 2009
33...33733...33(102n+1+12·10n-1)/3n≤75Completed / Oct 18, 2005Jan 18, 2009
33...33833...33(102n+1+15·10n-1)/3n≤75Completed / Jul 11, 2005Jan 18, 2009
77...77177...77(7·102n+1-54·10n-7)/9n≤75Completed / Sep 26, 2005Jan 18, 2009
77...77277...77(7·102n+1-45·10n-7)/9n≤75Completed / Oct 11, 2005Jan 18, 2009
77...77377...77(7·102n+1-36·10n-7)/9n≤75Completed / Oct 3, 2005Jan 18, 2009
77...77477...77(7·102n+1-27·10n-7)/9n≤75Completed / Jun 6, 2005Jan 18, 2009
77...77577...77(7·102n+1-18·10n-7)/9n≤75Completed / Oct 17, 2005Jan 18, 2009
77...77677...77(7·102n+1-9·10n-7)/9n≤75Completed / Oct 20, 2005Jan 18, 2009
77...77877...77(7·102n+1+9·10n-7)/9n≤75Completed / Oct 13, 2005Jan 18, 2009
77...77977...77(7·102n+1+18·10n-7)/9n≤75Completed / Sep 28, 2005Jan 18, 2009
99...99199...99102n+1-8·10n-1n≤75Completed / Sep 6, 2005Jan 18, 2009
99...99299...99102n+1-7·10n-1n≤75Completed / Sep 20, 2005Jan 18, 2009
99...99499...99102n+1-5·10n-1n≤75Completed / Sep 26, 2005Jan 18, 2009
99...99599...99102n+1-4·10n-1n≤75Completed / Aug 13, 2005Jan 18, 2009
99...99799...99102n+1-2·10n-1n≤75Completed / Jul 26, 2005Jan 18, 2009
99...99899...99102n+1-10n-1n≤75Completed / Jun 3, 2005Jan 18, 2009

Plateau and depression numbers of the form ABB...BBA

formgeneral termrangeterms which have not been factored yetlast update
133...331(4·10n-7)/3n≤200n=175, 176, 181, 184, 186, 188, 192, 194, 198, 200 (10/200)Nov 8, 2009
144...441(13·10n-31)/9n≤200n=172, 180, 184, 188, 190, 195, 197, 199 (8/200)Nov 8, 2009
155...551(14·10n-41)/9n≤200n=173, 174, 180, 181, 187, 188, 189, 191, 192, 193, 194, 195, 196, 197, 199, 200 (16/200)Nov 8, 2009
166...661(5·10n-17)/3n≤200n=172, 175, 176, 180, 181, 184, 186, 187, 190, 194, 195, 196, 197, 200 (14/200)Nov 8, 2009
177...771(16·10n-61)/9n≤250n=173, 176, 177, 179, 182, 183, 184, 185, 188, 193, 194, 198, 202, 203, 204, 207, 208, 209, 212, 213, 216, 217, 218, 219, 222, 223, 230, 231, 232, 233, 234, 239, 242, 244, 248 (35/250)Nov 8, 2009
188...881(17·10n-71)/9n≤200n=174, 180, 181, 182, 183, 184, 185, 186, 189, 191, 192, 193, 195, 197, 198, 199, 200 (17/200)Nov 8, 2009
199...9912·10n-9n≤200n=174, 176, 178, 182, 185, 186, 188, 189, 190, 193, 195, 196, 197, 198, 199 (15/200)Nov 8, 2009
311...113(28·10n+17)/9n≤200n=172, 177, 178, 180, 182, 186, 187, 189, 194, 195, 198, 199, 200 (13/200)Nov 5, 2009
322...223(29·10n+7)/9n≤200n=172, 175, 177, 180, 182, 188, 190, 192, 193, 196, 198 (11/200)Nov 5, 2009
344...443(31·10n-13)/9n≤200n=171, 173, 180, 190, 193, 195, 197, 199, 200 (9/200)Nov 5, 2009
355...553(32·10n-23)/9n≤200n=174, 175, 180, 181, 184, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200 (15/200)Nov 6, 2009
377...773(34·10n-43)/9n≤200n=178, 181, 183, 187, 188, 189, 190, 192, 194, 195, 197, 198, 199, 200 (14/200)Nov 6, 2009
388...883(35·10n-53)/9n≤200n=173, 176, 179, 183, 184, 185, 187, 189, 190, 191, 195, 197, 200 (13/200)Nov 6, 2009
711...117(64·10n+53)/9n≤250n=179, 182, 187, 188, 189, 191, 195, 197, 200, 204, 207, 209, 210, 211, 212, 213, 216, 217, 222, 224, 227, 230, 231, 233, 235, 236, 237, 239, 240, 241, 243, 247, 249, 250 (34/250)Oct 21, 2009
722...227(65·10n+43)/9n≤200n=172, 176, 177, 179, 182, 184, 185, 191, 192, 194, 196, 197, 199 (13/200)Oct 28, 2009
744...447(67·10n+23)/9n≤200n=178, 180, 182, 192, 193, 194, 195, 196, 198 (9/200)Oct 21, 2009
755...557(68·10n+13)/9n≤200n=174, 175, 178, 181, 182, 186, 189, 190, 191, 193, 197, 199, 200 (13/200)Oct 21, 2009
766...667(23·10n+1)/3n≤200n=172, 176, 180, 181, 184, 186, 189, 190, 191, 192, 194, 197, 198, 199 (14/200)Oct 21, 2009
788...887(71·10n-17)/9n≤200n=173, 179, 180, 181, 185, 186, 189, 191, 193, 194, 195, 196, 198 (13/200)Oct 21, 2009
799...9978·10n-3n≤200n=174, 176, 177, 181, 186, 188, 190, 191, 193, 195, 199, 200 (12/200)Oct 21, 2009
911...119(82·10n+71)/9n≤200n=173, 174, 177, 179, 180, 181, 187, 189, 190, 192, 196, 198, 200 (13/200)Oct 23, 2009
922...229(83·10n+61)/9n≤200n=171, 173, 175, 177, 179, 181, 184, 187, 191, 192, 193, 195, 196, 197, 199, 200 (16/200)Oct 23, 2009
944...449(85·10n+41)/9n≤200n=172, 173, 175, 176, 178, 181, 182, 187, 188, 190, 191, 193, 194, 197, 198, 199 (16/200)Oct 23, 2009
955...559(86·10n+31)/9n≤200n=175, 179, 180, 183, 185, 186, 188, 191, 196, 198, 200 (11/200)Oct 23, 2009
988...889(89·10n+1)/9n≤200n=176, 182, 184, 188, 192, 195, 196, 198, 200 (9/200)Oct 23, 2009

Quasi-repdigit numbers of the form ABB...BBC

formgeneral termrangeterms which have not been factored yetlast update
100...00310n+3n≤250n=201, 203, 205, 216, 218, 219, 220, 221, 222, 223, 224, 226, 227, 228, 229, 230, 231, 233, 234, 236, 239, 240, 241, 242, 243, 244, 245, 247, 248, 250 (30/250)Nov 8, 2009
100...00710n+7n≤200n=180, 181, 182, 183, 189, 191, 192, 194, 196, 198, 199, 200 (12/200)Nov 8, 2009
100...00910n+9n≤200n=176, 179, 182, 183, 186, 190, 195, 196, 198 (9/200)Nov 8, 2009
122...223(11·10n+7)/9n≤200n=178, 180, 181, 182, 183, 188, 189, 190, 192, 194, 196, 197, 199, 200 (14/200)Nov 8, 2009
122...227(11·10n+43)/9n≤200n=172, 178, 182, 183, 185, 186, 187, 190, 191, 192, 194, 199 (12/200)Nov 8, 2009
122...229(11·10n+61)/9n≤200n=174, 176, 181, 183, 188, 189, 190, 191, 193, 194, 195, 196, 197, 199 (14/200)Nov 8, 2009
133...337(4·10n+11)/3n≤200n=179, 182, 183, 185, 189, 191, 193, 194, 195, 197, 200 (11/200)Nov 8, 2009
133...339(4·10n+17)/3n≤200n=172, 178, 179, 180, 183, 185, 188, 189, 191, 193, 197, 199 (12/200)Nov 8, 2009
144...447(13·10n+23)/9n≤200n=175, 176, 177, 179, 180, 186, 189, 190, 191, 192, 196, 197 (12/200)Nov 8, 2009
144...449(13·10n+41)/9n≤200n=171, 173, 180, 183, 185, 186, 188, 190, 192, 194, 197, 198, 200 (13/200)Nov 8, 2009
155...553(14·10n-23)/9n≤200n=174, 176, 177, 182, 184, 186, 187, 188, 191, 194, 195, 196, 197, 198 (14/200)Nov 8, 2009
155...557(14·10n+13)/9n≤200n=172, 173, 175, 176, 177, 180, 182, 186, 187, 188, 189, 190, 192, 194, 195, 196 (16/200)Nov 8, 2009
155...559(14·10n+31)/9n≤200n=172, 173, 178, 181, 185, 187, 189, 191, 193, 197, 199, 200 (12/200)Nov 8, 2009
166...663(5·10n-11)/3n≤200n=171, 178, 179, 180, 182, 183, 184, 185, 186, 191, 192, 194, 195, 196, 200 (15/200)Nov 8, 2009
166...667(5·10n+1)/3n≤200n=177, 180, 182, 183, 184, 187, 188, 190, 191, 194, 197, 198 (12/200)Nov 8, 2009
166...669(5·10n+7)/3n≤200n=175, 176, 183, 192, 194, 196, 199, 200 (8/200)Nov 8, 2009
177...773(16·10n-43)/9n≤200n=174, 175, 179, 182, 183, 186, 189, 197, 198, 200 (10/200)Nov 8, 2009
177...779(16·10n+11)/9n≤200n=174, 175, 182, 185, 189, 191, 192, 193, 194, 197, 199, 200 (12/200)Nov 8, 2009
188...883(17·10n-53)/9n≤200n=175, 177, 179, 180, 181, 184, 188, 192, 193, 194, 195, 196 (12/200)Nov 8, 2009
188...889(17·10n+1)/9n≤200n=172, 175, 176, 177, 178, 180, 182, 186, 187, 191, 193, 194, 197, 198, 199 (15/200)Nov 8, 2009
199...9932·10n-7n≤200n=173, 179, 181, 182, 190, 193, 194, 195, 196, 197, 199 (11/200)Nov 8, 2009
199...9972·10n-3n≤200n=172, 178, 179, 183, 185, 187, 193, 195, 196 (9/200)Nov 8, 2009
200...0032·10n+3n≤200n=177, 179, 180, 181, 182, 186, 190, 192, 193, 194, 196, 198, 199, 200 (14/200)Nov 6, 2009
200...0092·10n+9n≤200Completed / Nov 3, 2009Nov 6, 2009
211...113(19·10n+17)/9n≤200n=174, 183, 186, 187, 188, 189, 193, 194, 196 (9/200)Nov 6, 2009
211...117(19·10n+53)/9n≤200n=174, 178, 180, 185, 186, 188, 191, 192, 195, 199 (10/200)Nov 6, 2009
211...119(19·10n+71)/9n≤200n=174, 179, 180, 182, 183, 185, 186, 188, 189, 191, 192, 194, 195, 198, 199, 200 (16/200)Nov 6, 2009
233...339(7·10n+17)/3n≤200n=175, 176, 181, 186, 188, 190, 192, 193, 196, 197 (10/200)Nov 6, 2009
244...441(22·10n-31)/9n≤200n=175, 176, 177, 178, 181, 187, 189, 190, 191, 195, 196, 198 (12/200)Nov 6, 2009
244...443(22·10n-13)/9n≤205n=175, 180, 181, 188, 189, 193, 194, 197, 198, 201, 203, 205 (12/205)Nov 6, 2009
244...447(22·10n+23)/9n≤205n=172, 173, 179, 182, 185, 186, 187, 189, 190, 192, 193, 195, 196, 198, 200, 201, 203 (17/205)Nov 6, 2009
244...449(22·10n+41)/9n≤205n=175, 177, 178, 179, 185, 188, 190, 191, 192, 193, 194, 199, 200, 202, 205 (15/205)Nov 6, 2009
255...551(23·10n-41)/9n≤205n=174, 175, 181, 182, 184, 187, 192, 193, 194, 197, 200, 202, 205 (13/205)Nov 6, 2009
255...557(23·10n+13)/9n≤205n=175, 176, 177, 181, 182, 185, 190, 192, 193, 194, 195, 196, 199 (13/205)Nov 6, 2009
255...559(23·10n+31)/9n≤205n=173, 175, 176, 178, 179, 180, 182, 183, 185, 188, 189, 190, 191, 192, 195, 197, 199, 200, 201, 202, 205 (21/205)Nov 6, 2009
266...663(8·10n-11)/3n≤205n=175, 177, 178, 181, 182, 183, 184, 185, 189, 190, 191, 193, 194, 195, 198, 199, 200, 201, 202, 204, 205 (21/205)Nov 6, 2009
266...669(8·10n+7)/3n≤225n=202, 205, 206, 207, 208, 209, 210, 212, 213, 214, 215, 216, 217, 218, 223, 224, 225 (17/225)Nov 6, 2009
277...771(25·10n-61)/9n≤205n=175, 176, 178, 179, 180, 183, 186, 187, 188, 192, 198, 200, 201 (13/205)Nov 6, 2009
277...773(25·10n-43)/9n≤205n=174, 175, 178, 187, 188, 190, 191, 192, 193, 194, 196, 199, 200, 201, 204 (15/205)Nov 14, 2009
277...779(25·10n+11)/9n≤205n=174, 175, 176, 178, 179, 180, 182, 186, 187, 188, 189, 190, 193, 195, 198, 199, 201, 203 (18/205)Nov 7, 2009
288...881(26·10n-71)/9n≤205n=174, 175, 177, 178, 179, 180, 184, 185, 189, 190, 191, 196, 200, 202, 204 (15/205)Nov 7, 2009
288...883(26·10n-53)/9n≤205n=177, 178, 179, 182, 183, 184, 187, 188, 190, 191, 192, 194, 199, 200, 201, 203, 205 (17/205)Nov 7, 2009
288...887(26·10n-17)/9n≤205n=184, 186, 189, 191, 194, 198, 199, 200, 201, 202, 205 (11/205)Nov 7, 2009
288...889(26·10n+1)/9n≤205n=174, 175, 176, 177, 180, 182, 183, 184, 185, 186, 187, 190, 191, 192, 196, 198, 199, 200, 201, 202, 204, 205 (22/205)Nov 7, 2009
299...9933·10n-7n≤200n=176, 180, 188, 191, 193, 194, 195, 196, 198 (9/200)Nov 7, 2009
300...0013·10n+1n≤200n=173, 174, 175, 176, 182, 183, 193, 194, 195, 196, 197, 200 (12/200)Nov 5, 2009
300...0073·10n+7n≤200n=178, 180, 182, 183, 187, 188, 189, 190, 192, 195, 196, 199, 200 (13/200)Nov 5, 2009
311...117(28·10n+53)/9n≤205n=176, 178, 180, 181, 184, 190, 191, 196, 199, 201, 202, 203, 204 (13/205)Nov 5, 2009
311...119(28·10n+71)/9n≤205n=175, 183, 187, 188, 190, 192, 195, 198, 199, 200, 203, 204, 205 (13/205)Nov 5, 2009
322...221(29·10n-11)/9n≤205n=173, 174, 175, 180, 181, 184, 186, 187, 188, 189, 194, 195, 196, 197, 200, 202, 203, 205 (18/205)Nov 5, 2009
322...227(29·10n+43)/9n≤205n=171, 174, 177, 182, 183, 185, 187, 189, 191, 194, 195, 198, 200, 202, 203, 204, 205 (17/205)Nov 5, 2009
322...229(29·10n+61)/9n≤205n=171, 173, 175, 177, 178, 179, 181, 182, 185, 188, 189, 191, 196, 199, 203, 204 (16/205)Nov 5, 2009
344...447(31·10n+23)/9n≤205n=174, 178, 179, 180, 181, 183, 186, 187, 188, 189, 193, 194, 196, 197, 198, 201, 203 (17/205)Nov 6, 2009
344...449(31·10n+41)/9n≤205n=174, 175, 177, 181, 182, 183, 187, 188, 190, 193, 194, 196, 197, 198, 201, 202, 204 (17/205)Nov 6, 2009
355...551(32·10n-41)/9n≤205n=174, 176, 179, 180, 184, 185, 189, 191, 192, 195, 199, 200, 202 (13/205)Nov 6, 2009
355...557(32·10n+13)/9n≤205n=174, 178, 179, 182, 183, 184, 185, 186, 190, 192, 196, 197, 198, 199, 203, 204 (16/205)Nov 6, 2009
355...559(32·10n+31)/9n≤205n=175, 182, 183, 184, 187, 191, 192, 197, 198, 203, 205 (11/205)Nov 6, 2009
366...661(11·10n-17)/3n≤205n=174, 179, 182, 186, 187, 189, 190, 192, 200, 202, 203 (11/205)Nov 6, 2009
366...667(11·10n+1)/3n≤205n=175, 176, 178, 179, 181, 183, 184, 185, 186, 188, 189, 190, 195, 197, 198, 200, 203, 204, 205 (19/205)Nov 6, 2009
377...771(34·10n-61)/9n≤205n=172, 176, 179, 187, 191, 192, 193, 194, 195, 196, 197, 201, 204, 205 (14/205)Nov 6, 2009
377...779(34·10n+11)/9n≤205n=174, 176, 178, 179, 182, 183, 187, 188, 189, 197, 199, 200, 201, 203, 204, 205 (16/205)Nov 6, 2009
388...881(35·10n-71)/9n≤205n=172, 173, 174, 181, 183, 184, 185, 186, 190, 194, 195, 197, 198, 201, 202, 204, 205 (17/205)Nov 6, 2009
388...887(35·10n-17)/9n≤205n=175, 177, 183, 185, 188, 190, 195, 197, 198, 199, 200, 201, 204 (13/205)Nov 6, 2009
388...889(35·10n+1)/9n≤205n=172, 175, 176, 181, 182, 185, 186, 195, 196, 197, 200, 201, 202, 205 (14/205)Nov 6, 2009
399...9914·10n-9n≤250n=189, 191, 193, 203, 205, 207, 209, 211, 213, 221, 225, 235, 237, 239, 243, 245, 247, 249 (18/250)Nov 6, 2009
399...9974·10n-3n≤200n=174, 177, 181, 184, 185, 186, 188, 189, 190, 191, 192, 193, 199 (13/200)Nov 6, 2009
400...0014·10n+1n≤250n=202, 206, 210, 211, 213, 215, 219, 222, 225, 226, 227, 231, 233, 235, 237, 238, 239, 243, 245, 246, 247, 250 (22/250)Nov 4, 2009
400...0034·10n+3n≤200n=179, 189, 190, 191, 193, 195, 199, 200 (8/200)Nov 4, 2009
400...0074·10n+7n≤200n=171, 174, 176, 178, 179, 184, 186, 187, 188, 192, 193, 197, 199 (13/200)Nov 6, 2009
400...0094·10n+9n≤250n=184, 186, 190, 197, 201, 204, 207, 208, 209, 211, 214, 215, 218, 220, 221, 223, 224, 225, 226, 227, 228, 230, 231, 232, 233, 234, 235, 238, 239, 240, 241, 244, 245, 246, 247, 248, 249 (37/250)Nov 4, 2009
411...113(37·10n+17)/9n≤205n=171, 176, 179, 181, 183, 184, 185, 187, 188, 189, 191, 192, 193, 194, 197, 198, 199, 202 (18/205)Nov 4, 2009
411...117(37·10n+53)/9n≤205n=174, 175, 180, 181, 182, 183, 184, 185, 191, 192, 193, 194, 197, 198, 202, 203, 204, 205 (18/205)Nov 4, 2009
411...119(37·10n+71)/9n≤205n=185, 188, 189, 190, 195, 196, 197, 204 (8/205)Nov 4, 2009
422...221(38·10n-11)/9n≤205n=171, 176, 179, 180, 182, 186, 190, 193, 194, 197, 198, 199, 201, 202, 203, 204, 205 (17/205)Nov 4, 2009
422...223(38·10n+7)/9n≤205n=173, 175, 178, 179, 180, 184, 186, 187, 188, 190, 192, 194, 196, 197, 198, 199, 200, 201, 202, 203, 204 (21/205)Nov 4, 2009
422...227(38·10n+43)/9n≤205n=171, 174, 179, 182, 185, 187, 190, 191, 194, 199, 200, 201, 202 (13/205)Nov 4, 2009
422...229(38·10n+61)/9n≤205n=172, 175, 179, 183, 184, 188, 189, 193, 197, 201, 202, 204, 205 (13/205)Nov 4, 2009
433...331(13·10n-7)/3n≤205n=175, 176, 181, 183, 184, 186, 192, 193, 195, 200, 201 (11/205)Nov 4, 2009
433...337(13·10n+11)/3n≤205n=178, 179, 181, 184, 186, 187, 188, 195, 198, 199, 200, 203, 204 (13/205)Nov 5, 2009
433...339(13·10n+17)/3n≤205n=171, 179, 187, 191, 196, 197, 198, 200, 201, 202 (10/205)Nov 5, 2009
455...553(41·10n-23)/9n≤205n=172, 175, 179, 187, 188, 189, 190, 192, 193, 195, 196, 199, 201, 202, 204 (15/205)Nov 5, 2009
455...557(41·10n+13)/9n≤205n=177, 178, 179, 186, 190, 191, 192, 193, 195, 197, 199, 202, 203, 204 (14/205)Nov 17, 2009
455...559(41·10n+31)/9n≤205n=174, 175, 176, 180, 183, 187, 188, 193, 194, 197, 201, 205 (12/205)Nov 5, 2009
466...661(14·10n-17)/3n≤205n=176, 177, 178, 179, 181, 183, 184, 186, 187, 188, 190, 193, 197, 198, 199, 202, 203, 205 (18/205)Nov 5, 2009
466...663(14·10n-11)/3n≤205n=174, 176, 177, 180, 181, 182, 183, 184, 186, 187, 188, 189, 190, 191, 192, 196, 198, 199, 202, 203 (20/205)Nov 5, 2009
466...667(14·10n+1)/3n≤205n=176, 177, 181, 186, 187, 188, 189, 190, 191, 198, 201, 202, 203, 205 (14/205)Nov 5, 2009
477...771(43·10n-61)/9n≤205n=172, 175, 178, 183, 185, 186, 188, 191, 194, 195, 197, 198, 200, 203 (14/205)Nov 5, 2009
477...779(43·10n+11)/9n≤205n=174, 176, 177, 181, 187, 188, 191, 194, 195, 196, 201, 202, 205 (13/205)Nov 5, 2009
488...881(44·10n-71)/9n≤205n=175, 180, 181, 183, 184, 185, 188, 190, 191, 192, 194, 195, 197, 199, 200, 201, 202, 204 (18/205)Nov 6, 2009
488...883(44·10n-53)/9n≤205n=174, 176, 177, 179, 180, 181, 182, 183, 184, 185, 188, 189, 191, 193, 194, 197, 198, 201, 203, 204 (20/205)Nov 5, 2009
488...887(44·10n-17)/9n≤205n=172, 174, 179, 183, 184, 185, 187, 189, 190, 194, 196, 198, 199, 200, 201, 203, 205 (17/205)Nov 5, 2009
488...889(44·10n+1)/9n≤205n=174, 177, 178, 181, 183, 188, 190, 191, 193, 194, 196, 198, 199, 200, 201, 202, 203 (17/205)Nov 5, 2009
499...9915·10n-9n≤200n=175, 176, 177, 178, 181, 182, 183, 186, 187, 188, 192, 195, 196, 200 (14/200)Nov 5, 2009
499...9935·10n-7n≤200n=172, 177, 183, 185, 187, 191, 192, 198 (8/200)Nov 6, 2009
499...9975·10n-3n≤200n=173, 175, 176, 181, 183, 185, 187, 188, 189, 190, 191, 194, 195, 197, 200 (15/200)Nov 6, 2009
500...0035·10n+3n≤200n=174, 177, 178, 182, 184, 190, 193, 194, 195, 197, 199, 200 (12/200)Nov 4, 2009
500...0095·10n+9n≤200n=172, 176, 180, 181, 182, 183, 184, 185, 190, 193, 197, 198, 199, 200 (14/200)Nov 4, 2009
511...113(46·10n+17)/9n≤205n=174, 175, 182, 183, 187, 188, 189, 190, 191, 192, 193, 196, 199, 201, 203, 204, 205 (17/205)Nov 4, 2009
511...117(46·10n+53)/9n≤205n=173, 178, 179, 180, 181, 183, 184, 188, 189, 190, 191, 192, 194, 197, 199, 203, 205 (17/205)Nov 4, 2009
511...119(46·10n+71)/9n≤205n=174, 177, 179, 181, 183, 184, 185, 186, 187, 190, 191, 192, 194, 197, 201, 202, 203, 204, 205 (19/205)Nov 4, 2009
522...221(47·10n-11)/9n≤205n=173, 174, 175, 178, 180, 181, 182, 184, 185, 186, 187, 191, 194, 195, 196, 199, 203, 205 (18/205)Nov 4, 2009
522...223(47·10n+7)/9n≤205n=172, 175, 176, 180, 182, 189, 192, 198, 201, 203, 205 (11/205)Nov 4, 2009
522...227(47·10n+43)/9n≤205n=173, 175, 176, 178, 183, 184, 187, 190, 191, 192, 196, 199, 201, 202, 203, 205 (16/205)Nov 4, 2009
522...229(47·10n+61)/9n≤205n=176, 177, 178, 180, 181, 183, 185, 189, 190, 192, 194, 200, 201, 202, 204, 205 (16/205)Nov 4, 2009
533...339(16·10n+17)/3n≤205n=172, 173, 174, 176, 179, 181, 184, 185, 187, 188, 189, 191, 192, 198, 199, 201, 202, 204, 205 (19/205)Nov 4, 2009
544...441(49·10n-31)/9n≤205n=175, 177, 179, 180, 181, 182, 183, 184, 186, 189, 190, 192, 193, 194, 195, 200, 201, 204 (18/205)Nov 4, 2009
544...443(49·10n-13)/9n≤205n=174, 175, 176, 179, 181, 187, 189, 191, 192, 195, 197, 201, 203, 204 (14/205)Nov 4, 2009
544...447(49·10n+23)/9n≤205n=172, 176, 179, 182, 184, 186, 188, 191, 193, 194, 196, 199, 201, 202, 203, 204, 205 (17/205)Nov 4, 2009
544...449(49·10n+41)/9n≤205n=179, 180, 181, 182, 183, 185, 189, 190, 191, 192, 193, 195, 202, 203, 204 (15/205)Nov 6, 2009
566...663(17·10n-11)/3n≤205n=173, 174, 176, 178, 181, 182, 184, 187, 188, 189, 190, 192, 197, 198, 199, 203, 204, 205 (18/205)Nov 4, 2009
566...669(17·10n+7)/3n≤205n=172, 175, 177, 178, 179, 181, 184, 186, 188, 189, 191, 193, 194, 196, 197, 198, 199, 201, 202, 203 (20/205)Nov 4, 2009
577...771(52·10n-61)/9n≤205n=175, 176, 179, 181, 182, 183, 188, 190, 192, 194, 195, 196, 197, 198, 199, 201, 202, 204 (18/205)Nov 4, 2009
577...773(52·10n-43)/9n≤205n=172, 174, 177, 179, 180, 182, 185, 186, 187, 188, 189, 190, 191, 194, 196, 198, 199, 201, 202, 203, 204, 205 (22/205)Nov 4, 2009
577...779(52·10n+11)/9n≤205n=171, 176, 179, 185, 186, 187, 191, 192, 193, 194, 198, 202, 203, 205 (14/205)Nov 4, 2009
588...881(53·10n-71)/9n≤205n=172, 174, 176, 177, 179, 180, 182, 184, 186, 187, 188, 189, 190, 198, 199, 200, 201, 202, 203, 205 (20/205)Nov 4, 2009
588...887(53·10n-17)/9n≤205n=173, 174, 175, 181, 182, 183, 185, 186, 188, 189, 190, 192, 193, 196, 199, 204, 205 (17/205)Nov 4, 2009
588...889(53·10n+1)/9n≤205n=175, 177, 181, 182, 184, 186, 188, 189, 191, 192, 194, 196, 198, 200, 201, 203, 205 (17/205)Nov 4, 2009
599...9936·10n-7n≤200n=174, 177, 178, 181, 182, 186, 187, 188, 191, 192, 195, 198, 199, 200 (14/200)Nov 4, 2009
600...0016·10n+1n≤250n=201, 203, 204, 206, 207, 208, 209, 210, 212, 213, 215, 216, 217, 218, 219, 220, 222, 223, 226, 227, 228, 231, 232, 233, 234, 235, 237, 238, 239, 240, 242, 243, 245, 246, 247, 249 (36/250)Nov 4, 2009
600...0076·10n+7n≤200n=174, 175, 177, 181, 184, 186, 189, 190, 191, 193, 196, 197, 199 (13/200)Nov 4, 2009
611...113(55·10n+17)/9n≤205n=174, 176, 177, 178, 182, 184, 185, 186, 187, 195, 196, 197, 202, 204, 205 (15/205)Nov 17, 2009
611...117(55·10n+53)/9n≤205n=174, 175, 176, 177, 180, 181, 182, 183, 185, 187, 188, 189, 190, 193, 195, 196, 201, 203 (18/205)Nov 4, 2009
611...119(55·10n+71)/9n≤205n=175, 177, 178, 179, 180, 184, 185, 187, 188, 189, 193, 194, 195, 198, 200, 202, 203, 204 (18/205)Nov 4, 2009
622...221(56·10n-11)/9n≤205n=172, 177, 181, 184, 187, 188, 191, 193, 195, 196, 197, 200, 202, 203, 204, 205 (16/205)Nov 4, 2009
622...227(56·10n+43)/9n≤205n=177, 180, 182, 183, 185, 187, 188, 192, 194, 195, 196, 197, 198, 201 (14/205)Nov 4, 2009
622...229(56·10n+61)/9n≤205n=171, 172, 178, 179, 181, 182, 183, 184, 188, 189, 193, 194, 195, 197, 198, 202, 203, 204, 205 (19/205)Nov 4, 2009
633...331(19·10n-7)/3n≤205n=171, 173, 174, 177, 182, 187, 189, 191, 192, 193, 194, 195, 196, 198, 199, 201, 202 (17/205)Nov 4, 2009
633...337(19·10n+11)/3n≤205n=173, 174, 177, 179, 180, 183, 186, 187, 188, 190, 193, 195, 196, 198, 200, 203, 204 (17/205)Nov 4, 2009
644...441(58·10n-31)/9n≤205n=176, 180, 183, 184, 185, 186, 187, 190, 191, 192, 194, 197, 198, 199, 200, 201, 203, 204, 205 (19/205)Nov 4, 2009
644...443(58·10n-13)/9n≤205n=176, 178, 181, 184, 187, 188, 193, 194, 196, 197, 199, 200, 202, 203, 204, 205 (16/205)Nov 4, 2009
644...447(58·10n+23)/9n≤205n=173, 174, 177, 178, 180, 181, 182, 183, 184, 188, 189, 190, 192, 193, 195, 196, 199, 202, 203, 204, 205 (21/205)Nov 4, 2009
644...449(58·10n+41)/9n≤205n=176, 178, 181, 182, 183, 184, 185, 186, 191, 193, 196, 197, 198, 199, 201, 202 (16/205)Nov 4, 2009
655...551(59·10n-41)/9n≤205n=173, 174, 180, 181, 183, 189, 190, 191, 196, 197, 198, 199, 200, 201, 203, 204 (16/205)Nov 19, 2009
655...553(59·10n-23)/9n≤205n=171, 181, 183, 186, 189, 191, 192, 193, 194, 196, 201, 205 (12/205)Nov 4, 2009
655...557(59·10n+13)/9n≤200n=158, 161, 170, 171, 172, 173, 175, 182, 183, 186, 187, 190, 192, 193, 195, 196, 199, 200 (18/200)Nov 20, 2009
655...559(59·10n+31)/9n≤200n=161, 167, 172, 176, 182, 183, 184, 186, 187, 188, 191, 193, 194, 195, 197, 198 (16/200)Nov 20, 2009
677...773(61·10n-43)/9n≤200n=166, 172, 175, 177, 185, 187, 190, 194, 195, 196, 197, 198, 199 (13/200)Nov 17, 2009
677...779(61·10n+11)/9n≤150Completed / Nov 15, 2009Nov 16, 2009
688...881(62·10n-71)/9n≤200n=164, 172, 173, 175, 177, 179, 181, 182, 183, 185, 187, 190, 194, 196, 197, 198 (16/200)Nov 18, 2009
688...883(62·10n-53)/9n≤150Completed / Nov 4, 2009Nov 5, 2009
688...887(62·10n-17)/9n≤150Completed / Nov 7, 2009Nov 8, 2009
688...889(62·10n+1)/9n≤150Completed / Nov 4, 2009Nov 5, 2009
699...9917·10n-9n≤200n=177, 179, 183, 185, 188, 189, 192, 193, 195 (9/200)Nov 4, 2009
699...9977·10n-3n≤200n=180, 182, 184, 188, 189, 192, 196, 197, 198, 199 (10/200)Nov 4, 2009
700...0017·10n+1n≤200n=172, 177, 180, 181, 184, 185, 186, 191, 193, 195, 196, 197, 199 (13/200)Oct 21, 2009
700...0037·10n+3n≤200n=173, 179, 180, 181, 183, 184, 186, 195, 196, 197, 198 (11/200)Nov 7, 2009
700...0097·10n+9n≤200n=183, 185, 186, 190, 193, 194, 197, 198, 200 (9/200)Oct 21, 2009
711...113(64·10n+17)/9n≤200n=161, 164, 165, 168, 169, 170, 173, 174, 175, 177, 178, 181, 182, 184, 185, 186, 187, 191, 192, 193, 194, 195, 196, 197, 200 (25/200)Nov 13, 2009
711...119(64·10n+71)/9n≤200n=166, 169, 171, 174, 175, 176, 179, 180, 181, 186, 187, 188, 189, 190, 191, 192, 194, 195, 196, 197, 198, 199, 200 (23/200)Nov 18, 2009
722...221(65·10n-11)/9n≤200n=161, 162, 164, 165, 166, 172, 175, 180, 182, 183, 186, 189, 190, 191, 192, 195, 197 (17/200)Nov 14, 2009
722...223(65·10n+7)/9n≤200n=163, 165, 166, 168, 172, 182, 185, 187, 192, 195, 196, 197, 198, 199, 200 (15/200)Nov 20, 2009
722...229(65·10n+61)/9n≤200n=164, 166, 168, 171, 172, 174, 175, 177, 178, 181, 182, 183, 185, 186, 188, 191, 192, 193, 194, 196, 198 (21/200)Nov 20, 2009
733...331(22·10n-7)/3n≤200n=164, 166, 172, 177, 180, 182, 187, 189, 190, 191, 192, 193, 195, 196, 197, 198, 199, 200 (18/200)Nov 16, 2009
733...339(22·10n+17)/3n≤200n=163, 165, 169, 170, 171, 172, 175, 176, 178, 181, 183, 186, 187, 188, 189, 192, 193, 194, 195, 196, 197, 200 (22/200)Nov 20, 2009
744...441(67·10n-31)/9n≤200n=166, 171, 174, 176, 177, 180, 185, 186, 189, 190, 196, 198 (12/200)Nov 19, 2009
744...443(67·10n-13)/9n≤200n=165, 166, 168, 170, 172, 177, 178, 179, 180, 181, 182, 186, 189, 190, 191, 192, 193, 196 (18/200)Nov 20, 2009
744...449(67·10n+41)/9n≤200n=160, 161, 167, 171, 172, 173, 175, 179, 180, 183, 184, 185, 187, 188, 189, 190, 193, 194, 195, 196, 197, 200 (22/200)Nov 18, 2009
755...551(68·10n-41)/9n≤100Completed / Jan 6, 2005Nov 19, 2009
755...553(68·10n-23)/9n≤100Completed / Dec 6, 2004Oct 21, 2009
755...559(68·10n+31)/9n≤100Completed / Nov 29, 2004Oct 21, 2009
766...661(23·10n-17)/3n≤100Completed / Jan 7, 2005Oct 21, 2009
766...663(23·10n-11)/3n≤100Completed / Jan 7, 2005Oct 21, 2009
766...669(23·10n+7)/3n≤100Completed / Jan 7, 2005Oct 21, 2009
788...883(71·10n-53)/9n≤100Completed / Jan 7, 2005Oct 21, 2009
788...889(71·10n+1)/9n≤100Completed / Dec 6, 2004Oct 21, 2009
799...9918·10n-9n≤200n=177, 186, 188, 189, 191, 196, 197 (7/200)Oct 21, 2009
799...9938·10n-7n≤200n=173, 176, 178, 180, 185, 187, 190, 192, 193, 197, 198, 199, 200 (13/200)Oct 21, 2009
800...0038·10n+3n≤200n=173, 174, 179, 180, 182, 183, 184, 186, 188, 190, 191, 192, 193, 195, 197, 199, 200 (17/200)Oct 22, 2009
800...0098·10n+9n≤200n=178, 179, 191, 192, 193, 195, 196 (7/200)Oct 22, 2009
811...113(73·10n+17)/9n≤100Completed / Jan 7, 2005Oct 22, 2009
811...117(73·10n+53)/9n≤100Completed / Jan 7, 2005Oct 22, 2009
811...119(73·10n+71)/9n≤100Completed / Jan 6, 2005Oct 22, 2009
822...221(74·10n-11)/9n≤100Completed / Jan 7, 2005Oct 22, 2009
822...223(74·10n+7)/9n≤100Completed / Jan 7, 2005Oct 22, 2009
822...227(74·10n+43)/9n≤100Completed / Jan 7, 2005Oct 22, 2009
822...229(74·10n+61)/9n≤100Completed / Jan 6, 2005Oct 22, 2009
833...339(25·10n+17)/3n≤100Completed / Jan 7, 2005Oct 22, 2009
844...441(76·10n-31)/9n≤100Completed / Jan 7, 2005Oct 22, 2009
844...443(76·10n-13)/9n≤100Completed / Jan 7, 2005Oct 22, 2009
844...447(76·10n+23)/9n≤100Completed / Jan 6, 2005Oct 22, 2009
844...449(76·10n+41)/9n≤100Completed / Jan 7, 2005Oct 22, 2009
855...551(77·10n-41)/9n≤100Completed / Dec 6, 2004Oct 22, 2009
855...553(77·10n-23)/9n≤100Completed / Jan 8, 2005Oct 22, 2009
855...557(77·10n+13)/9n≤100Completed / Dec 6, 2004Oct 22, 2009
855...559(77·10n+31)/9n≤100Completed / Jan 8, 2005Oct 22, 2009
866...663(26·10n-11)/3n≤200n=161, 163, 166, 167, 169, 172, 173, 175, 176, 179, 186, 190, 194, 196, 198, 199, 200 (17/200)Nov 17, 2009
866...669(26·10n+7)/3n≤100Completed / Jan 8, 2005Oct 22, 2009
877...771(79·10n-61)/9n≤100Completed / Jan 8, 2005Oct 22, 2009
877...773(79·10n-43)/9n≤100Completed / Nov 29, 2004Oct 22, 2009
877...779(79·10n+11)/9n≤100Completed / Jan 8, 2005Oct 22, 2009
899...9939·10n-7n≤200n=172, 175, 176, 177, 179, 183, 185, 186, 187, 189, 190, 193, 197, 198, 200 (15/200)Oct 22, 2009
900...0019·10n+1n≤200n=176, 178, 179, 181, 182, 185, 187, 188, 191, 195, 196, 199, 200 (13/200)Oct 23, 2009
900...0079·10n+7n≤200n=172, 178, 187, 188, 190, 193, 194, 195, 197, 198 (10/200)Oct 23, 2009
911...113(82·10n+17)/9n≤100Completed / Dec 7, 2004Oct 23, 2009
911...117(82·10n+53)/9n≤100Completed / Jan 8, 2005Oct 23, 2009
922...221(83·10n-11)/9n≤100Completed / Jan 8, 2005Oct 23, 2009
922...223(83·10n+7)/9n≤200n=165, 167, 168, 171, 173, 174, 175, 179, 180, 184, 185, 188, 189, 191, 192, 193, 194, 196, 197, 200 (20/200)Nov 14, 2009
922...227(83·10n+43)/9n≤100Completed / Jan 8, 2005Oct 23, 2009
933...337(28·10n+11)/3n≤100Completed / Dec 1, 2004Oct 23, 2009
944...441(85·10n-31)/9n≤100Completed / Dec 7, 2004Oct 23, 2009
944...443(85·10n-13)/9n≤100Completed / Jan 8, 2005Oct 23, 2009
944...447(85·10n+23)/9n≤100Completed / Jan 8, 2005Oct 23, 2009
955...551(86·10n-41)/9n≤100Completed / Jan 8, 2005Oct 23, 2009
955...553(86·10n-23)/9n≤100Completed / Nov 29, 2004Oct 23, 2009
955...557(86·10n+13)/9n≤100Completed / Jan 8, 2005Oct 23, 2009
966...661(29·10n-17)/3n≤100Completed / Jan 6, 2005Oct 23, 2009
966...667(29·10n+1)/3n≤100Completed / Jan 8, 2005Oct 23, 2009
977...771(88·10n-61)/9n≤100Completed / Jan 8, 2005Oct 23, 2009
977...773(88·10n-43)/9n≤100Completed / Dec 7, 2004Oct 23, 2009
988...881(89·10n-71)/9n≤100Completed / Jan 8, 2005Oct 23, 2009
988...883(89·10n-53)/9n≤100Completed / Jan 8, 2005Oct 23, 2009
988...887(89·10n-17)/9n≤100Completed / Jan 8, 2005Oct 23, 2009

10. List of near-repdigit-related prime numbers

11. Expression generator of near-repdigit-related numbers

For example, enter "33331" or "3w1" to the left box, and click "→" button. The corresponding expression appears in the right box. More complex labels, such as "1w2w3w", are also available. This program is written in JavaScript.

12. Implementations

13. Related links