Since June 16, 2000

STUDIO KAMADA

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Last update

Sequence

General term

Prime numbers

1. 10³-8·10¹-1 = 919 is prime. (Patrick De Geest / Sep 23, 2002)
2. 10¹¹-8·10⁵-1 = 99999199999_<11> is prime. (Patrick De Geest / Sep 23, 2002)
3. 10²⁷-8·10¹³-1 = (9)₁₃1(9)_13<27> is prime. (Patrick De Geest / Sep 23, 2002)
4. 10⁸⁷-8·10⁴³-1 = (9)₄₃1(9)_43<87> is prime. (Patrick De Geest / Sep 23, 2002)
5. 10³³⁹-8·10¹⁶⁹-1 = (9)₁₆₉1(9)_169<339> is prime. (Patrick De Geest / Sep 23, 2002)
6. 10³⁶³-8·10¹⁸¹-1 = (9)₁₈₁1(9)_181<363> is prime. (Patrick De Geest / Sep 23, 2002)
7. 10³¹⁵⁹-8·10¹⁵⁷⁹-1 = (9)₁₅₇₉1(9)_1579<3159> is prime. (Patrick De Geest / Sep 23, 2002)
8. 10³⁶¹⁵⁵-8·10¹⁸⁰⁷⁷-1 = (9)₁₈₀₇₇1(9)_18077<36155> is prime. (Daniel Heuer / Jul 21, 2001)
9. 10⁴⁵³⁰⁵-8·10²²⁶⁵²-1 = (9)₂₂₆₅₂1(9)_22652<45305> is prime. (Daniel Heuer / Sep 18, 2001)

• Palindromic Wing Primes (Patrick De Geest)
• A114643 (On-Line Encyclopedia of Integer Sequences)

Condition

Status

Factorization results

10³-8·10¹-1 =

919

= definitely prime number

10⁵-8·10²-1 =

99199

= 19 · 23 · 227

10⁷-8·10³-1 =

9991999

= 79 · 126481

10⁹-8·10⁴-1 =

999919999

= 13 · 76916923

10¹¹-8·10⁵-1 =

99999199999_<11>

= definitely prime number

10¹³-8·10⁶-1 =

9999991999999_<13>

= 19 · 526315368421_<12>

10¹⁵-8·10⁷-1 =

999999919999999_<15>

= 6131 · 163105516229_<12>

10¹⁷-8·10⁸-1 =

99999999199999999_<17>

= 17 · 23 · 127 · 1307 · 24733 · 62297

10¹⁹-8·10⁹-1 =

9999999991999999999_<19>

= 67 · 21523 · 257837 · 26895347

10²¹-8·10¹⁰-1 =

999999999919999999999_<21>

= 13 · 1447 · 76649 · 693556143941_<12>

10²³-8·10¹¹-1 =

99999999999199999999999_<23>

= 3119 · 6873161 · 4664747150761_<13>

10²⁵-8·10¹²-1 =

9999999999991999999999999_<25>

= 127 · 1511 · 52111288868465895767_<20>

10²⁷-8·10¹³-1 =

999999999999919999999999999_<27>

= definitely prime number

10²⁹-8·10¹⁴-1 =

99999999999999199999999999999_<29>

= 7688627 · 162701111 · 79939364076067_<14>

10³¹-8·10¹⁵-1 =

9999999999999991999999999999999_<31>

= 17 · 2063 · 285135867240739984602663169_<27>

10³³-8·10¹⁶-1 =

999999999999999919999999999999999_<33>

= 13 · 79 · 4859513 · 200371896210449084572349_<24>

10³⁵-8·10¹⁷-1 =

99999999999999999199999999999999999_<35>

= 4877 · 13183 · 115875647 · 474810569 · 28269650723_<11>

10³⁷-8·10¹⁸-1 =

9999999999999999991999999999999999999_<37>

= 36083 · 277138818834354127760995482637253_<33>

10³⁹-8·10¹⁹-1 =

999999999999999999919999999999999999999_<39>

= 109 · 685039 · 34036967 · 211794299 · 1857774877544953_<16>

10⁴¹-8·10²⁰-1 =

99999999999999999999199999999999999999999_<41>

= 19 · 439 · 61328751196183_<14> · 195486943947596742826933_<24>

10⁴³-8·10²¹-1 =

9999999999999999999991999999999999999999999_<43>

= 51941 · 9093325445303715281_<19> · 21172247334699162019_<20>

10⁴⁵-8·10²²-1 =

999999999999999999999919999999999999999999999_<45>

= 13 · 14249 · 62459 · 378493 · 228359657333277685437716049421_<30>

10⁴⁷-8·10²³-1 =

99999999999999999999999199999999999999999999999_<47>

= 113 · 619 · 1474628993245813_<16> · 969500726856482969681994809_<27>

10⁴⁹-8·10²⁴-1 =

9999999999999999999999991999999999999999999999999_<49>

= 17 · 19 · 23 · 307 · 1746744057775001253151_<22> · 2510163392527721929183_<22>

10⁵¹-8·10²⁵-1 =

999999999999999999999999919999999999999999999999999_<51>

= 2971 · 50475392255917_<14> · 684952804408487_<15> · 9735471672030132311_<19>

10⁵³-8·10²⁶-1 =

99999999999999999999999999199999999999999999999999999_<53>

= 709 · 114865818283_<12> · 1227899871890575574218026439264857005017_<40>

10⁵⁵-8·10²⁷-1 =

9999999999999999999999999991999999999999999999999999999_<55>

= 821 · 186301 · 2107525878912829428881_<22> · 31021924795581386818727599_<26>

10⁵⁷-8·10²⁸-1 =

999999999999999999999999999919999999999999999999999999999_<57>

= 13 · 15654887 · 46910957 · 104744786951586897251271213882444621182497_<42>

10⁵⁹-8·10²⁹-1 =

99999999999999999999999999999199999999999999999999999999999_<59>

= 79 · 33911093 · 5067443033_<10> · 47811708034534183_<17> · 154066418497255998908803_<24>

10⁶¹-8·10³⁰-1 =

9999999999999999999999999999991999999999999999999999999999999_<61>

= 23 · 6571 · 647003809 · 88149253097_<11> · 1160152880236523539582758455347073011_<37>

10⁶³-8·10³¹-1 =

999999999999999999999999999999919999999999999999999999999999999_<63>

= 17 · 10317031 · 344387909 · 67035795598903_<14> · 246968565693225008135065452965731_<33>

10⁶⁵-8·10³²-1 =

99999999999999999999999999999999199999999999999999999999999999999_<65>

= 113 · 15942179123859419238173576594719_<32> · 55510338037034407250677309418417_<32>

10⁶⁷-8·10³³-1 =

9999999999999999999999999999999991999999999999999999999999999999999_<67>

= 2687 · 3290579 · 24881873 · 45454506054374476832787760623844419253510069098731_<50>

10⁶⁹-8·10³⁴-1 =

999999999999999999999999999999999919999999999999999999999999999999999_<69>

= 13 · 109 · 1077107650217050755443597_<25> · 655195701102268240363374634844028831004451_<42>

10⁷¹-8·10³⁵-1 =

99999999999999999999999999999999999199999999999999999999999999999999999_<71>

= 2207 · 326797472200460409732297151_<27> · 138649714059990198816937387610253846280607_<42>

10⁷³-8·10³⁶-1 =

9999999999999999999999999999999999991999999999999999999999999999999999999_<73>

= 739 · 756754961 · 94132170193595000267517210407_<29> · 189960023021447065884541005982483_<33>

10⁷⁵-8·10³⁷-1 =

999999999999999999999999999999999999919999999999999999999999999999999999999_<75>

= 70490999036439981131047105940143_<32> · 14186208362333676601114110453273238264066993_<44>

10⁷⁷-8·10³⁸-1 =

99999999999999999999999999999999999999199999999999999999999999999999999999999_<77>

= 19 · 397 · 2099 · 9049 · 697979818409716616758757574713857558364208682844716929296984854043_<66>

10⁷⁹-8·10³⁹-1 =

9999999999999999999999999999999999999991999999999999999999999999999999999999999_<79>

= 83 · 2347 · 43761989 · 2244601651630210678314583_<25> · 522603708505007920910446285438895570985877_<42>

10⁸¹-8·10⁴⁰-1 =

999999999999999999999999999999999999999919999999999999999999999999999999999999999_<81>

= 13 · 17² · 33457411321_<11> · 2225694811079476871_<19> · 3574381108618506295290908370998150887194823722677_<49>

10⁸³-8·10⁴¹-1 =

99999999999999999999999999999999999999999199999999999999999999999999999999999999999_<83>

= 59 · 7477 · 54495120366676220893278796872550561699_<38> · 4159709399494495891975119257857732345907_<40>

10⁸⁵-8·10⁴²-1 =

9999999999999999999999999999999999999999991999999999999999999999999999999999999999999_<85>

= 19 · 67 · 79 · 809 · 6217 · 991931 · 19931209447165513364284354306520240847681605141981248373422939921579_<68>

10⁸⁷-8·10⁴³-1 =

999999999999999999999999999999999999999999919999999999999999999999999999999999999999999_<87>

= definitely prime number

10⁸⁹-8·10⁴⁴-1 =

99999999999999999999999999999999999999999999199999999999999999999999999999999999999999999_<89>

= 199 · 1353080514375407_<16> · 371384080603683993494866612869808012487690643003594999162490879483851143_<72>

10⁹¹-8·10⁴⁵-1 =

9999999999999999999999999999999999999999999991999999999999999999999999999999999999999999999_<91>

= 59 · 41617 · 166987 · 2794449929270998505056756253449_<31> · 8727668113992304734811397487631827792659827509791_<49>

10⁹³-8·10⁴⁶-1 =

999999999999999999999999999999999999999999999919999999999999999999999999999999999999999999999_<93>

= 13 · 23 · 1633033 · 2048018383799452043260529891128346246229191111607587176559810276656010410585353411797_<85>

10⁹⁵-8·10⁴⁷-1 =

99999999999999999999999999999999999999999999999199999999999999999999999999999999999999999999999_<95>

= 17 · 264991 · 57679357 · 1264108316166947551_<19> · 304449493477795754592016280359627163392781175705453342781140731_<63>

10⁹⁷-8·10⁴⁸-1 =

9999999999999999999999999999999999999999999999991999999999999999999999999999999999999999999999999_<97>

= 55553081 · 395303393 · 455366741355377298736018147830538902362626236819403657375559692873514994519884503_<81>

10⁹⁹-8·10⁴⁹-1 =

999999999999999999999999999999999999999999999999919999999999999999999999999999999999999999999999999_<99>

= 6701459 · 51986051975215563583303_<23> · 99269206328873431576283567_<26> · 28915402951265110837130990524621566155179261_<44>

10¹⁰¹-8·10⁵⁰-1 =

99999999999999999999999999999999999999999999999999199999999999999999999999999999999999999999999999999_<101>

= 127 · 787401574803149606299212598425196850393700787401568503937007874015748031496062992125984251968503937_<99>

10¹⁰³-8·10⁵¹-1 =

9999999999999999999999999999999999999999999999999991999999999999999999999999999999999999999999999999999_<103>

= 33811 · 8013832879987988879280484662735092200878796103_<46> · 36906401565395945334412131190452741609887798913426803_<53> (Makoto Kamada / GGNFS-0.72.7 / 0.66 hours)

10¹⁰⁵-8·10⁵²-1 =

999999999999999999999999999999999999999999999999999919999999999999999999999999999999999999999999999999999_<105>

= 13 · 23 · 7549777 · 3554457705692497033_<19> · 9849075689288913081825617_<25> · 12653942649770387767124787319266046298893937805735733_<53>

10¹⁰⁷-8·10⁵³-1 =

99999999999999999999999999999999999999999999999999999199999999999999999999999999999999999999999999999999999_<107>

= 857 · 3152693 · 414356618114911461820039730429966789779_<39> · 89322982506893702114203748740442802204720125497732825880281_<59> (Kenichiro Yamaguchi / GGNFS-0.77.0 / 1.24 hours on Pentium 4 2.4BGHz / May 29, 2005)

10¹⁰⁹-8·10⁵⁴-1 =

9999999999999999999999999999999999999999999999999999991999999999999999999999999999999999999999999999999999999_<109>

= 127 · 71761 · 7456148442940953114594620702636947234993_<40> · 147161176532989056677907743727305226400991662335578342609981569_<63> (Kenichiro Yamaguchi / GGNFS-0.77.0 / 1.13 hours on Pentium M 1.3GHz / May 31, 2005)

10¹¹¹-8·10⁵⁵-1 =

999999999999999999999999999999999999999999999999999999919999999999999999999999999999999999999999999999999999999_<111>

= 79 · 5016332105457035533508494815374477_<34> · 2523403072601785194850307494500371919914170316323356023807466059956538685653_<76> (Kenichiro Yamaguchi / GGNFS-0.77.0 / 1.67 hours on Pentium 4 2.4BGHz / Jun 3, 2005)

10¹¹³-8·10⁵⁶-1 =

99999999999999999999999999999999999999999999999999999999199999999999999999999999999999999999999999999999999999999_<113>

= 17 · 19 · 313543 · 159335397601_<12> · 6197094229842667286156771479358884977109429692718683339030152891125256481542077869213157913891_<94>

10¹¹⁵-8·10⁵⁷-1 =

9999999999999999999999999999999999999999999999999999999991999999999999999999999999999999999999999999999999999999999_<115>

= 7447549 · 1342723626256101168317254441696187564526262264269761769944984584861408766830537133760382106918665456246075051_<109>

10¹¹⁷-8·10⁵⁸-1 =

999999999999999999999999999999999999999999999999999999999919999999999999999999999999999999999999999999999999999999999_<117>

= 13 · 809 · 432537038237_<12> · 41672282143267057_<17> · 551001035033436280372014708069058402493_<39> · 9573817057775709650651888717778755693138590331_<46> (Makoto Kamada / msieve 0.88 / 1.1 hours)

10¹¹⁹-8·10⁵⁹-1 =

99999999999999999999999999999999999999999999999999999999999199999999999999999999999999999999999999999999999999999999999_<119>

= 4491966554993345408153_<22> · 22261964503907163281959454395007405647836927093756760477087489611300536105321260065934128485636183_<98>

10¹²¹-8·10⁶⁰-1 =

9999999999999999999999999999999999999999999999999999999999991999999999999999999999999999999999999999999999999999999999999_<121>

= 19 · 4481 · 503941416165261131_<18> · 233072697756471881138623029823601928024450509953075430672658551441090252414557104002700144689687311_<99>

10¹²³-8·10⁶¹-1 =

999999999999999999999999999999999999999999999999999999999999919999999999999999999999999999999999999999999999999999999999999_<123>

= 911 · 136916487667_<12> · 518589890837_<12> · 15459727224713996345038585535150624413766630490660986469154624418407048560059777921691871993523071_<98>

10¹²⁵-8·10⁶²-1 =

99999999999999999999999999999999999999999999999999999999999999199999999999999999999999999999999999999999999999999999999999999_<125>

= 311 · 91807 · 283007 · 316851147327813119486859679_<27> · 39058121600449204641292977018475065659076049457477469068459067018722999549731875886279_<86> (Makoto Kamada / GMP-ECM 6.0 B1=3000000, sigma=495719048 for P27 / May 24, 2005)

10¹²⁷-8·10⁶³-1 =

9999999999999999999999999999999999999999999999999999999999999991999999999999999999999999999999999999999999999999999999999999999_<127>

= 17 · 4724051 · 1060225916314822690553170423_<28> · 117445960798160808874889516667862686525004294847424941869359285457466958648247564886087157139_<93> (Makoto Kamada / GMP-ECM 6.0 B1=3000000, sigma=4226633517 for P28 / May 22, 2005)

10¹²⁹-8·10⁶⁴-1 =

999999999999999999999999999999999999999999999999999999999999999919999999999999999999999999999999999999999999999999999999999999999_<129>

= 13 · 355137916961_<12> · 8620582561926197_<16> · 17394065538852265094936421036067329135787440209_<47> · 1444514437885723676563046033646529294763844095412943391_<55> (Kenichiro Yamaguchi / GGNFS-0.77.0 / 9.29 hours on Pentium 4 2.4BGHz / Jun 11, 2005)

10¹³¹-8·10⁶⁵-1 =

99999999999999999999999999999999999999999999999999999999999999999199999999999999999999999999999999999999999999999999999999999999999_<131>

= 86623547452681511_<17> · 12349682394629342671581050237_<29> · 93477749070193650427659700633795469514655311383408098352436339811727829399507869649757_<86>

10¹³³-8·10⁶⁶-1 =

9999999999999999999999999999999999999999999999999999999999999999991999999999999999999999999999999999999999999999999999999999999999999_<133>

= 19993 · 3643201 · 402634549021948039744699_<24> · 6118147212141979493205298499_<28> · 55732425111329964667434258909633836387073169890728743732317075162507143_<71>

10¹³⁵-8·10⁶⁷-1 =

999999999999999999999999999999999999999999999999999999999999999999919999999999999999999999999999999999999999999999999999999999999999999_<135>

= 313 · 551241850199_<12> · 5795801203701013592550760375985289941601679448894953240153574970000182552342008222428829851835929181469596104931354919777_<121>

10¹³⁷-8·10⁶⁸-1 =

99999999999999999999999999999999999999999999999999999999999999999999199999999999999999999999999999999999999999999999999999999999999999999_<137>

= 23 · 79 · 33641 · 699133 · 37153102097025281291_<20> · 62982702663225536917015672618162162150781940869849663197870842762832416119023724563879623917427964393889_<104>

10¹³⁹-8·10⁶⁹-1 =

9999999999999999999999999999999999999999999999999999999999999999999991999999999999999999999999999999999999999999999999999999999999999999999_<139>

= 163 · 1062432269_<10> · 302855476516074177647629415714756028303921414367_<48> · 190667078116784852082971325091397033054587376040953643790001855636676885107219351_<81> (Kenichiro Yamaguchi / GGNFS-0.77.1 / 208.65 hours on Pentium M 1.3GHz / Aug 9, 2005)

10¹⁴¹-8·10⁷⁰-1 =

999999999999999999999999999999999999999999999999999999999999999999999919999999999999999999999999999999999999999999999999999999999999999999999_<141>

= 13 · 12491 · 114682796422603_<15> · 53698377678516309152911620590144736286824531722474351248278451171994068187539834635247175428318039584359788238173227370451_<122>

10¹⁴³-8·10⁷¹-1 =

99999999999999999999999999999999999999999999999999999999999999999999999199999999999999999999999999999999999999999999999999999999999999999999999_<143>

= 939623 · 692765651 · 5545315714417291165686064725832927750643_<40> · 27703442430900092553537300647051906583048198294477171096908738767897374226177031471283041_<89> (Sinkiti Sibata / GGNFS-0.77.1 / 174.95 hours / Sep 6, 2005)

10¹⁴⁵-8·10⁷²-1 =

9999999999999999999999999999999999999999999999999999999999999999999999991999999999999999999999999999999999999999999999999999999999999999999999999_<145>

= 17 · 12281 · 47897996426809466560013794622970921126369283972851415625284394353784181169381684764126316596176781925212068379179698913194461075693203753287_<140>

10¹⁴⁷-8·10⁷³-1 =

999999999999999999999999999999999999999999999999999999999999999999999999919999999999999999999999999999999999999999999999999999999999999999999999999_<147>

= 268621621 · 1246336831459_<13> · 3257510230715911_<16> · 6918532079648681928624227305677184757812901_<43> · 132532947820656116347673308311597774490809937550021677979979509663531_<69> (Sinkiti Sibata / GGNFS-0.77.1 gnfs / 46.39 hours / Aug 17, 2005)

10¹⁴⁹-8·10⁷⁴-1 =

99999999999999999999999999999999999999999999999999999999999999999999999999199999999999999999999999999999999999999999999999999999999999999999999999999_<149>

= 19 · 23 · 246289 · 1886729098152791531_<19> · 492452107297163657920285541552714078377479844183760949367334964747832811911605974270369012672538993838138892728044167041753_<123>

10¹⁵¹-8·10⁷⁵-1 =

9999999999999999999999999999999999999999999999999999999999999999999999999991999999999999999999999999999999999999999999999999999999999999999999999999999_<151>

= 67 · 149253731343283582089552238805970149253731343283582089552238805970149253731223880597014925373134328358208955223880597014925373134328358208955223880597_<150>