Factorizations of 99...99899...99

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Factorizations of 99...99899...99	2005-12-28(Wed) 17:39

Last update

Dec 28, 2005 17:39 JST

Sequence

8, 989, 99899, 9998999, 999989999, ...

General term

10²ⁿ⁺¹-10ⁿ-1

Prime numbers

10⁵³-10²⁶-1 = (9)₂₆8(9)₂₆_<53> is prime. (Patrick De Geest / Sep 23, 2002)
10⁷⁵⁷-10³⁷⁸-1 = (9)₃₇₈8(9)₃₇₈_<757> is prime. (Patrick De Geest / Sep 23, 2002)
10²⁴⁹³-10¹²⁴⁶-1 = (9)₁₂₄₆8(9)₁₂₄₆_<2493> is prime. (Harvey Dubner / 1989)
10³⁵⁹⁷-10¹⁷⁹⁸-1 = (9)₁₇₉₈8(9)₁₇₉₈_<3597> is prime. (Patrick De Geest / Sep 23, 2002)
10⁵⁸³⁵-10²⁹¹⁷-1 = (9)₂₉₁₇8(9)₂₉₁₇_<5835> is prime. (Patrick De Geest / Oct 4, 2002)
10⁴⁶⁰⁶⁹-10²³⁰³⁴-1 = (9)₂₃₀₃₄8(9)₂₃₀₃₄_<46069> is prime. (Daniel Heuer / Sep 22, 2001)
10⁹⁵⁰¹⁹-10⁴⁷⁵⁰⁹-1 = (9)₄₇₅₀₉8(9)₄₇₅₀₉_<95019> is prime. (Daniel Heuer / Jan 2, 2003)
10¹⁰⁴²⁸¹-10⁵²¹⁴⁰-1 = (9)₅₂₁₄₀8(9)₅₂₁₄₀_<104281> is prime. (Daniel Heuer / Jan 27, 2003)

References:

Palindromic Wing Primes (Patrick De Geest)
A114647 (On-Line Encyclopedia of Integer Sequences)

Condition

n≤75

Status

Completed up to n=50. (Aug 16, 2004)
Completed up to n=75. (Jun 3, 2005)

Factorization results

10³-10¹-1 =: 989; = 23 · 43

10⁵-10²-1 =: 99899; = 283 · 353

10⁷-10³-1 =: 9998999; = 269 · 37171

10⁹-10⁴-1 =: 999989999; = 127 · 7873937

10¹¹-10⁵-1 =: 99999899999_<11>; = 139 · 719423741

10¹³-10⁶-1 =: 9999998999999_<13>; = 131 · 22091 · 3455519

10¹⁵-10⁷-1 =: 999999989999999_<15>; = 173267 · 5771439397_<10>

10¹⁷-10⁸-1 =: 99999999899999999_<17>; = 107 · 934579438317757_<15>

10¹⁹-10⁹-1 =: 9999999998999999999_<19>; = 23 · 59 · 163 · 599 · 75475452511_<11>

10²¹-10¹⁰-1 =: 999999999989999999999_<21>; = 31394683 · 31852527384653_<14>

10²³-10¹¹-1 =: 99999999999899999999999_<23>; = 349 · 1567 · 220719539 · 828447127

10²⁵-10¹²-1 =: 9999999999998999999999999_<25>; = 31 · 2957 · 2907601 · 37519079267797_<14>

10²⁷-10¹³-1 =: 999999999999989999999999999_<27>; = 353 · 389 · 23087 · 315433772731765981_<18>

10²⁹-10¹⁴-1 =: 99999999999999899999999999999_<29>; = 61 · 223 · 5717 · 13166701 · 97660768252549_<14>

10³¹-10¹⁵-1 =: 9999999999999998999999999999999_<31>; = 61 · 35345033599_<11> · 4638117708116885141_<19>

10³³-10¹⁶-1 =: 999999999999999989999999999999999_<33>; = 127 · 183959 · 42803101495613131101234343_<26>

10³⁵-10¹⁷-1 =: 99999999999999999899999999999999999_<35>; = 139 · 487727 · 705073 · 84437999 · 24776296201229_<14>

10³⁷-10¹⁸-1 =: 9999999999999999998999999999999999999_<37>; = 157697971 · 1168460597_<10> · 54270000151843535377_<20>

10³⁹-10¹⁹-1 =: 999999999999999999989999999999999999999_<39>; = 59 · 24563993 · 325018590983_<12> · 2122955154480399619_<19>

10⁴¹-10²⁰-1 =: 99999999999999999999899999999999999999999_<41>; = 42902192475991_<14> · 2330883207331703966521684889_<28>

10⁴³-10²¹-1 =: 9999999999999999999998999999999999999999999_<43>; = 631 · 4241 · 241327 · 15484473893986641360107966833447_<32>

10⁴⁵-10²²-1 =: 999999999999999999999989999999999999999999999_<45>; = 43 · 3527 · 82705169 · 5675131815569_<13> · 14048096376829785019_<20>

10⁴⁷-10²³-1 =: 99999999999999999999999899999999999999999999999_<47>; = 23 · 2794031 · 237252523 · 6558886326738351092137453084901_<31>

10⁴⁹-10²⁴-1 =: 9999999999999999999999998999999999999999999999999_<49>; = 367 · 6551 · 2957197 · 102780163 · 13684747144040102169978836977_<29>

10⁵¹-10²⁵-1 =: 999999999999999999999999989999999999999999999999999_<51>; = 907 · 81053616549270254621_<20> · 13602549514176858412352500417_<29>

10⁵³-10²⁶-1 =: 99999999999999999999999999899999999999999999999999999_<53>; = definitely prime number

10⁵⁵-10²⁷-1 =: 9999999999999999999999999998999999999999999999999999999_<55>; = 31 · 10106851 · 11870776909_<11> · 16110162912853_<14> · 166895016016144064626427_<24>

10⁵⁷-10²⁸-1 =: 999999999999999999999999999989999999999999999999999999999_<57>; = 733 · 51933367 · 1457767381841_<13> · 1969632706761913_<16> · 9149051439944564773_<19>

10⁵⁹-10²⁹-1 =: 99999999999999999999999999999899999999999999999999999999999_<59>; = 34191344695471031_<17> · 2924716792821721097400097205789950134427129_<43>

10⁶¹-10³⁰-1 =: 9999999999999999999999999999998999999999999999999999999999999_<61>; = 1392269 · 84525695164721_<14> · 13599425109257257_<17> · 6248381612447367512408243_<25>

10⁶³-10³¹-1 =: 999999999999999999999999999999989999999999999999999999999999999_<63>; = 23 · 1366288931549436361_<19> · 31822156987145325308294176988056244464534033_<44>

10⁶⁵-10³²-1 =: 99999999999999999999999999999999899999999999999999999999999999999_<65>; = 83 · 289543 · 337859239 · 345154766951_<12> · 2311564232375456083_<19> · 15436654946555037233_<20>

10⁶⁷-10³³-1 =: 9999999999999999999999999999999998999999999999999999999999999999999_<67>; = 373 · 1117375391975261_<16> · 3409253042687528261598517_<25> · 7037733686918958126150499_<25>

10⁶⁹-10³⁴-1 =: 999999999999999999999999999999999989999999999999999999999999999999999_<69>; = 353 · 45008407 · 62940712160768091985879016331993893947041629777747298891769_<59>

10⁷¹-10³⁵-1 =: 99999999999999999999999999999999999899999999999999999999999999999999999_<71>; = 7001 · 3963465146691984353452727_<25> · 3603834834478825495086710600284569969394337_<43>

10⁷³-10³⁶-1 =: 9999999999999999999999999999999999998999999999999999999999999999999999999_<73>; = 4952345079280229_<16> · 341653603917544643_<18> · 5910212486264108940083164612452458258417_<40>

10⁷⁵-10³⁷-1 =: 999999999999999999999999999999999999989999999999999999999999999999999999999_<75>; = 15567230256149571193_<20> · 64237502981942911916009739093489034309955934566208805943_<56>

10⁷⁷-10³⁸-1 =: 99999999999999999999999999999999999999899999999999999999999999999999999999999_<77>; = 359² · 65239 · 559591 · 128793261445584607_<18> · 165021277683845028870492331516761817141866353_<45>

10⁷⁹-10³⁹-1 =: 9999999999999999999999999999999999999998999999999999999999999999999999999999999_<79>; = 4040255276580827_<16> · 116812817413393767057762776117_<30> · 21188523531074432543884994105182361_<35>

10⁸¹-10⁴⁰-1 =: 999999999999999999999999999999999999999989999999999999999999999999999999999999999_<81>; = 5526359227_<10> · 691044797694261181_<18> · 181291064358740245125683_<24> · 1444369428878735443946701647019_<31>

10⁸³-10⁴¹-1 =: 99999999999999999999999999999999999999999899999999999999999999999999999999999999999_<83>; = 1591841 · 325860793 · 39166994854175921447168042353_<29> · 4922071891109276417023906267948361568391_<40>

10⁸⁵-10⁴²-1 =: 9999999999999999999999999999999999999999998999999999999999999999999999999999999999999_<85>; = 31 · 15887 · 20304692211323114658566448120496165458875889599327508593960978442508279238249167_<80>

10⁸⁷-10⁴³-1 =: 999999999999999999999999999999999999999999989999999999999999999999999999999999999999999_<87>; = 43 · 307 · 234128897 · 323547575513700107831007741566580683678903727964754138044628049188101044367_<75>

10⁸⁹-10⁴⁴-1 =: 99999999999999999999999999999999999999999999899999999999999999999999999999999999999999999_<89>; = 13548553 · 8051046785123261109669994435396781_<34> · 916758056129819848192822914320507817024404674243_<48>

10⁹¹-10⁴⁵-1 =: 9999999999999999999999999999999999999999999998999999999999999999999999999999999999999999999_<91>; = 23 · 353 · 13203263 · 93285938345290255200185413317576457478793327426576986238669490709850779245191367_<80>

10⁹³-10⁴⁶-1 =: 999999999999999999999999999999999999999999999989999999999999999999999999999999999999999999999_<93>; = 127 · 349 · 1481 · 1567607706133097_<16> · 31094372946638945208619623498991_<32> · 312533518044068406724766034725680985099_<39>

10⁹⁵-10⁴⁷-1 =: 99999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999_<95>; = 27909570243413814130901772554828693_<35> · 3583000351773539267800974555826777531487049822276097779173443_<61> (Makoto Kamada / GGNFS-0.50.2 / Total time: 0.80 hours (actual time: 2.0 hours))

10⁹⁷-10⁴⁸-1 =: 9999999999999999999999999999999999999999999999998999999999999999999999999999999999999999999999999_<97>; = 490913 · 1916951 · 3939521 · 1880129243_<10> · 1434674340811183606548319461218669781287749904796273309161995753909691_<70>

10⁹⁹-10⁴⁹-1 =: 999999999999999999999999999999999999999999999999989999999999999999999999999999999999999999999999999_<99>; = 9749 · 11237753507624591_<17> · 9127680453986244150392840833873266696712898279308227257525736684312919750469261_<79>

10¹⁰¹-10⁵⁰-1 =: 99999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999_<101>; = 277 · 9844258787141_<13> · 315929612074325379869310190187693_<33> · 116077186952663070405343709194883721743038816553782499_<54> (Makoto Kamada / GGNFS-0.50.2-k2 / Total time: 0.61 hours (actual time: 0.73 hours))

10¹⁰³-10⁵¹-1 =: 9999999999999999999999999999999999999999999999999998999999999999999999999999999999999999999999999999999_<103>; = 139 · 11540370533_<11> · 6233980602047751218933871347607237902308672865486253916113487276192569844553179155757661977_<91>

10¹⁰⁵-10⁵²-1 =: 999999999999999999999999999999999999999999999999999989999999999999999999999999999999999999999999999999999_<105>; = 337 · 14518287073_<11> · 9366495289372359673865144882571886727_<37> · 21821148284857181963150552519403939629066397499627226137_<56> (Makoto Kamada / GGNFS-0.72.7 / 0.62 hours)

10¹⁰⁷-10⁵³-1 =: 99999999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999999_<107>; = 23 · 32839 · 173651 · 3062906343272328403335314588051_<31> · 248926558232605450464903638036099864754505132117548139106701056967_<66> (Sinkiti Sibata / GGNFS-0.73.4 / 1.84 hours / May 19, 2005)

10¹⁰⁹-10⁵⁴-1 =: 9999999999999999999999999999999999999999999999999999998999999999999999999999999999999999999999999999999999999_<109>; = 365839 · 13835897 · 5480292912533378123538546154177489_<34> · 360494719038064366749818935134129293322105503442872232632531977_<63> (Sinkiti Sibata / GGNFS-0.73.4 / 2.69 hours / May 20, 2005)

10¹¹¹-10⁵⁵-1 =: 999999999999999999999999999999999999999999999999999999989999999999999999999999999999999999999999999999999999999_<111>; = 1097 · 20618985152145703_<17> · 44210567180316589412501580367018014076723995435424524805378771588467816225800478451735469089_<92>

10¹¹³-10⁵⁶-1 =: 99999999999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999999999_<113>; = 1087 · 50095838034814903462011545148739_<32> · 1836406451235725389377129252823059601781791833991426950438618187866012010892843_<79> (Sinkiti Sibata / GGNFS-0.73.4 / 3.16 hours / May 20, 2005)

10¹¹⁵-10⁵⁷-1 =: 9999999999999999999999999999999999999999999999999999999998999999999999999999999999999999999999999999999999999999999_<115>; = 31² · 2940707668138657_<16> · 3973249710067366420956494214167_<31> · 890592222105420775989886473748923695401195757525847169120130701561_<66> (Sinkiti Sibata / GGNFS-0.73.4 / 3.92 hours / May 21, 2005)

10¹¹⁷-10⁵⁸-1 =: 999999999999999999999999999999999999999999999999999999999989999999999999999999999999999999999999999999999999999999999_<117>; = 127 · 131 · 60397 · 66173 · 263711764951_<12> · 9739375666816007_<16> · 1882110043281803856777181_<25> · 3111165804827677456546971759247249642436589158140351_<52>

10¹¹⁹-10⁵⁹-1 =: 99999999999999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999999999999_<119>; = 373 · 3823 · 3007030997_<10> · 7247415287213_<13> · 557279419977487912170601_<24> · 1309253586979421996922270881381_<31> · 4410309218022549660523324395940334641_<37> (Makoto Kamada / msieve 0.81 / 2.1 minutes)

10¹²¹-10⁶⁰-1 =: 9999999999999999999999999999999999999999999999999999999999998999999999999999999999999999999999999999999999999999999999999_<121>; = 164963 · 495988049 · 141711241752071084469553066263261787_<36> · 862457966742904708912917315169458428756335831525053401912917042242675071_<72> (Sinkiti Sibata / GGNFS-0.73.4 / 5.28 hours / May 21, 2005)

10¹²³-10⁶¹-1 =: 999999999999999999999999999999999999999999999999999999999999989999999999999999999999999999999999999999999999999999999999999_<123>; = 107 · 8887 · 20707 · 591566821 · 85849950830736198868395865628820470479255606934716031206837188247339471156132681178701680782255334840613_<104>

10¹²⁵-10⁶²-1 =: 99999999999999999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999999999999999_<125>; = 759210964394892258539_<21> · 17917584972714049336810799980595241433_<38> · 7351196906759077269924957981770147293433930420124404381630195708677_<67> (Sinkiti Sibata / GGNFS-0.73.4 / 6.50 hours / May 22, 2005)

10¹²⁷-10⁶³-1 =: 9999999999999999999999999999999999999999999999999999999999999998999999999999999999999999999999999999999999999999999999999999999_<127>; = 139 · 19963 · 3774747091927625657743729451228357_<34> · 954710136764649859877801672538641593146625737922693616350593097127077693656695281647451_<87> (Sinkiti Sibata / 8.79 hours / May 22, 2005)

10¹²⁹-10⁶⁴-1 =: 999999999999999999999999999999999999999999999999999999999999999989999999999999999999999999999999999999999999999999999999999999999_<129>; = 43 · 491 · 19655059563859_<14> · 1266822658254916747764361237_<28> · 1196242807645941468977500951234458571367_<40> · 1590158905895296818289853912013192282867836543_<46> (Makoto Kamada / msieve 0.88 / 40 minutes)

10¹³¹-10⁶⁵-1 =: 99999999999999999999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999999999999999999_<131>; = 134534758392309648280446413525895437621_<39> · 743302334615975765465545033092533822909903868321676440025588043284561046359265067290782741219_<93> (Sinkiti Sibata / GGNFS-0.73.4 / 13.08 hours / May 23, 2005)

10¹³³-10⁶⁶-1 =: 9999999999999999999999999999999999999999999999999999999999999999998999999999999999999999999999999999999999999999999999999999999999999_<133>; = 353 · 5223404198864323076899326379413653580057029684034084525587_<58> · 5423400299784617038126491337385214152139516430815776771963160171909199109_<73> (Sinkiti Sibata / GGNFS-0.73.4 / 18.21 hours / May 24, 2005)

10¹³⁵-10⁶⁷-1 =: 999999999999999999999999999999999999999999999999999999999999999999989999999999999999999999999999999999999999999999999999999999999999999_<135>; = 23 · 59 · 39724027106266234183_<20> · 457218875534555213276407439012533005109793918496731_<51> · 40573524158501361881716107525796537655755812002892882570878359_<62> (Sinkiti Sibata / GGNFS-0.77.1 / 32.58 hours / May 28, 2005)

10¹³⁷-10⁶⁸-1 =: 99999999999999999999999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999999999999999999999_<137>; = 1109 · 10111 · 8918141184698360372988769652350344895733106432039884781183150171063316216150414796123712097788488267159685293066617890379813823101_<130>

10¹³⁹-10⁶⁹-1 =: 9999999999999999999999999999999999999999999999999999999999999999999998999999999999999999999999999999999999999999999999999999999999999999999_<139>; = 3137 · 458663 · 2154899 · 34697241587098301383_<20> · 92954389819967583294799410578798471446877028263417284583528177631749174895881412379878091766839435311637_<104>

10¹⁴¹-10⁷⁰-1 =: 999999999999999999999999999999999999999999999999999999999999999999999989999999999999999999999999999999999999999999999999999999999999999999999_<141>; = 211966639 · 4717723528182187197863716657789719447313593532046333008091900725943953803032183757935606083747924124984592504672397999385176834360241_<133>

10¹⁴³-10⁷¹-1 =: 99999999999999999999999999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999999999999999999999999_<143>; = 83008147 · 61472649501964109609_<20> · 19597350000037221348317850777298048149828170302996847565744793394887360712136624889864406185227447272334135804104413_<116>

10¹⁴⁵-10⁷²-1 =: 9999999999999999999999999999999999999999999999999999999999999999999999998999999999999999999999999999999999999999999999999999999999999999999999999_<145>; = 31 · 1368793 · 22237603 · 10597722855424188072822206751894247196197941457784418105452351775452103838922983657131636733082859266090678709247678411826699246051_<131>

10¹⁴⁷-10⁷³-1 =: 999999999999999999999999999999999999999999999999999999999999999999999999989999999999999999999999999999999999999999999999999999999999999999999999999_<147>; = 83 · 113 · 3708202526668109917228307_<25> · 15862558419952376316679770375454352915971_<41> · 1812620068912988621361116139700801998459166922290934821642168987677184217078173_<79> (Sinkiti Sibata / GGNFS-0.77.1 / 85.26 hours / May 31, 2005)

10¹⁴⁹-10⁷⁴-1 =: 99999999999999999999999999999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999999999999999999999999999_<149>; = 61 · 18917 · 44457307 · 2986416743_<10> · 34754472743_<11> · 34517731760870911581764325642423398651167757_<44> · 544090801698841188467997932847833144106032723664810376251870210457031777_<72> (Sinkiti Sibata / GGNFS-0.77.1 / 64.30 hours / Jun 3, 2005)

10¹⁵¹-10⁷⁵-1 =: 9999999999999999999999999999999999999999999999999999999999999999999999999998999999999999999999999999999999999999999999999999999999999999999999999999999_<151>; = 23 · 61 · 49177 · 168009464541559_<15> · 862673683618300651289725538445729629343776366298501594932974038681389563496817833037381221227696854235954292578368978185831958931_<129>

Factorizations

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