Factorizations of 99...99499...99

Since June 16, 2000

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Factorizations of 99...99499...99	2005-12-28(Wed) 17:39

Last update

Dec 28, 2005 17:39 JST

Sequence

4, 949, 99499, 9994999, 999949999, ...

General term

10²ⁿ⁺¹-5·10ⁿ-1

Prime numbers

10²⁹-5·10¹⁴-1 = (9)₁₄4(9)₁₄_<29> is prime. (Patrick De Geest / Sep 23, 2002)
10⁴⁵-5·10²²-1 = (9)₂₂4(9)₂₂_<45> is prime. (Patrick De Geest / Sep 23, 2002)
10⁷³-5·10³⁶-1 = (9)₃₆4(9)₃₆_<73> is prime. (Patrick De Geest / Sep 23, 2002)
10²⁰⁹-5·10¹⁰⁴-1 = (9)₁₀₄4(9)₁₀₄_<209> is prime. (Patrick De Geest / Sep 23, 2002)
10²²⁷³-5·10¹¹³⁶-1 = (9)₁₁₃₆4(9)₁₁₃₆_<2273> is prime. (Jeff Heleen / Oct 13, 2002)
10³⁵⁷²⁹-5·10¹⁷⁸⁶⁴-1 = (9)₁₇₈₆₄4(9)₁₇₈₆₄_<35729> is prime. (Daniel Heuer / Jul 2, 2001)
10⁵⁰⁸⁹⁷-5·10²⁵⁴⁴⁸-1 = (9)₂₅₄₄₈4(9)₂₅₄₄₈_<50897> is prime. (Daniel Heuer / Oct 29, 2001)

References:

Palindromic Wing Primes (Patrick De Geest)
A114645 (On-Line Encyclopedia of Integer Sequences)

Condition

n≤75

Status

Completed up to n=50. (Aug 3, 2004)
Completed up to n=75. (Sep 26, 2005)

Factorization results

10³-5·10¹-1 =: 949; = 13 · 73

10⁵-5·10²-1 =: 99499; = 29 · 47 · 73

10⁷-5·10³-1 =: 9994999; = 7 · 307 · 4651

10⁹-5·10⁴-1 =: 999949999; = 30109 · 33211

10¹¹-5·10⁵-1 =: 99999499999_<11>; = 7 · 83 · 172116179

10¹³-5·10⁶-1 =: 9999994999999_<13>; = 48109 · 207861211

10¹⁵-5·10⁷-1 =: 999999949999999_<15>; = 13 · 7963 · 9660061921_<10>

10¹⁷-5·10⁸-1 =: 99999999499999999_<17>; = 8956609 · 11164939711_<11>

10¹⁹-5·10⁹-1 =: 9999999994999999999_<19>; = 7 · 73² · 1913 · 140133274241_<12>

10²¹-5·10¹⁰-1 =: 999999999949999999999_<21>; = 73 · 13698630136301369863_<20>

10²³-5·10¹¹-1 =: 99999999999499999999999_<23>; = 7 · 29 · 877321 · 561494410182773_<15>

10²⁵-5·10¹²-1 =: 9999999999994999999999999_<25>; = 2341 · 22072039477_<11> · 193533487207_<12>

10²⁷-5·10¹³-1 =: 999999999999949999999999999_<27>; = 13 · 98459 · 781270142120812489697_<21>

10²⁹-5·10¹⁴-1 =: 99999999999999499999999999999_<29>; = definitely prime number

10³¹-5·10¹⁵-1 =: 9999999999999994999999999999999_<31>; = 7 · 133187 · 393257 · 27274931056435128523_<20>

10³³-5·10¹⁶-1 =: 999999999999999949999999999999999_<33>; = 269 · 3717472118959107620817843866171_<31>

10³⁵-5·10¹⁷-1 =: 99999999999999999499999999999999999_<35>; = 7 · 73 · 1877 · 6156901 · 23079316361_<11> · 733718917297_<12>

10³⁷-5·10¹⁸-1 =: 9999999999999999994999999999999999999_<37>; = 73 · 97 · 1171 · 50377 · 219217 · 109204863203521929061_<21>

10³⁹-5·10¹⁹-1 =: 999999999999999999949999999999999999999_<39>; = 13 · 13239539239733899_<17> · 5810102264905028303377_<22>

10⁴¹-5·10²⁰-1 =: 99999999999999999999499999999999999999999_<41>; = 47 · 163 · 419 · 3323 · 29996257033_<11> · 312538200345577394579_<21>

10⁴³-5·10²¹-1 =: 9999999999999999999994999999999999999999999_<43>; = 7 · 22997475217_<11> · 62118620200334514461055724804921_<32>

10⁴⁵-5·10²²-1 =: 999999999999999999999949999999999999999999999_<45>; = definitely prime number

10⁴⁷-5·10²³-1 =: 99999999999999999999999499999999999999999999999_<47>; = 7² · 7459 · 40177 · 482281237441_<12> · 14120349335323832944493077_<26>

10⁴⁹-5·10²⁴-1 =: 9999999999999999999999994999999999999999999999999_<49>; = 25801 · 976380407 · 2302520591101_<13> · 172401437490400765009157_<24>

10⁵¹-5·10²⁵-1 =: 999999999999999999999999949999999999999999999999999_<51>; = 13 · 67 · 73 · 1787 · 127235302477924244063_<21> · 69171438235751571811213_<23>

10⁵³-5·10²⁶-1 =: 99999999999999999999999999499999999999999999999999999_<53>; = 73 · 852652992145636311554731_<24> · 1606589112238349389966039573_<28>

10⁵⁵-5·10²⁷-1 =: 9999999999999999999999999994999999999999999999999999999_<55>; = 7 · 2131 · 1872582196826688353_<19> · 357995543329132365872773576271699_<33>

10⁵⁷-5·10²⁸-1 =: 999999999999999999999999999949999999999999999999999999999_<57>; = 3404730839554091347889762281_<28> · 293708973520787144658793555879_<30>

10⁵⁹-5·10²⁹-1 =: 99999999999999999999999999999499999999999999999999999999999_<59>; = 7 · 97 · 317 · 17211022013688365887_<20> · 26993817253793992967719610044427939_<35>

10⁶¹-5·10³⁰-1 =: 9999999999999999999999999999994999999999999999999999999999999_<61>; = 29 · 2017 · 306731299709_<12> · 8999137581647_<13> · 278587252596073_<15> · 222318640049427617_<18>

10⁶³-5·10³¹-1 =: 999999999999999999999999999999949999999999999999999999999999999_<63>; = 13 · 179 · 1239643 · 193525564942277550190007_<24> · 1791301297217519873468303098237_<31>

10⁶⁵-5·10³²-1 =: 99999999999999999999999999999999499999999999999999999999999999999_<65>; = 28181 · 144307 · 287223900610919_<15> · 4686750558921377_<16> · 18266855200714892105010119_<26>

10⁶⁷-5·10³³-1 =: 9999999999999999999999999999999994999999999999999999999999999999999_<67>; = 7 · 73 · 178439 · 456203021 · 1325485186171_<13> · 340948627029706849_<18> · 531945743351557069609_<21>

10⁶⁹-5·10³⁴-1 =: 999999999999999999999999999999999949999999999999999999999999999999999_<69>; = 73 · 482513 · 1034027 · 113837077763_<12> · 42783529213250537213_<20> · 5637361650656357833904227_<25>

10⁷¹-5·10³⁵-1 =: 99999999999999999999999999999999999499999999999999999999999999999999999_<71>; = 7 · 61² · 719 · 22713308591_<11> · 8469160191241_<13> · 27758286293920173239480832056163894738553_<41>

10⁷³-5·10³⁶-1 =: 9999999999999999999999999999999999994999999999999999999999999999999999999_<73>; = definitely prime number

10⁷⁵-5·10³⁷-1 =: 999999999999999999999999999999999999949999999999999999999999999999999999999_<75>; = 13 · 199 · 2953 · 3583 · 36533671226136873562261962807823744276645706145142000100465915323_<65>

10⁷⁷-5·10³⁸-1 =: 99999999999999999999999999999999999999499999999999999999999999999999999999999_<77>; = 2609 · 15149 · 11272583863_<11> · 1087839905797_<13> · 206325779304608070973258023209704093143478649449_<48>

10⁷⁹-5·10³⁹-1 =: 9999999999999999999999999999999999999994999999999999999999999999999999999999999_<79>; = 7² · 29 · 340094622883214671_<18> · 89250497908187067885187373_<26> · 231843812022208525224137871025993_<33>

10⁸¹-5·10⁴⁰-1 =: 999999999999999999999999999999999999999949999999999999999999999999999999999999999_<81>; = 4229 · 52597673 · 10249000651663_<14> · 81931002008498759_<17> · 5353847507331679718627203983754502271491_<40>

10⁸³-5·10⁴¹-1 =: 99999999999999999999999999999999999999999499999999999999999999999999999999999999999_<83>; = 7 · 73 · 266239 · 735033996682159443736267773296610348827358735672138497398960922130726252031_<75>

10⁸⁵-5·10⁴²-1 =: 9999999999999999999999999999999999999999994999999999999999999999999999999999999999999_<85>; = 73 · 389 · 1109 · 1291 · 48259 · 436132348572881_<15> · 1543505227485072799_<19> · 7571205374825151755066433676233596033_<37>

10⁸⁷-5·10⁴³-1 =: 999999999999999999999999999999999999999999949999999999999999999999999999999999999999999_<87>; = 13 · 84533810727393720761_<20> · 14130473765000206235844997_<26> · 64397569651470927192571654520543136580919_<41>

10⁸⁹-5·10⁴⁴-1 =: 99999999999999999999999999999999999999999999499999999999999999999999999999999999999999999_<89>; = 354037 · 282456353431985922375344949821628812807700888607687897027711792835212138844245093027_<84>

10⁹¹-5·10⁴⁵-1 =: 9999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999_<91>; = 7 · 14436181031_<11> · 32266288409_<11> · 6727855881284073515673536775054251_<34> · 455852088953288354385781243603265333_<36>

10⁹³-5·10⁴⁶-1 =: 999999999999999999999999999999999999999999999949999999999999999999999999999999999999999999999_<93>; = 83 · 11783 · 4575799569961_<13> · 81972002618942963157750810637_<29> · 2726047955744136809720687062402830504300514663_<46>

10⁹⁵-5·10⁴⁷-1 =: 99999999999999999999999999999999999999999999999499999999999999999999999999999999999999999999999_<95>; = 7 · 794119 · 13537233152295961_<17> · 77743797612443513_<17> · 17093095260501667738725757062563476151646267266405763071_<56>

10⁹⁷-5·10⁴⁸-1 =: 9999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999_<97>; = 47 · 611476932635213_<15> · 347954184518253403593489235802593537531879891529468508597556002417980499277345909_<81>

10⁹⁹-5·10⁴⁹-1 =: 999999999999999999999999999999999999999999999999949999999999999999999999999999999999999999999999999_<99>; = 13 · 73 · 15889 · 66318886007185916574422622804504988871359333564163953284711420994211621310406806015467819059_<92>

10¹⁰¹-5·10⁵⁰-1 =: 99999999999999999999999999999999999999999999999999499999999999999999999999999999999999999999999999999_<101>; = 73 · 1369863013698630136986301369863013698630136986301363013698630136986301369863013698630136986301369863_<100>

10¹⁰³-5·10⁵¹-1 =: 9999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999_<103>; = 7 · 94677613487661089747353_<23> · 71269943060057227761238102966919925787_<38> · 211713350845509700316662285486233591892387_<42> (Makoto Kamada / msieve 0.88)

10¹⁰⁵-5·10⁵²-1 =: 999999999999999999999999999999999999999999999999999949999999999999999999999999999999999999999999999999999_<105>; = 17977 · 76296532761998391957077_<23> · 67568759393935788396520294335743_<32> · 10790263100751394184921067728683591121445228517_<47> (Makoto Kamada / msieve 0.88 / 13 minutes)

10¹⁰⁷-5·10⁵³-1 =: 99999999999999999999999999999999999999999999999999999499999999999999999999999999999999999999999999999999999_<107>; = 7 · 191 · 3691 · 2196600844153716033361_<22> · 69822974648095467867384822091_<29> · 132121974192898635000693635977899135467129312194847_<51>

10¹⁰⁹-5·10⁵⁴-1 =: 9999999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999999_<109>; = 61 · 2886557 · 123548692649705108867369047_<27> · 459676045988134598841901403865169123469696182453617425910704733986220806321_<75>

10¹¹¹-5·10⁵⁵-1 =: 999999999999999999999999999999999999999999999999999999949999999999999999999999999999999999999999999999999999999_<111>; = 13 · 76923076923076923076923076923076923076923076923076923073076923076923076923076923076923076923076923076923076923_<110>

10¹¹³-5·10⁵⁶-1 =: 99999999999999999999999999999999999999999999999999999999499999999999999999999999999999999999999999999999999999999_<113>; = 58207 · 637053467 · 38613981283_<11> · 192805168162571930340967679_<27> · 362231027180937258755991397381297488820571071563655831949356303_<63>

10¹¹⁵-5·10⁵⁷-1 =: 9999999999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999999999_<115>; = 7 · 73 · 179 · 487 · 12269 · 561378329685167_<15> · 2355987824090587_<16> · 5198813831459935688390319272941_<31> · 2661061978958705483136906369853516795231313_<43> (Makoto Kamada / msieve 0.88 / 3.8 minutes)

10¹¹⁷-5·10⁵⁸-1 =: 999999999999999999999999999999999999999999999999999999999949999999999999999999999999999999999999999999999999999999999_<117>; = 29 · 67 · 73 · 1091 · 98407050041_<11> · 2990795615219_<13> · 21956678375774763943507732736494249805763129729735373021234563979202159132401812576769_<86>

10¹¹⁹-5·10⁵⁹-1 =: 99999999999999999999999999999999999999999999999999999999999499999999999999999999999999999999999999999999999999999999999_<119>; = 7 · 3869743 · 2433114977184083421515578291_<28> · 31856661382193055759391714907693_<32> · 47627407843568202553750431024175318259489165660722673_<53> (Makoto Kamada / msieve 0.88 for P32 x P53 / May 14, 2005)

10¹²¹-5·10⁶⁰-1 =: 9999999999999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999999999999_<121>; = 165149106706211_<15> · 27611806515679263468269678707072310135743844147387_<50> · 2192951110112010923330726818171905685664179773222579832207_<58> (Kenichiro Yamaguchi / GGNFS-0.77.0 / 3.35 hours on Pentium 4 2.4BGHz / Jun 1, 2005)

10¹²³-5·10⁶¹-1 =: 999999999999999999999999999999999999999999999999999999999999949999999999999999999999999999999999999999999999999999999999999_<123>; = 13 · 1501496951535744377_<19> · 51230924474671306449496909813914846348057673568519980025511866368154068911967420164056013166681080066899_<104>

10¹²⁵-5·10⁶²-1 =: 99999999999999999999999999999999999999999999999999999999999999499999999999999999999999999999999999999999999999999999999999999_<125>; = 1559 · 13063 · 13470606010794028627413277182587_<32> · 364522066719977324206584098453136145655901219209892192548908624460176317930811233012781_<87> (Makoto Kamada / GMP-ECM 6.0 B1=3000000, sigma=4018826674 for P32 / May 7, 2005)

10¹²⁷-5·10⁶³-1 =: 9999999999999999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999999999999999_<127>; = 7 · 70145326613_<11> · 75696543614080484504716919314397_<32> · 269046389681757996273662117203132637492382734106421397965951960948824725296394410537_<84> (Makoto Kamada / GMP-ECM 6.0 B1=3000000, sigma=1156737498 for P32 / May 8, 2005)

10¹²⁹-5·10⁶⁴-1 =: 999999999999999999999999999999999999999999999999999999999999999949999999999999999999999999999999999999999999999999999999999999999_<129>; = 43499 · 2294077 · 4370312208203526199_<19> · 2292980032032098110814478639056559014096341426507710343582937375201191240183016690243284145196522887_<100>

10¹³¹-5·10⁶⁵-1 =: 99999999999999999999999999999999999999999999999999999999999999999499999999999999999999999999999999999999999999999999999999999999999_<131>; = 7² · 73 · 1560457 · 68144661076921193_<17> · 262904135862192854578920499183594181666955863150775846848994582475519423179025020205417250611670306282087_<105>

10¹³³-5·10⁶⁶-1 =: 9999999999999999999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999999999999999999_<133>; = 47 · 73 · 829 · 6761 · 50506030969_<11> · 131323299422472148930024532895341746762555988587153_<51> · 78402297452355609333372855409892683866758653385085863058626413_<62> (Kenichiro Yamaguchi / GGNFS-0.77.1 / 18.98 hours on Pentium 4 2.4BGHz / Jun 18, 2005)

10¹³⁵-5·10⁶⁷-1 =: 999999999999999999999999999999999999999999999999999999999999999999949999999999999999999999999999999999999999999999999999999999999999999_<135>; = 13 · 29 · 1373 · 8933 · 1266483249403_<13> · 3436340835467_<13> · 49692986175320536435189903896666450296818394840550345711371990802826675859541439517584333278186452143_<101>

10¹³⁷-5·10⁶⁸-1 =: 99999999999999999999999999999999999999999999999999999999999999999999499999999999999999999999999999999999999999999999999999999999999999999_<137>; = 4111 · 480019613 · 2198963711051_<13> · 21130146323149142509_<20> · 1090618785308088765443858022747074445985851349080727378101608203604294493462187899806861402827_<94>

10¹³⁹-5·10⁶⁹-1 =: 9999999999999999999999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999999999999999999999_<139>; = 7 · 991 · 15621479 · 25218953 · 151297957 · 14062828861246736581_<20> · 157705627562565010111_<21> · 1021498112798088086668342168804543_<34> · 10675508950385419139525256445370382764881_<41> (Makoto Kamada / msieve 0.88 / 4.1 minutes)

10¹⁴¹-5·10⁷⁰-1 =: 999999999999999999999999999999999999999999999999999999999999999999999949999999999999999999999999999999999999999999999999999999999999999999999_<141>; = 94199759 · 45991197802202921691212410956857205150918173681404816125050149_<62> · 230821090102296748368286382776743795682256488181171518047153819469404989_<72> (Kenichiro Yamaguchi / GGNFS-0.77.0 / 49.67 hours on Pentium M 1.3GHz / Jun 15, 2005)

10¹⁴³-5·10⁷¹-1 =: 99999999999999999999999999999999999999999999999999999999999999999999999499999999999999999999999999999999999999999999999999999999999999999999999_<143>; = 7 · 829 · 51157 · 4226983455085368113131838522651325280201438948126519944281685689_<64> · 79691465468688137474165323187199380282822368311237342631970794505834321_<71> (Sinkiti Sibata / GGNFS-0.77.1 / 29.81 hours / Sep 24, 2005)

10¹⁴⁵-5·10⁷²-1 =: 9999999999999999999999999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999999999999999999999999_<145>; = 81839 · 98272507 · 152850960360368016481796770480122031721_<39> · 8134661370956745828048953759976786314450618333909639195969999821733276700744096239942518707403_<94> (Sinkiti Sibata / GGNFS-0.77.1 / 46.05 hours / Sep 26, 2005)

10¹⁴⁷-5·10⁷³-1 =: 999999999999999999999999999999999999999999999999999999999999999999999999949999999999999999999999999999999999999999999999999999999999999999999999999_<147>; = 13 · 73 · 430384049 · 3785599269557668325208323767_<28> · 646759745389145739294384287863834036907191004239058094454150857219428878001033162701912468496120968325731397_<108>

10¹⁴⁹-5·10⁷⁴-1 =: 99999999999999999999999999999999999999999999999999999999999999999999999999499999999999999999999999999999999999999999999999999999999999999999999999999_<149>; = 73 · 1697 · 4253 · 94379 · 140363 · 419683619 · 7607082794944975537132889579438640845935478194747_<49> · 4487781874349498160146767447626885491119476257355891326606162986068662363_<73> (Sinkiti Sibata / GGNFS-0.77.1 / 67.74 hours / Sep 23, 2005)

10¹⁵¹-5·10⁷⁵-1 =: 9999999999999999999999999999999999999999999999999999999999999999999999999994999999999999999999999999999999999999999999999999999999999999999999999999999_<151>; = 7 · 293 · 9539 · 15683 · 54258411269768597_<17> · 427783759648005329_<18> · 3517062300547732144252876581838513053265293857_<46> · 399237126270832542031473445700832275264923599868927241797897_<60> (Sinkiti Sibata / GGNFS-0.77.1 gnfs / 20.20 hours for P46 x P60 / Jun 25, 2005)

Factorizations

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