Factorizations of 99...99299...99

Since June 16, 2000

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Factorizations of 99...99299...99	2005-12-28(Wed) 17:39

Last update

Dec 28, 2005 17:39 JST

Sequence

2, 929, 99299, 9992999, 999929999, ...

General term

10²ⁿ⁺¹-7·10ⁿ-1

Prime numbers

10³-7·10¹-1 = 929 is prime. (Patrick De Geest / Sep 23, 2002)
10¹⁷-7·10⁸-1 = 99999999299999999_<17> is prime. (Patrick De Geest / Sep 23, 2002)
10¹⁹-7·10⁹-1 = 9999999992999999999_<19> is prime. (Patrick De Geest / Sep 23, 2002)
10⁷⁰⁵-7·10³⁵²-1 = (9)₃₅₂2(9)₃₅₂_<705> is prime. (Patrick De Geest / Sep 23, 2002)
10¹⁰⁶¹-7·10⁵³⁰-1 = (9)₅₃₀2(9)₅₃₀_<1061> is prime. (Jeff Heleen / Sep 28, 2002)
10¹³⁹⁵-7·10⁶⁹⁷-1 = (9)₆₉₇2(9)₆₉₇_<1395> is prime. (Jeff Heleen / Sep 28, 2002)
10²⁶³¹-7·10¹³¹⁵-1 = (9)₁₃₁₅2(9)₁₃₁₅_<2631> is prime. (Harvey Dubner / 1989)
10³⁸³⁷-7·10¹⁹¹⁸-1 = (9)₁₉₁₈2(9)₁₉₁₈_<3837> is prime. (Harvey Dubner / 1999)
10⁵⁷⁴⁹-7·10²⁸⁷⁴-1 = (9)₂₈₇₄2(9)₂₈₇₄_<5749> is prime. (Harvey Dubner / 1999)
10¹¹⁷⁵³-7·10⁵⁸⁷⁶-1 = (9)₅₈₇₆2(9)₅₈₇₆_<11753> is prime. (Harvey Dubner / 1999)
10¹³⁵³⁷-7·10⁶⁷⁶⁸-1 = (9)₆₇₆₈2(9)₆₇₆₈_<13537> is prime. (Harvey Dubner / 1999)

References:

Palindromic Wing Primes (Patrick De Geest)
A114644 (On-Line Encyclopedia of Integer Sequences)

Condition

n≤75

Status

Completed up to n=50. (Aug 16, 2004)
Completed up to n=75. (Sep 20, 2005)

Factorization results

10³-7·10¹-1 =: 929; = definitely prime number

10⁵-7·10²-1 =: 99299; = 109 · 911

10⁷-7·10³-1 =: 9992999; = 47 · 173 · 1229

10⁹-7·10⁴-1 =: 999929999; = 139 · 311 · 23131

10¹¹-7·10⁵-1 =: 99999299999_<11>; = 205537 · 486527

10¹³-7·10⁶-1 =: 9999992999999_<13>; = 67049 · 149144551

10¹⁵-7·10⁷-1 =: 999999929999999_<15>; = 2782723 · 359360213

10¹⁷-7·10⁸-1 =: 99999999299999999_<17>; = definitely prime number

10¹⁹-7·10⁹-1 =: 9999999992999999999_<19>; = definitely prime number

10²¹-7·10¹⁰-1 =: 999999999929999999999_<21>; = 1531031 · 653154638887129_<15>

10²³-7·10¹¹-1 =: 99999999999299999999999_<23>; = 17 · 114203 · 3339151 · 15425438099_<11>

10²⁵-7·10¹²-1 =: 9999999999992999999999999_<25>; = 17 · 588235294117235294117647_<24>

10²⁷-7·10¹³-1 =: 999999999999929999999999999_<27>; = 233 · 4291845493561931330472103_<25>

10²⁹-7·10¹⁴-1 =: 99999999999999299999999999999_<29>; = 80146861 · 10577745863_<11> · 117956086093_<12>

10³¹-7·10¹⁵-1 =: 9999999999999992999999999999999_<31>; = 331 · 12024223661137_<14> · 2512551430674317_<16>

10³³-7·10¹⁶-1 =: 999999999999999929999999999999999_<33>; = 1945549 · 38158024423_<11> · 13470134899397837_<17>

10³⁵-7·10¹⁷-1 =: 99999999999999999299999999999999999_<35>; = 19469 · 37397 · 1653521 · 609570613 · 136265481091_<12>

10³⁷-7·10¹⁸-1 =: 9999999999999999992999999999999999999_<37>; = 139 · 71942446043165467575539568345323741_<35>

10³⁹-7·10¹⁹-1 =: 999999999999999999929999999999999999999_<39>; = 47 · 107 · 289084649652697963_<18> · 687849352919694137_<18>

10⁴¹-7·10²⁰-1 =: 99999999999999999999299999999999999999999_<41>; = 6485243 · 15419622672581428328791997462546893_<35>

10⁴³-7·10²¹-1 =: 9999999999999999999992999999999999999999999_<43>; = 2215006022870241309047_<22> · 4514660410287207794617_<22>

10⁴⁵-7·10²²-1 =: 999999999999999999999929999999999999999999999_<45>; = 2503195320607_<13> · 399489401313481975270969442772257_<33>

10⁴⁷-7·10²³-1 =: 99999999999999999999999299999999999999999999999_<47>; = 1879 · 37509061 · 386057758970623_<15> · 3675231857582380954427_<22>

10⁴⁹-7·10²⁴-1 =: 9999999999999999999999992999999999999999999999999_<49>; = 67 · 179 · 2791 · 514375321 · 1752364011187_<13> · 331442259440932014499_<21>

10⁵¹-7·10²⁵-1 =: 999999999999999999999999929999999999999999999999999_<51>; = 913873 · 1911745747330748779_<19> · 572379433868351998767479597_<27>

10⁵³-7·10²⁶-1 =: 99999999999999999999999999299999999999999999999999999_<53>; = 204923 · 487988171166730918442536949488344402531682632013_<48>

10⁵⁵-7·10²⁷-1 =: 9999999999999999999999999992999999999999999999999999999_<55>; = 17 · 71 · 43093483 · 7893526957_<10> · 25829075603_<11> · 942977158192333734995149_<24>

10⁵⁷-7·10²⁸-1 =: 999999999999999999999999999929999999999999999999999999999_<57>; = 17 · 131 · 7481 · 397314300333200966923_<21> · 151072679292396361548824834599_<30>

10⁵⁹-7·10²⁹-1 =: 99999999999999999999999999999299999999999999999999999999999_<59>; = 368572252583_<12> · 1419515173027907_<16> · 191133725113584418887941927137379_<33>

10⁶¹-7·10³⁰-1 =: 9999999999999999999999999999992999999999999999999999999999999_<61>; = 769 · 1308411588478906396849933_<25> · 9938693057181485043670562261622587_<34>

10⁶³-7·10³¹-1 =: 999999999999999999999999999999929999999999999999999999999999999_<63>; = 317 · 10987 · 49741 · 4649339 · 20711497 · 2900338505025763_<16> · 20667869429991283340429_<23>

10⁶⁵-7·10³²-1 =: 99999999999999999999999999999999299999999999999999999999999999999_<65>; = 2164535610451_<13> · 46199286127320456491163235758678361809365685983782949_<53>

10⁶⁷-7·10³³-1 =: 9999999999999999999999999999999992999999999999999999999999999999999_<67>; = 367 · 1013 · 33617 · 4045763 · 956464973 · 206774046923017974178724028448156679002043_<42>

10⁶⁹-7·10³⁴-1 =: 999999999999999999999999999999999929999999999999999999999999999999999_<69>; = 156511 · 605778599 · 10547297772287232120877843824250903001948313146748395191_<56>

10⁷¹-7·10³⁵-1 =: 99999999999999999999999999999999999299999999999999999999999999999999999_<71>; = 1619 · 1647280127041391_<16> · 1643479245242580227_<19> · 22815052276530734674485880911517753_<35>

10⁷³-7·10³⁶-1 =: 9999999999999999999999999999999999992999999999999999999999999999999999999_<73>; = 131 · 1877 · 4730269 · 38584648463453530566055973_<26> · 222825066635850970198951407381447121_<36>

10⁷⁵-7·10³⁷-1 =: 999999999999999999999999999999999999929999999999999999999999999999999999999_<75>; = 2267 · 35831 · 419882909269851194684129_<24> · 29319823610349718187062827530908751420618203_<44>

10⁷⁷-7·10³⁸-1 =: 99999999999999999999999999999999999999299999999999999999999999999999999999999_<77>; = 336899 · 1282657 · 231414060364729755320541953515328899522337120965491931492340421493_<66>

10⁷⁹-7·10³⁹-1 =: 9999999999999999999999999999999999999992999999999999999999999999999999999999999_<79>; = 331 · 4931 · 6126846554966084840894985237363225809214287070944594313918786198175302559_<73>

10⁸¹-7·10⁴⁰-1 =: 999999999999999999999999999999999999999929999999999999999999999999999999999999999_<81>; = 373 · 1291139 · 10899697 · 75411827 · 39669772243_<11> · 571482481373_<12> · 111429877238054909080802692544333437_<36>

10⁸³-7·10⁴¹-1 =: 99999999999999999999999999999999999999999299999999999999999999999999999999999999999_<83>; = 761 · 12149 · 44189496733_<11> · 810297372421463_<15> · 6465752309654563_<16> · 46718862642650617634127078501296683_<35>

10⁸⁵-7·10⁴²-1 =: 9999999999999999999999999999999999999999992999999999999999999999999999999999999999999_<85>; = 97014041 · 357566120950464235927585600631_<30> · 288276368143785857996479750280845867947450935969_<48>

10⁸⁷-7·10⁴³-1 =: 999999999999999999999999999999999999999999929999999999999999999999999999999999999999999_<87>; = 17 · 58823529411764705882352941176470588235294113529411764705882352941176470588235294117647_<86>

10⁸⁹-7·10⁴⁴-1 =: 99999999999999999999999999999999999999999999299999999999999999999999999999999999999999999_<89>; = 17 · 5571559771_<10> · 575207833999709488073_<21> · 27427091052889042865456723_<26> · 66922128285880634318721216056983_<32>

10⁹¹-7·10⁴⁵-1 =: 9999999999999999999999999999999999999999999992999999999999999999999999999999999999999999999_<91>; = 227 · 39079 · 818861533042451_<15> · 1376639513046334505087599718409948368697036378074109797717236234033553_<70>

10⁹³-7·10⁴⁶-1 =: 999999999999999999999999999999999999999999999929999999999999999999999999999999999999999999999_<93>; = 173 · 31464780866796657207031_<23> · 183708472189265552171256057870678971434280389094498140482388867648573_<69>

10⁹⁵-7·10⁴⁷-1 =: 99999999999999999999999999999999999999999999999299999999999999999999999999999999999999999999999_<95>; = 1467136308647_<13> · 225730318172089_<15> · 135932507737607079122779_<24> · 2221346521636550338659780833602789543266260707_<46>

10⁹⁷-7·10⁴⁸-1 =: 9999999999999999999999999999999999999999999999992999999999999999999999999999999999999999999999999_<97>; = 41941 · 82183891 · 1813347328491823674543198431724239211389_<40> · 1599902521762693438787591381215338979751428261_<46> (Makoto Kamada / GGNFS-0.50.2-k2 / Total time: 0.43 hours (actual time: 0.52 hours))

10⁹⁹-7·10⁴⁹-1 =: 999999999999999999999999999999999999999999999999929999999999999999999999999999999999999999999999999_<99>; = 47 · 5584583 · 3809880835271111748868230131782901819435643037649573873781794889038001698300100892121315399_<91>

10¹⁰¹-7·10⁵⁰-1 =: 99999999999999999999999999999999999999999999999999299999999999999999999999999999999999999999999999999_<101>; = 139 · 673 · 1068981367654761777502218136337883630688317102632893625664104674655520754273253017199910205565117_<97>

10¹⁰³-7·10⁵¹-1 =: 9999999999999999999999999999999999999999999999999992999999999999999999999999999999999999999999999999999_<103>; = 109 · 347 · 479 · 95597 · 96601 · 107581 · 279863 · 22761204866749602731_<20> · 87218039076828850959861664839941665588630867531057358107_<56>

10¹⁰⁵-7·10⁵²-1 =: 999999999999999999999999999999999999999999999999999929999999999999999999999999999999999999999999999999999_<105>; = 263 · 373 · 2667600042931_<13> · 6828094416452291_<16> · 6583470735125718395053_<22> · 85008093615649948794042003413989433068137041908577_<50>

10¹⁰⁷-7·10⁵³-1 =: 99999999999999999999999999999999999999999999999999999299999999999999999999999999999999999999999999999999999_<107>; = 383573 · 260706566937714594092910606325262727042831481882197128838578314949175254775492539881587077296890031363_<102>

10¹⁰⁹-7·10⁵⁴-1 =: 9999999999999999999999999999999999999999999999999999992999999999999999999999999999999999999999999999999999999_<109>; = 15575939 · 49294699 · 3251950302580251089849442830097243673_<37> · 4004991911122812313206006402584252891736108995278772639383_<58> (Kenichiro Yamaguchi / msieve.exe 0.88 for P37 x P58 / 10:17:22 on Pentium4 2.4BGHz / May 28, 2005)

10¹¹¹-7·10⁵⁵-1 =: 999999999999999999999999999999999999999999999999999999929999999999999999999999999999999999999999999999999999999_<111>; = 733 · 2791 · 5393 · 1336891 · 67796889490723267706722347052500937570521090827341589269006205897234820145257628597246880415991_<95>

10¹¹³-7·10⁵⁶-1 =: 99999999999999999999999999999999999999999999999999999999299999999999999999999999999999999999999999999999999999999_<113>; = 18699203 · 67228147867_<11> · 261946999079_<12> · 303677300083244831632250154883642907712328922365362173528681542177077487261849867481_<84>

10¹¹⁵-7·10⁵⁷-1 =: 9999999999999999999999999999999999999999999999999999999992999999999999999999999999999999999999999999999999999999999_<115>; = 67 · 1597 · 78853 · 15698663 · 4453729593176247033369383_<25> · 7402911973339244342588281_<25> · 2289881259627362886427200690921129350158747087133_<49>

10¹¹⁷-7·10⁵⁸-1 =: 999999999999999999999999999999999999999999999999999999999929999999999999999999999999999999999999999999999999999999999_<117>; = 2039 · 7753 · 5869294693987_<13> · 10777724414020322846126170248245847850469639190337549637670845306707420235947470188250395037359131_<98>

10¹¹⁹-7·10⁵⁹-1 =: 99999999999999999999999999999999999999999999999999999999999299999999999999999999999999999999999999999999999999999999999_<119>; = 17 · 22395757 · 41946286906913353_<17> · 123658819313817785102748137207_<30> · 50636853728000579351440494333921542032222013836569228421518693701_<65> (Kenichiro Yamaguchi / GMP-ECM 6.0 B1=3000000, sigma=1215098690 for P30 / May 20, 2005)

10¹²¹-7·10⁶⁰-1 =: 9999999999999999999999999999999999999999999999999999999999992999999999999999999999999999999999999999999999999999999999999_<121>; = 17² · 2679387385562077_<16> · 1335873289098187876976634772360781468609_<40> · 9667215115747825770030400192699700127010095463540775936360554987_<64> (Anton Korobeynikov / GGNFS-0.77.1 / 3.44 hours / May 31, 2005)

10¹²³-7·10⁶¹-1 =: 999999999999999999999999999999999999999999999999999999999999929999999999999999999999999999999999999999999999999999999999999_<123>; = 269 · 673 · 98037133 · 56343270642372413547462477350259424716300787338975763923358531262102920779426938345908773453625377377787088519_<110>

10¹²⁵-7·10⁶²-1 =: 99999999999999999999999999999999999999999999999999999999999999299999999999999999999999999999999999999999999999999999999999999_<125>; = 71 · 26144460523_<11> · 472286871059656343279061123671_<30> · 55356921844173914450279278756291_<32> · 2060554760283018418628476621621143873632350669384223_<52> (Kenichiro Yamaguchi / GGNFS-0.77.0 / 6.20 hours on Pentium 4 2.4BGHz / Jun 5, 2005)

10¹²⁷-7·10⁶³-1 =: 9999999999999999999999999999999999999999999999999999999999999992999999999999999999999999999999999999999999999999999999999999999_<127>; = 97 · 701 · 54799 · 279354377 · 717976517 · 2835109296977_<13> · 145195695426547_<15> · 61474340889102797765273_<23> · 528754973956412310078619620613655505879245820268651_<51>

10¹²⁹-7·10⁶⁴-1 =: 999999999999999999999999999999999999999999999999999999999999999929999999999999999999999999999999999999999999999999999999999999999_<129>; = 139 · 179 · 13099 · 84155191976690091375532717318429_<32> · 36459701740409770008678743621002179900547434706089737737604298284369304773209328624822449_<89> (Makoto Kamada / GMP-ECM 6.0 B1=3000000, sigma=2973101344 for P32 / May 30, 2005)

10¹³¹-7·10⁶⁵-1 =: 99999999999999999999999999999999999999999999999999999999999999999299999999999999999999999999999999999999999999999999999999999999999_<131>; = 47 · 769 · 49199 · 485897117863919_<15> · 758238983448091_<15> · 152640259108836065578323345688715951253788676773987291695922346345612194208611759982230106883_<93>

10¹³³-7·10⁶⁶-1 =: 9999999999999999999999999999999999999999999999999999999999999999992999999999999999999999999999999999999999999999999999999999999999999_<133>; = 12659 · 746602123 · 4410268848809_<13> · 4106583907717825483024796569_<28> · 16190892924788094823835303809_<29> · 3608234986227038227691374458344815738114921516487663_<52> (Makoto Kamada / GMP-ECM 6.0 B1=3000000, sigma=810115398 for P28, msieve 0.88 for P29 x P52 / May 26, 2005)

10¹³⁵-7·10⁶⁷-1 =: 999999999999999999999999999999999999999999999999999999999999999999929999999999999999999999999999999999999999999999999999999999999999999_<135>; = 1759 · 11202396544008702793_<20> · 50748501006699662535505093076974286313180024697117500554973596240482675920806086770558738333064264593039698537177_<113>

10¹³⁷-7·10⁶⁸-1 =: 99999999999999999999999999999999999999999999999999999999999999999999299999999999999999999999999999999999999999999999999999999999999999999_<137>; = 15511 · 66037 · 30477113 · 7097309627_<10> · 145231263439_<12> · 225171188093_<12> · 20720716874674361792249_<23> · 666081816298578810840362779064227851634546720747815255220148963909_<66>

10¹³⁹-7·10⁶⁹-1 =: 9999999999999999999999999999999999999999999999999999999999999999999992999999999999999999999999999999999999999999999999999999999999999999999_<139>; = 11640271 · 8594963011_<10> · 100985135531476103167999_<24> · 889631446596705888137903_<24> · 1112564806943572976320554443825519370722463398257969779350986386082506281707_<76>

10¹⁴¹-7·10⁷⁰-1 =: 999999999999999999999999999999999999999999999999999999999999999999999929999999999999999999999999999999999999999999999999999999999999999999999_<141>; = 2144063848942308174619150267_<28> · 466404020800645335317603705077097139450003543693708997687015676910602837533958429083018374604282996186473046432397_<114> (Makoto Kamada / GMP-ECM 6.0 B1=3000000, sigma=3912877471 for P28 / May 29, 2005)

10¹⁴³-7·10⁷¹-1 =: 99999999999999999999999999999999999999999999999999999999999999999999999299999999999999999999999999999999999999999999999999999999999999999999999_<143>; = 631 · 4993 · 113021 · 711889 · 8174189 · 1018445325323_<13> · 124081059014402609188910712167753797_<36> · 381900090388147519926382272844193239916998973958499765471774268565374743_<72> (Kenichiro Yamaguchi / GMP-ECM 6.0 B1=11000000, sigma=4224398204 for P36 / Jul 8, 2005)

10¹⁴⁵-7·10⁷²-1 =: 9999999999999999999999999999999999999999999999999999999999999999999999992999999999999999999999999999999999999999999999999999999999999999999999999_<145>; = 107 · 269 · 4025029 · 7691253463_<10> · 10037114963_<11> · 1357432142821_<13> · 823703246538141133108995931540283390161164324078153224904984920530185346213774608028999938448706464693_<102>

10¹⁴⁷-7·10⁷³-1 =: 999999999999999999999999999999999999999999999999999999999999999999999999929999999999999999999999999999999999999999999999999999999999999999999999999_<147>; = 1523 · 33359 · 163141831126890373902190714753_<30> · 6771196048922895791023493473450472633_<37> · 17817893241367170326405819488787733173549447168880253186019589405975907843_<74> (Makoto Kamada / GMP-ECM 6.0 B1=3000000, sigma=1818063565 for P30 / May 6, 2005) (Sinkiti Sibata / GGNFS-0.77.1 gnfs / 50.84 hours for P37 x P74 / Jul 29, 2005)

10¹⁴⁹-7·10⁷⁴-1 =: 99999999999999999999999999999999999999999999999999999999999999999999999999299999999999999999999999999999999999999999999999999999999999999999999999999_<149>; = 9721 · 4189623909880529_<16> · 7690770857933312118597753750628516117910872540228607770081_<58> · 319259732546553198230034160874462037912072645302944776190499583078669031_<72> (Sinkiti Sibata / GGNFS-0.77.1 / 64.62 hours / Sep 20, 2005)

10¹⁵¹-7·10⁷⁵-1 =: 9999999999999999999999999999999999999999999999999999999999999999999999999992999999999999999999999999999999999999999999999999999999999999999999999999999_<151>; = 17² · 6230153 · 772038462749_<12> · 1375058674458523_<16> · 5231705363333506832058567959119668521872579487266650018676731183489928905287274299448455542573451594011537716712361_<115>

Factorizations

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