Factorizations of 899...99

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Since June 16, 2000

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Factorizations of 899...99	2008-12-07(Sun) 16:16

Last update

Dec 7, 2008 16:16 JST

Sequence

8, 89, 899, 8999, 89999, ...

General term

9·10ⁿ-1

Algebraic factorizations

9·10^2k-1 = (3·10^k-1)(3·10^k+1)
See also 299...99, 300...001.

Room for prime numbers

upper limit of periods: 10000
upper limit of periodical factors: 4294967296
checked terms: 100000000
terms divided by periodical factors: 81983389
room for prime numbers: 18.02%

Prime numbers

9·10¹-1 = 89 is prime.
9·10³-1 = 8999 is prime.
9·10⁷-1 = 89999999 is prime.
9·10¹⁹-1 = 8(9)₁₉_<20> is prime.
9·10²⁹-1 = 8(9)₂₉_<30> is prime.
9·10³⁷-1 = 8(9)₃₇_<38> is prime.
9·10⁹³-1 = 8(9)₉₃_<94> is prime.
9·10⁹³⁵-1 = 8(9)₉₃₅_<936> is prime.
9·10⁸⁴¹⁵-1 = 8(9)₈₄₁₅_<8416> is prime. (Harvey Dubner / Dubner Cruncher / Oct 1, 1994)
9·10⁹⁶³¹-1 = 8(9)₉₆₃₁_<9632> is prime. (Harvey Dubner / Dubner Cruncher / Oct 1, 1994)
9·10¹¹¹⁴³-1 = 8(9)₁₁₁₄₃_<11144> is prime. (Harvey Dubner / Dubner Cruncher / Dec 1, 1994)
9·10⁴¹⁴⁷⁵-1 = 8(9)₄₁₄₇₅_<41476> is prime. (Dirk Augustin / Yves Gallot's Proth.exe / Oct 27, 2000)
9·10⁴¹⁹¹⁷-1 = 8(9)₄₁₉₁₇_<41918> is prime. (Eric J. Sorensen / Yves Gallot's Proth.exe / Jan 23, 2002)
9·10⁴⁸⁰⁵¹-1 = 8(9)₄₈₀₅₁_<48052> is prime. (Harvey Dubner / Yves Gallot's Proth.exe / Dec 10, 2000)
9·10¹⁰⁷⁶⁶³-1 = 8(9)₁₀₇₆₆₃_<107664> is prime. (Jiong Sun / George Woltman's PRP, Paul Jobling's NewPGen, OpenPFGW / Jan 21, 2004)

Searched:

1-10000

References:

The Prime Database: The List of Largest Known Primes Home Page (Chris K. Caldwell)
The Top Twenty: Near-repdigit (Chris K. Caldwell)
A056725 (On-Line Encyclopedia of Integer Sequences)
A093948 (On-Line Encyclopedia of Integer Sequences)

Condition

n≤250

Status

Completed up to n=100. (Jun 12, 2003)
Completed up to n=110. (Jul 1, 2003)
Completed up to n=150. (Jul 10, 2004)
The following numbers are not factored yet. (n≤250)
n= 171, 181, 185, 187, 189, 191, 197, 201, 203, 205, 207, 209, 211, 215, 217, 219, 221, 225, 229, 231, 235, 237, 241, 243, 245, 247, 249 (27/250)

Factorization results

9·10¹-1 =: 89; = definitely prime number

9·10²-1 =: 899; = 29 · 31

9·10³-1 =: 8999; = definitely prime number

9·10⁴-1 =: 89999; = 7 · 13 · 23 · 43

9·10⁵-1 =: 899999; = 397 · 2267

9·10⁶-1 =: 8999999; = 2999 · 3001

9·10⁷-1 =: 89999999; = definitely prime number

9·10⁸-1 =: 899999999; = 19 · 131 · 229 · 1579

9·10⁹-1 =: 8999999999_<10>; = 151 · 523 · 113963

9·10¹⁰-1 =: 89999999999_<11>; = 7 · 13 · 17 · 47 · 491 · 2521

9·10¹¹-1 =: 899999999999_<12>; = 677 · 1329394387_<10>

9·10¹²-1 =: 8999999999999_<13>; = 853 · 3517 · 2999999

9·10¹³-1 =: 89999999999999_<14>; = 3547 · 69427 · 365471

9·10¹⁴-1 =: 899999999999999_<15>; = 29999999 · 30000001

9·10¹⁵-1 =: 8999999999999999_<16>; = 757 · 7639 · 1556360213_<10>

9·10¹⁶-1 =: 89999999999999999_<17>; = 7² · 13 · 6122449 · 23076923

9·10¹⁷-1 =: 899999999999999999_<18>; = 31 · 71 · 408905043162199_<15>

9·10¹⁸-1 =: 8999999999999999999_<19>; = 7589 · 16937 · 177127 · 395309

9·10¹⁹-1 =: 89999999999999999999_<20>; = definitely prime number

9·10²⁰-1 =: 899999999999999999999_<21>; = 2113 · 3767 · 3769 · 30000000001_<11>

9·10²¹-1 =: 8999999999999999999999_<22>; = 20173 · 446140881376096763_<18>

9·10²²-1 =: 89999999999999999999999_<23>; = 7 · 13² · 683 · 953 · 65843 · 1775147929_<10>

9·10²³-1 =: 899999999999999999999999_<24>; = 613 · 1468189233278955954323_<22>

9·10²⁴-1 =: 8999999999999999999999999_<25>; = 67 · 359 · 8356545961_<10> · 44776119403_<11>

9·10²⁵-1 =: 89999999999999999999999999_<26>; = 43 · 2093023255813953488372093_<25>

9·10²⁶-1 =: 899999999999999999999999999_<27>; = 17 · 19 · 23 · 62191 · 1233721 · 1578947368421_<13>

9·10²⁷-1 =: 8999999999999999999999999999_<28>; = 401 · 2221158668683_<13> · 10104586669453_<14>

9·10²⁸-1 =: 89999999999999999999999999999_<29>; = 7 · 13 · 107 · 33203 · 95773 · 6495563 · 447486691

9·10²⁹-1 =: 899999999999999999999999999999_<30>; = definitely prime number

9·10³⁰-1 =: 8999999999999999999999999999999_<31>; = 29 · 83 · 103 · 227 · 1545895313_<10> · 103448275862069_<15>

9·10³¹-1 =: 89999999999999999999999999999999_<32>; = 33168293 · 2713434785444038377253843_<25>

9·10³²-1 =: 899999999999999999999999999999999_<33>; = 31 · 379 · 15901 · 100126307 · 160581649 · 299621557

9·10³³-1 =: 8999999999999999999999999999999999_<34>; = 197 · 5879 · 13729 · 566022790462260918263237_<24>

9·10³⁴-1 =: 89999999999999999999999999999999999_<35>; = 7 · 13 · 157 · 2281 · 3257 · 6961 · 23911 · 12040213 · 423111547

9·10³⁵-1 =: 899999999999999999999999999999999999_<36>; = 347 · 2593659942363112391930835734870317_<34>

9·10³⁶-1 =: 8999999999999999999999999999999999999_<37>; = 61 · 16921 · 3145189 · 5188801 · 34168681 · 15636684431_<11>

9·10³⁷-1 =: 89999999999999999999999999999999999999_<38>; = definitely prime number

9·10³⁸-1 =: 899999999999999999999999999999999999999_<39>; = 163 · 184049079754601227_<18> · 29999999999999999999_<20>

9·10³⁹-1 =: 8999999999999999999999999999999999999999_<40>; = 1399 · 1920599 · 479099653 · 6991369252979250035683_<22>

9·10⁴⁰-1 =: 89999999999999999999999999999999999999999_<41>; = 7 · 13 · 23076923076923076923_<20> · 42857142857142857143_<20>

9·10⁴¹-1 =: 899999999999999999999999999999999999999999_<42>; = 283 · 10756524547_<11> · 295654232948432987792498206799_<30>

9·10⁴²-1 =: 8999999999999999999999999999999999999999999_<43>; = 17 · 191 · 263 · 757 · 11059 · 13472579 · 110363948159_<12> · 846671161213_<12>

9·10⁴³-1 =: 89999999999999999999999999999999999999999999_<44>; = 199 · 1321 · 3098747 · 110484281593087312987107983402323_<33>

9·10⁴⁴-1 =: 899999999999999999999999999999999999999999999_<45>; = 19 · 167 · 181 · 311 · 337 · 1381 · 1559 · 10452973 · 604304143 · 1099432012969_<13>

9·10⁴⁵-1 =: 8999999999999999999999999999999999999999999999_<46>; = 89 · 2663569 · 37965449930382121705159463727220672039_<38>

9·10⁴⁶-1 =: 89999999999999999999999999999999999999999999999_<47>; = 7 · 13 · 43 · 233 · 50367072601_<11> · 850896044657_<12> · 2303316007278478583_<19>

9·10⁴⁷-1 =: 899999999999999999999999999999999999999999999999_<48>; = 31 · 8045533 · 496034351476796569_<18> · 7274685820245550016477_<22>

9·10⁴⁸-1 =: 8999999999999999999999999999999999999999999999999_<49>; = 23 · 6709 · 15056940637_<11> · 29697967297_<11> · 130434782608695652173913_<24>

9·10⁴⁹-1 =: 89999999999999999999999999999999999999999999999999_<50>; = 563 · 1597 · 2250041 · 44487578424013102272197374535613136049_<38>

9·10⁵⁰-1 =: 899999999999999999999999999999999999999999999999999_<51>; = 2309 · 23057 · 10833241 · 120104713180327_<15> · 12992637505413598960589_<23>

9·10⁵¹-1 =: 8999999999999999999999999999999999999999999999999999_<52>; = 498703999 · 18046777282810599639887788427379344114704001_<44>

9·10⁵²-1 =: 89999999999999999999999999999999999999999999999999999_<53>; = 7 · 13 · 59 · 71 · 109 · 877 · 17011 · 26355258412811941_<17> · 5508933654075692748407_<22>

9·10⁵³-1 =: 899999999999999999999999999999999999999999999999999999_<54>; = 6803 · 132294575922387182125532853153020726150227840658533_<51>

9·10⁵⁴-1 =: 8999999999999999999999999999999999999999999999999999999_<55>; = 2069 · 85577 · 4296989 · 3943115191193_<13> · 2999999999999999999999999999_<28>

9·10⁵⁵-1 =: 89999999999999999999999999999999999999999999999999999999_<56>; = 10111 · 266886276333463982401_<21> · 33352021088284568499350580217409_<32>

9·10⁵⁶-1 =: 899999999999999999999999999999999999999999999999999999999_<57>; = 47 · 638297872340425531914893617_<27> · 30000000000000000000000000001_<29>

9·10⁵⁷-1 =: 8999999999999999999999999999999999999999999999999999999999_<58>; = 67 · 43963 · 1028901501145942434599_<22> · 2969659015069271464332605919481_<31>

9·10⁵⁸-1 =: 89999999999999999999999999999999999999999999999999999999999_<59>; = 7⁴ · 13 · 17 · 29 · 6389 · 212469253928379447424129_<24> · 4308549598586795731663531_<25>

9·10⁵⁹-1 =: 899999999999999999999999999999999999999999999999999999999999_<60>; = 277 · 8360003 · 136729631331044067193877_<24> · 2842455434324503230899065277_<28>

9·10⁶⁰-1 =: 8999999999999999999999999999999999999999999999999999999999999_<61>; = 19441 · 45949 · 1637539 · 671304589 · 5002728961799_<13> · 1832017435920610135086859_<25>

9·10⁶¹-1 =: 89999999999999999999999999999999999999999999999999999999999999_<62>; = 3271 · 487728452339437218839_<21> · 56413607656198423151756876816941602271_<38>

9·10⁶²-1 =: 899999999999999999999999999999999999999999999999999999999999999_<63>; = 19 · 31 · 383 · 16187 · 546924986987_<12> · 178350167647709_<15> · 2526741345910890255200875937_<28>

9·10⁶³-1 =: 8999999999999999999999999999999999999999999999999999999999999999_<64>; = 7507 · 3750042827_<10> · 319697960707742776204872853555157517164263616445391_<51>

9·10⁶⁴-1 =: 89999999999999999999999999999999999999999999999999999999999999999_<65>; = 7 · 13 · 103 · 326707 · 146437799 · 157588568214707166713677_<24> · 1273583870573108963459083_<25>

9·10⁶⁵-1 =: 899999999999999999999999999999999999999999999999999999999999999999_<66>; = 547 · 167443 · 167713163761626573605467_<24> · 58589667726693100081417128713675957_<35>

9·10⁶⁶-1 =: 8999999999999999999999999999999999999999999999999999999999999999999_<67>; = 113 · 149 · 6287 · 34303 · 42299 · 5194269029314101397578509_<25> · 11281002465075774324342877_<26>

9·10⁶⁷-1 =: 89999999999999999999999999999999999999999999999999999999999999999999_<68>; = 43 · 293 · 443563 · 644416991 · 24991029011406741167065731522199613715156685911797_<50>

9·10⁶⁸-1 =: 899999999999999999999999999999999999999999999999999999999999999999999_<69>; = 20107 · 28711 · 46811 · 51047 · 12554606696004419459257547_<26> · 51966762052062599154639013_<26>

9·10⁶⁹-1 =: 8999999999999999999999999999999999999999999999999999999999999999999999_<70>; = 757 · 2591 · 392256582083_<12> · 21780210678601_<14> · 537089795232790722426894637937014549319_<39>

9·10⁷⁰-1 =: 89999999999999999999999999999999999999999999999999999999999999999999999_<71>; = 7 · 13 · 23 · 478631 · 3887236453_<10> · 2618448681461_<13> · 23034640168453340899_<20> · 383182793960858193559_<21>

9·10⁷¹-1 =: 899999999999999999999999999999999999999999999999999999999999999999999999_<72>; = 83 · 1733 · 1498377899910864444260923_<25> · 4175846206181211096667355922507161379269267_<43>

9·10⁷²-1 =: 8999999999999999999999999999999999999999999999999999999999999999999999999_<73>; = 193 · 2347451 · 6621668120347220058071014093_<28> · 3000000000000000000000000000000000001_<37>

9·10⁷³-1 =: 89999999999999999999999999999999999999999999999999999999999999999999999999_<74>; = 140502570236729_<15> · 235496966083627_<15> · 1512112539516804163933_<22> · 1798824562611511313552041_<25>

9·10⁷⁴-1 =: 899999999999999999999999999999999999999999999999999999999999999999999999999_<75>; = 17³ · 179 · 613 · 1569611 · 3874630228127_<13> · 44955771308579_<14> · 6106248727864848361489924689599023_<34>

9·10⁷⁵-1 =: 8999999999999999999999999999999999999999999999999999999999999999999999999999_<76>; = 3187 · 311603 · 84476058053251419255636408187321_<32> · 107281583641067522945308063892662879_<36>

9·10⁷⁶-1 =: 89999999999999999999999999999999999999999999999999999999999999999999999999999_<77>; = 7 · 13 · 2423 · 3571 · 2173333 · 1283942706199_<13> · 4300920803658799_<16> · 9524111876567510079685069367281501_<34>

9·10⁷⁷-1 =: 899999999999999999999999999999999999999999999999999999999999999999999999999999_<78>; = 31 · 18011849 · 1611842185914179551042098149730715167446968722035825309468013474477721_<70>

9·10⁷⁸-1 =: 8999999999999999999999999999999999999999999999999999999999999999999999999999999_<79>; = 2990993 · 20474512935513701_<17> · 146523632061420300823699_<24> · 1003011374483323765719277845183857_<34>

9·10⁷⁹-1 =: 89999999999999999999999999999999999999999999999999999999999999999999999999999999_<80>; = 146677 · 613593133211069220123127688731021223504707622872024925516611329656319668387_<75>

9·10⁸⁰-1 =: 899999999999999999999999999999999999999999999999999999999999999999999999999999999_<81>; = 19 · 1316507 · 13940701 · 979150369 · 5634413557_<10> · 24313333578409_<14> · 67230905546473_<14> · 286199942061324334063_<21>

9·10⁸¹-1 =: 8999999999999999999999999999999999999999999999999999999999999999999999999999999999_<82>; = 107 · 881 · 1289 · 74067878585596169433169141580363117445575313729107580902512656492774188773_<74>

9·10⁸²-1 =: 89999999999999999999999999999999999999999999999999999999999999999999999999999999999_<83>; = 7 · 13 · 257 · 17107 · 4735035242785279_<16> · 1108530656089810937_<19> · 42857142857142857142857142857142857142857_<41>

9·10⁸³-1 =: 899999999999999999999999999999999999999999999999999999999999999999999999999999999999_<84>; = 75151717 · 34075476493_<11> · 1189363009648277267277306121_<28> · 295493027153652320799403521100632052199_<39>

9·10⁸⁴-1 =: 8999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<85>; = 151 · 1669 · 119299 · 9063097 · 39546174097_<11> · 2523171052478922495193_<22> · 331012677013166691253552731477992567_<36>

9·10⁸⁵-1 =: 89999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<86>; = 4079 · 113969197 · 424929061889_<12> · 997291710148063198144733_<24> · 456838474047838579932292360842873376729_<39>

9·10⁸⁶-1 =: 899999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<87>; = 29 · 12654046331183595167_<20> · 81751143590441508737707_<23> · 29999999999999999999999999999999999999999999_<44>

9·10⁸⁷-1 =: 8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<88>; = 71 · 1670665903849_<13> · 75874274496320064714620165130539981500883716490481715486373775461808043681_<74>

9·10⁸⁸-1 =: 89999999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<89>; = 7 · 13 · 43 · 37021 · 594332567 · 4191314061691_<13> · 10550048513531_<14> · 3680390637464286032999_<22> · 6423273420722757827509291_<25>

9·10⁸⁹-1 =: 899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<90>; = 89 · 11959 · 1099117 · 1914361 · 12296003050864343151685451606293_<32> · 32683300833001233692001425701333824461689_<41>

9·10⁹⁰-1 =: 8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<91>; = 17 · 67 · 269 · 499 · 1249 · 7839399777505813901392825897156132039_<37> · 6012024048096192384769539078156312625250501_<43>

9·10⁹¹-1 =: 89999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<92>; = 643 · 1161022741558831_<16> · 177336476131893903178439219449597_<33> · 679818119154979438389142378569498499291799_<42>

9·10⁹²-1 =: 899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<93>; = 23 · 31 · 97 · 700963 · 77575909 · 968862613 · 189366722010724917133_<21> · 1304347826086956521739130434782608695652173913_<46>

9·10⁹³-1 =: 8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<94>; = definitely prime number

9·10⁹⁴-1 =: 89999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<95>; = 7 · 13 · 1404819661871_<13> · 109311862154664874542821_<24> · 211110876917197143984737_<24> · 30507220264887130087041437378722567_<35>

9·10⁹⁵-1 =: 899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<96>; = 494191 · 1559287059348753978721_<22> · 5784258946596082121965138243_<28> · 201917460656553827347624605886704346651163_<42>

9·10⁹⁶-1 =: 8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<97>; = 61 · 443 · 757 · 8221 · 334127 · 864195651219961261_<18> · 6922368189145372572420061_<25> · 26773803868940651228170563387195934487_<38>

9·10⁹⁷-1 =: 89999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<98>; = 406919384203_<12> · 67062260616887028659416429612783594799_<38> · 3298040175592624102239396210899246476628237804467_<49> (Robert Backstrom / PPSIQS Ver 1.1)

9·10⁹⁸-1 =: 899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<99>; = 19 · 103 · 1321 · 1879 · 665293 · 35278466088721848125359_<23> · 452568977610245073188041_<24> · 17442737999925077569064711017059757319_<38>

9·10⁹⁹-1 =: 8999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999_<100>; = 10042199 · 29021107 · 178865803 · 62059279373249_<14> · 3322781922608843_<16> · 237070102292577121_<18> · 3531726310132797957392482014523_<31>

9·10¹⁰⁰-1 =: 8(9)₁₀₀_<101>; = 7² · 13² · 431 · 586335359385372763185511_<24> · 10441889409517628903684359_<26> · 4118672689081398701245212042998942874009802441_<46>

9·10¹⁰¹-1 =: 8(9)₁₀₁_<102>; = 1319 · 19161787 · 1469369655409_<13> · 659073760694235716803_<21> · 36770252919761093913960286455819525700098586256563863022729_<59>

9·10¹⁰²-1 =: 8(9)₁₀₂_<103>; = 47 · 994953497 · 1066480229_<10> · 1356476046074293_<16> · 2073749608604567097036502567_<28> · 64153538257318726918841475967120159360039_<41>

9·10¹⁰³-1 =: 8(9)₁₀₃_<104>; = 49356163 · 9091817694893_<13> · 169626415128661787_<18> · 1182379569593309002107675592099711153725997386470829858657218695403_<67>

9·10¹⁰⁴-1 =: 8(9)₁₀₄_<105>; = 397 · 409369 · 589291 · 390621169 · 72645380763102632869_<20> · 1057200780089282053600259_<25> · 313246327159464677685910911080355191527_<39>

9·10¹⁰⁵-1 =: 8(9)₁₀₅_<106>; = 569 · 15817223198594024604569420035149384885764499121265377855887521968365553602811950790861159929701230228471_<104>

9·10¹⁰⁶-1 =: 8(9)₁₀₆_<107>; = 7 · 13 · 17 · 6581 · 6132679193_<10> · 679927496140561_<15> · 604590671733065589907762577_<27> · 3506598249038607646721915070190408284922796395217_<49>

9·10¹⁰⁷-1 =: 8(9)₁₀₇_<108>; = 31 · 90375751 · 321239466817997772790381177757837190841872131486157808686050410051453564309844930174516791888481879_<99>

9·10¹⁰⁸-1 =: 8(9)₁₀₈_<109>; = 3217 · 1011559 · 754590459935761_<15> · 1390016294869897_<16> · 3930236875017125218405813407578599_<34> · 670888430310272971761577811789656151_<36>

9·10¹⁰⁹-1 =: 8(9)₁₀₉_<110>; = 43 · 257952658918547_<15> · 8113982094965966882913022903825652784116805670330081715571245645005923072638770280742633395119_<94>

9·10¹¹⁰-1 =: 8(9)₁₁₀_<111>; = 59 · 409 · 3299 · 321114319 · 1645263250196710211_<19> · 713293966588391497181_<21> · 29999999999999999999999999999999999999999999999999999999_<56>

9·10¹¹¹-1 =: 8(9)₁₁₁_<112>; = 57911347104281043346744436873757530216532584665017043759_<56> · 155409957633927725277408352755179538794416195817608717361_<57> (Robert Backstrom / NFSX v1.8 / Sep 19, 2003)

9·10¹¹²-1 =: 8(9)₁₁₂_<113>; = 7 · 13 · 83 · 157 · 4331167543529607187088879_<25> · 64194057375964295426367330839_<29> · 272975432211101000909918107370336669699727024567788899_<54>

9·10¹¹³-1 =: 8(9)₁₁₃_<114>; = 15566337715963_<14> · 1844388924344907947_<19> · 3111951006249079679_<19> · 10073277648984868000793647415535559194360160011293741583417872921_<65>

9·10¹¹⁴-1 =: 8(9)₁₁₄_<115>; = 23 · 29 · 1117 · 23447 · 1136834253520662461_<19> · 3339120189577212023_<19> · 1491491939550947497031924913731_<31> · 90996797063160225886700832599613151271_<38>

9·10¹¹⁵-1 =: 8(9)₁₁₅_<116>; = 18947 · 32191 · 189046327186963_<15> · 341959240782299323_<18> · 1701788651525214775643_<22> · 1341279770756789373831679980291996574469540696232940241_<55>

9·10¹¹⁶-1 =: 8(9)₁₁₆_<117>; = 19 · 21871 · 6686869667_<10> · 52776674411_<11> · 626931419603_<12> · 135592709679897593746997509_<27> · 72193652252802918548715073312653862721363786220156949_<53>

9·10¹¹⁷-1 =: 8(9)₁₁₇_<118>; = 12853 · 348827 · 11387293 · 773615041 · 227867563523506276061507599487908080754267671542431861210571087958319647416988375015231858733_<93>

9·10¹¹⁸-1 =: 8(9)₁₁₈_<119>; = 7 · 13 · 1039 · 19531 · 641317 · 338082920595701_<15> · 17500711862350918541_<20> · 3753906133691874100123_<22> · 3421574356367246644163949706650392458891569799391_<49>

9·10¹¹⁹-1 =: 8(9)₁₁₉_<120>; = 163 · 557 · 1907 · 6433003 · 28275072734748305314573_<23> · 28577980272943488159095038515733572330735309004719529484965168826870990782736731133_<83>

9·10¹²⁰-1 =: 8(9)₁₂₀_<121>; = 577 · 743 · 808716498647_<12> · 1057972676861663008729_<22> · 4719127225971742808162711_<25> · 5199306759098786828422876949740034662045060658578856152513_<58>

9·10¹²¹-1 =: 8(9)₁₂₁_<122>; = 3115546111_<10> · 532239416828107_<15> · 16227736442292637_<17> · 3344593534603521012190562638941239530793459663861323024832822206675524934481857151_<82>

9·10¹²²-1 =: 8(9)₁₂₂_<123>; = 17 · 31 · 71 · 10103893 · 392494829757049332889_<21> · 14354496404471703713440320501419_<32> · 422535211267605633802816901408450704225352112676056338028169_<60>

9·10¹²³-1 =: 8(9)₁₂₃_<124>; = 67 · 757 · 1009 · 2853732877_<10> · 2928134549833431345521_<22> · 21046326978627893893642405241813254831500226029451768720143892395483726603325958317957_<86>

9·10¹²⁴-1 =: 8(9)₁₂₄_<125>; = 7 · 13 · 14811936975361976113_<20> · 2893419201582547140630722876441221402622311_<43> · 23076923076923076923076923076923076923076923076923076923076923_<62>

9·10¹²⁵-1 =: 8(9)₁₂₅_<126>; = 613 · 5757253 · 421434479 · 13085937734441050241784803_<26> · 46241488644874736742662004807641849153986050652868738868818218301387466307168035443_<83>

9·10¹²⁶-1 =: 8(9)₁₂₆_<127>; = 389 · 1867 · 1728967 · 7703231 · 1605051241_<10> · 140337174186780324552365181567296961903007_<42> · 4130735009218423628905782065174736975448288016875429424327_<58>

9·10¹²⁷-1 =: 8(9)₁₂₇_<128>; = 5114630123_<10> · 60258797969_<11> · 9550600474282622707_<19> · 2054569117136440829401479323_<28> · 22503817322752644844861904639_<29> · 661302532344055465819400753846963_<33>

9·10¹²⁸-1 =: 8(9)₁₂₈_<129>; = 277 · 7927 · 1026139 · 3688129845545438409852942740111089271467757989074336517_<55> · 108303249097472924187725631768953068592057761732851985559566787_<63>

9·10¹²⁹-1 =: 8(9)₁₂₉_<130>; = 2488670444801039122027_<22> · 3616388830751562164695567680810031305706130669466325149662667495187284610366974843928941556852902980883055037_<109>

9·10¹³⁰-1 =: 8(9)₁₃₀_<131>; = 7 · 13 · 43 · 1525331 · 1434687874937293_<16> · 1663870743431261569_<19> · 147390107888415272711657_<24> · 611704123343575338233723_<24> · 70061883223682835822554541457490468968459_<41>

9·10¹³¹-1 =: 8(9)₁₃₁_<132>; = 197 · 4568527918781725888324873096446700507614213197969543147208121827411167512690355329949238578680203045685279187817258883248730964467_<130>

9·10¹³²-1 =: 8(9)₁₃₂_<133>; = 103 · 503 · 15763439 · 50162659539371570232061_<23> · 7542611608385988025064828485248227_<34> · 29126213592233009708737864077669902912621359223300970873786407767_<65>

9·10¹³³-1 =: 8(9)₁₃₃_<134>; = 89 · 1011235955056179775280898876404494382022471910112359550561797752808988764044943820224719101123595505617977528089887640449438202247191_<133>

9·10¹³⁴-1 =: 8(9)₁₃₄_<135>; = 19 · 107 · 15920843 · 10644771958592162966987_<23> · 87072588295411188803975078531858983_<35> · 30000000000000000000000000000000000000000000000000000000000000000001_<68>

9·10¹³⁵-1 =: 8(9)₁₃₅_<136>; = 307 · 23053 · 190837 · 6663679532492486082436027119610049449264833150151608508638140565200828143270809367528992570566338049019410075675926996337237_<124>

9·10¹³⁶-1 =: 8(9)₁₃₆_<137>; = 7 · 13 · 23 · 1003344481605351170568561872909698996655518394648829431438127090301_<67> · 42857142857142857142857142857142857142857142857142857142857142857143_<68>

9·10¹³⁷-1 =: 8(9)₁₃₇_<138>; = 31 · 191 · 1373 · 2557 · 17118340529663775761_<20> · 175528354159933984438280203_<27> · 113999489871325457335482883679_<30> · 126396291857824621117649973702535113094004864696623547_<54>

9·10¹³⁸-1 =: 8(9)₁₃₈_<139>; = 17 · 131 · 1193 · 36493 · 13010688596546599947627907_<26> · 329860332209700670780056854383_<30> · 14659956248770104285450993620607013_<35> · 1475398144671508730120834597876984040721_<40>

9·10¹³⁹-1 =: 8(9)₁₃₉_<140>; = 361192209361_<12> · 1576375569625015882582733569_<28> · 158068175129660699440495594381607684640976655757346105877589668692644831393506386802023923223289218511_<102> (Robert Backstrom / GMP-ECM 5.0c)

9·10¹⁴⁰-1 =: 8(9)₁₄₀_<141>; = 661 · 434132891 · 246245887325083_<15> · 637935136493979035228233_<24> · 163877972349517148682713565578488753_<36> · 121829445867639276545602652290090242139072129211660761747_<57>

9·10¹⁴¹-1 =: 8(9)₁₄₁_<142>; = 3088098192434236868514129081431_<31> · 2914415099250980525087836816093806062043396989421160680186718286929717431403185618664074628448524836833717733529_<112> (Robert Backstrom / GMP-ECM 5.0c)

9·10¹⁴²-1 =: 8(9)₁₄₂_<143>; = 7² · 13 · 29 · 199 · 2371 · 185621 · 736259 · 738845467 · 1270904911_<10> · 31160357553605870175480621392732932109_<38> · 2582222260477366821886915879806161182313498997237022181289217500581_<67>

9·10¹⁴³-1 =: 8(9)₁₄₃_<144>; = 227 · 3333067 · 1189522355611543758822100810964928256357991373554799891947489952464823084738919978913363635904288488333037192931627131280917098580141311_<136>

9·10¹⁴⁴-1 =: 8(9)₁₄₄_<145>; = 4188054211417_<13> · 4267778689730745828517_<22> · 294984638384826331048078719260608561_<36> · 10170021111697037216236753300358009041_<38> · 167844482547367204773786131605885255691_<39>

9·10¹⁴⁵-1 =: 8(9)₁₄₅_<146>; = 467 · 4363 · 44171323878379658418244523614725934113071718033826399826063142416691656184157120343790321670304256986799154462702470305827522759274628335119_<140>

9·10¹⁴⁶-1 =: 8(9)₁₄₆_<147>; = 373 · 22739 · 117485247043_<12> · 275676723385625913658191645377_<30> · 291750980771364417216161647598876663509219_<42> · 11229658739992996031059261706955788780792567645986856808713_<59>

9·10¹⁴⁷-1 =: 8(9)₁₄₇_<148>; = 245811829401098369_<18> · 44854455549564788096962189425408270743305049_<44> · 816270574399695328594421683160134958538390249344775592075492092574375764259533960310679_<87> (Tetsuya Kobayashi / NFSX / 128 hours)

9·10¹⁴⁸-1 =: 8(9)₁₄₈_<149>; = 7 · 13 · 47 · 1069 · 1873 · 22189 · 46861 · 367823 · 3179107 · 363937864783_<12> · 90855262284385309_<17> · 19019704578369356396789725755065110611923659_<44> · 13744007092186107278415663200174774248999883123_<47>

9·10¹⁴⁹-1 =: 8(9)₁₄₉_<150>; = 63311 · 120680249231_<12> · 4845174713445464969_<19> · 1769758061206129497344911_<25> · 2370379070062373950322764021016099899973_<40> · 5795434379521086306033002324642348356418074944582677_<52> (Robert Backstrom / PPSIQS Ver 1.1)

9·10¹⁵⁰-1 =: 8(9)₁₅₀_<151>; = 757 · 5815181 · 242995654571_<12> · 30296635088429_<14> · 51378297061009_<14> · 558665640875791_<15> · 1405847460733497973_<19> · 125433387853024282821592391909_<30> · 54866526792220496038143451174747976388551_<41>

9·10¹⁵¹-1 =: 8(9)₁₅₁_<152>; = 43 · 14827 · 456116917 · 179731384178285533302271_<24> · 1721950516998024380415578396384985182297058118806541188405885728003478172983414981063001642029372359426306786893637_<115>

9·10¹⁵²-1 =: 8(9)₁₅₂_<153>; = 19 · 31 · 1291 · 415543 · 2402214527_<10> · 4516945831_<10> · 135999956282039_<15> · 91827063621559306927394843586328922240326571839259783_<53> · 21019329800602844759367800353109139799041028297946332303_<56>

9·10¹⁵³-1 =: 8(9)₁₅₃_<154>; = 83 · 439 · 1321 · 255239 · 732571543742082600902906509573882920452058244205322963068764577538584500131043321313808298931759821413544052372970501976655713377851769823133_<141>

9·10¹⁵⁴-1 =: 8(9)₁₅₄_<155>; = 7 · 13 · 17 · 23677 · 40949 · 4275127 · 4369427 · 7243627 · 3621327289_<10> · 189330424333774697273_<21> · 247502724582139745843_<21> · 108112340743472502401674533227_<30> · 24171811200974383408786576437714478568683739_<44>

9·10¹⁵⁵-1 =: 8(9)₁₅₅_<156>; = 20201 · 1225603 · 884030473598129112046273401306743817009226878392237244963203638811597_<69> · 41119951100362876196136581974904931337399314543041289673940222500296800769089_<77> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon / 28.22 hours on Athlon XP 3000+ / Apr 4, 2007)

9·10¹⁵⁶-1 =: 8(9)₁₅₆_<157>; = 61 · 67 · 547 · 1427 · 1783 · 2713 · 5851837 · 29488903 · 5410076687_<10> · 774480196801059841_<18> · 4849502882804430492203_<22> · 343515729084853263740131391420318235853_<39> · 484191331287271863114267578513481652669_<39>

9·10¹⁵⁷-1 =: 8(9)₁₅₇_<158>; = 71 · 63884014085651210449_<20> · 19842297825920895868076869512333486451963849498579143936408592898904669063601930034114973826323985369401002583755484203670540836150708281_<137>

9·10¹⁵⁸-1 =: 8(9)₁₅₈_<159>; = 23 · 31588957 · 64560983 · 293611531788139_<15> · 822776055137967966312899_<24> · 777331654853277695714263410548853568823_<39> · 102175823331241199704581398426177346644437517656619757456424151741_<66>

9·10¹⁵⁹-1 =: 8(9)₁₅₉_<160>; = 151 · 2081 · 37756997 · 2749349496945658330354039617246556963_<37> · 275909138843910536233458866490589939907450080666251250831272212920006003585355634397268342209549828865520254039_<111> (Wataru Sakai / GMP-ECM B1=10000000, sigma=1818651899)

9·10¹⁶⁰-1 =: 8(9)₁₆₀_<161>; = 7 · 13 · 109 · 997 · 502441 · 156742903 · 394460147 · 121000994263045222745790261071_<30> · 8828242660013348139969025855696091_<34> · 274245916962662936878665224768927142918789143313534242324532556092973_<69>

9·10¹⁶¹-1 =: 8(9)₁₆₁_<162>; = 19719536661599_<14> · 364476297372081551843_<21> · 350687078928628930904081_<24> · 357072782623657793890645461337532959671489824735156071156272420215234324125007941980132527605527295321147_<105>

9·10¹⁶²-1 =: 8(9)₁₆₂_<163>; = 198347 · 580610829637_<12> · 546035880317951_<15> · 47707790680126762810965842706145250687293836957191_<50> · 3000000000000000000000000000000000000000000000000000000000000000000000000000000001_<82>

9·10¹⁶³-1 =: 8(9)₁₆₃_<164>; = 9311 · 9923 · 1563631 · 2134098490901084289819240413_<28> · 60061438682395359593398744400877001_<35> · 4860251353176521897528790975585779837716210646651067100277891814302127723420307300678561_<88> (Sander Hoogendoorn / P-1 for P28) (Wataru Sakai / GMP-ECM B1=10000000, sigma=1023421099 for P35)

9·10¹⁶⁴-1 =: 8(9)₁₆₄_<165>; = 3623 · 1179592811783_<13> · 396556147820323_<15> · 7877327463333877_<16> · 81901814233106783_<17> · 85709168379882713447112804288382078260973732635217_<50> · 9603679718327062465169317706939506976097026342997631_<52>

9·10¹⁶⁵-1 =: 8(9)₁₆₅_<166>; = 1139239 · 3500008777892854273507_<22> · 107006813752674037531328510242074918993021462449577391740200262799_<66> · 21093424816570316132097077241926854067827836439105917046567434042812717837_<74> (Sander Hoogendoorn / GMP-ECM) (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.34 / Apr 14, 2008)

9·10¹⁶⁶-1 =: 8(9)₁₆₆_<167>; = 7 · 13 · 103 · 2917 · 9532847 · 2092564310751650241184817_<25> · 55817750862408931155328183_<26> · 1221232670144955999083128837_<28> · 2420779760434954733153372027991540924036326511578658182920267479056684422091_<76>

9·10¹⁶⁷-1 =: 8(9)₁₆₇_<168>; = 31 · 319757 · 754329661637_<12> · 120364819700553846638797060139385759413189559742346095183692229222962686316649830243684679949703382813179419866699952709431562628548833450954366190881_<150>

9·10¹⁶⁸-1 =: 8(9)₁₆₈_<169>; = 59 · 367 · 84631 · 440527 · 981319 · 3037200296737_<13> · 223430768225151152811482584017892586519419195709078993848314952801_<66> · 16741555597023462687292691535071815284183972598585064174887691519199853_<71>

9·10¹⁶⁹-1 =: 8(9)₁₆₉_<170>; = 90911 · 303273671083_<12> · 561921476752175312039_<21> · 5809192057492029790189790649473348809407304780607105559887659626527691939992391503927629486440677147928852285888430859909715432233957_<133> (Sander Hoogendoorn / P-1)

9·10¹⁷⁰-1 =: 8(9)₁₇₀_<171>; = 17 · 19 · 29 · 223 · 977 · 6563 · 14653 · 1661583485297_<13> · 54023475012308291507621_<23> · 334207792110584172091449693805941060369350577909373_<51> · 152859471551123480004843160977546975097365506330010478081244364258113_<69>

9·10¹⁷¹-1 =: 8(9)₁₇₁_<172>; = 136963579157_<12> · 429373702687757_<15> · [153038947651244726688666449207685636156794373899467047177951914194053059387772278586968400747355401308035645995849761200170389692110687828408878351_<147>] SUBMIT/RESERVE

9·10¹⁷²-1 =: 8(9)₁₇₂_<173>; = 7 · 13 · 43 · 17309375399_<11> · 147929130938493357761877823_<27> · 1207510782643354586857133772644363_<34> · 1104092571873395520541318241400785866473479_<43> · 6737535295047400422939574997854853936889567773370251541787_<58>

9·10¹⁷³-1 =: 8(9)₁₇₃_<174>; = 1289 · 1997 · 34668071675443361_<17> · 3806940299291622726460350337947914704889277467532053374128676991_<64> · 2649145276309295977725794028033536754856664922424512618104600287851523960480215455939453_<88> (Serge Batalov / Msieve-1.38 snfs / 20.00 hours on Opteron-2.6GHz; Linux x86_64 / Oct 8, 2008)

9·10¹⁷⁴-1 =: 8(9)₁₇₄_<175>; = 2741 · 964927 · 57704100757_<11> · 394211670918873961_<18> · 78212992366947111793224659_<26> · 664715300063407687268091985902707716360249006586927_<51> · 2877320783415929720655717276789004987147764455948869723172437_<61>

9·10¹⁷⁵-1 =: 8(9)₁₇₅_<176>; = 13121 · 38329823123_<11> · 4599492339001072307_<19> · 38907099798570231897603470622116937108505920099498106776524393816994508400543016486790808673861173494962222191538268942891622488072438703124679_<143>

9·10¹⁷⁶-1 =: 8(9)₁₇₆_<177>; = 613 · 1304488873_<10> · 3751676989_<10> · 3300924483140581825965792499050421_<34> · 6966991598609698357143166308824300493706869803_<46> · 13044737394181493541891572756624031685359114648899761380720804186090822001393_<77>

9·10¹⁷⁷-1 =: 8(9)₁₇₇_<178>; = 89 · 757 · 2795376519729848150784923706882701877318922481507609115407740172075186231071_<76> · 47787719999108578060151819968036562451065721814882830579492456551763376466710619837746260674550853_<98> (Serge Batalov / Msieve 1.36 snfs / 76.00 hours on Opteron-2.6GHz; Linux x86_64 / Aug 21, 2008)

9·10¹⁷⁸-1 =: 8(9)₁₇₈_<179>; = 7 · 13² · 113 · 250451 · 278917 · 4115541273187_<13> · 81816795564710189_<17> · 12594245972471028228269_<23> · 186182086789309759054543090955981_<33> · 18277346698490628671886518504139713_<35> · 667865368081651529733187254777823845221359793_<45>

9·10¹⁷⁹-1 =: 8(9)₁₇₉_<180>; = 2326512347_<10> · 7735574032453_<13> · 13523336658151_<14> · 3697947499634836846572228151356031258255841276556757089615402605153955880412188967672797717739121202635047054593576835933232331288153309349852239_<145>

9·10¹⁸⁰-1 =: 8(9)₁₈₀_<181>; = 23 · 3967 · 180331 · 381318197437_<12> · 416998450980192814055629_<24> · 564094907179255318210761991225027_<33> · 19496154286820318385804086168513204587_<38> · 312794405595744596969514780116162611260899355352176462266677835197_<66>

9·10¹⁸¹-1 =: 8(9)₁₈₁_<182>; = 2347 · 18121 · 14881545317_<11> · 18520231788365026399039_<23> · [7678083141389664656001425818220694158822776458038611028631283111975249628251012772571482748321660481753969878560664066088398797796345069148879_<142>] (Sander Hoogendoorn / GMP-ECM) SUBMIT/RESERVE

9·10¹⁸²-1 =: 8(9)₁₈₂_<183>; = 31 · 283 · 883 · 1597 · 184553 · 446028257 · 14076488831_<11> · 16347505193_<11> · 52155548314181870086767536446091569_<35> · 4542139018383436278421775174894971465367_<40> · 16212071708719648632278491157629276678664053603353596806375780717_<65>

9·10¹⁸³-1 =: 8(9)₁₈₃_<184>; = 9587 · 44803933 · 328987231 · 2440572839378229347582719_<25> · 26095932910686069765618451295488481733475751249529060617603572778843532932969652780988006968716186630596900105613502368966849560241018262121_<140> (Sander Hoogendoorn / P-1)

9·10¹⁸⁴-1 =: 8(9)₁₈₄_<185>; = 7² · 13 · 769 · 2473 · 17929 · 8354651 · 1795678883533_<13> · 1896995229026274291292255877683_<31> · 130361051090105258563806462474876437765791_<42> · 1116928758657913030746751251796032617863380560312387775178668625667297149218675001_<82>

9·10¹⁸⁵-1 =: 8(9)₁₈₅_<186>; = 51506797 · 6651080365041166203291134547420211961_<37> · [2627155446018583376056001129947388070101320462055070329967261485572839484407296033679509907414358095104997570766676583504598716504545452477747_<142>] (Wataru Sakai / GMP-ECM B1=10000000, sigma=308127902 for P37) SUBMIT/RESERVE

9·10¹⁸⁶-1 =: 8(9)₁₈₆_<187>; = 17 · 863 · 9439 · 503699641 · 1290996163_<10> · 48503123144589502741752878729057_<32> · 122794781146491779173462117695893007175726748617613527_<54> · 16780720353433491782468421724289387703811042473187542015809353308503757977083_<77>

9·10¹⁸⁷-1 =: 8(9)₁₈₇_<188>; = 107 · 3091427 · 119847129180121192841_<21> · [2270241721559984930272736143311910112693495887639753969987718778079115797333387754225729923122144151094026523595963349024633942322055857934743702122096103206951_<160>] (Sander Hoogendoorn / P-1 for P21) SUBMIT/RESERVE

9·10¹⁸⁸-1 =: 8(9)₁₈₈_<189>; = 19 · 97 · 140395141 · 770083117 · 4819894883232336708373_<22> · 1001770522456725752538019_<25> · 3024629329448324924475066105061_<31> · 380774519116859555009563691113510103_<36> · 812234892273730400146403072480506371926158526721772968889_<57>

9·10¹⁸⁹-1 =: 8(9)₁₈₉_<190>; = 67 · 133187 · 2078087862871_<13> · 234621664993637_<15> · 5363095884001110231789672199_<28> · [385707683405733164444530365933755816046832242345670430607839333744882290009141947111896835408591178894659692587255754972460523547_<129>] (Sander Hoogendoorn / GMP-ECM) SUBMIT/RESERVE

9·10¹⁹⁰-1 =: 8(9)₁₉₀_<191>; = 7 · 13 · 157 · 40093 · 6579763843_<10> · 7544219843_<10> · 10684622854603_<14> · 14044244326009837_<17> · 2576385525477167077559755888656850563188888467559516732456150855611_<67> · 8187283801493673414908347666397742188102045797947618728529480372841_<67>

9·10¹⁹¹-1 =: 8(9)₁₉₁_<192>; = 8267003 · 541664839 · [200985056839070774211703719218863167187397355454176638538374940626274567941047076989756634924171661984503150725799055015559922208288911435130605435632537697415565069217878435147_<177>] SUBMIT/RESERVE

9·10¹⁹²-1 =: 8(9)₁₉₂_<193>; = 71 · 2833205979816856630365091_<25> · 225175496540201364974370054300058530191_<39> · 187647065404458407478575579255133377195945562460800825959_<57> · 1058871123868630697170279213402229282716267254260527378849368062541824011_<73>

9·10¹⁹³-1 =: 8(9)₁₉₃_<194>; = 43 · 1821585162697457488304296102273254935173081_<43> · 577907847913674910737796883693373565504125011795363899114213268519_<66> · 1988227065562338941228938824773608620242017418041162968604820660552549013425070142387_<85> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon, Msieve 1.36 snfs / 161.42 hours, 9.99 hours / Sep 17, 2008)

9·10¹⁹⁴-1 =: 8(9)₁₉₄_<195>; = 47 · 83² · 1129 · 6823 · 23264344193_<11> · 199771102072963_<15> · 18929164970412319489_<20> · 336014103925942214219_<21> · 1283729395505707376279023867054907059411215130486873257049_<58> · 9508964463243707970091052874294858739920079951513408696616239_<61>

9·10¹⁹⁵-1 =: 8(9)₁₉₅_<196>; = 1093 · 1523 · 6053 · 5800422267260147_<16> · 153989872412992395581191134339026335265738004835304876698908351736754429755549700376348268128472842956417110081496940644806387980047471097189853728379962366481054768297951_<171>

9·10¹⁹⁶-1 =: 8(9)₁₉₆_<197>; = 7 · 13 · 1019 · 187379 · 376657 · 3756512436102370044614142122779_<31> · 2065995084482425229722350759373801066391_<40> · 155312880582011749094355956606205409844262829_<45> · 11408758412526373980350866244775600239574193508591183341548280948117_<68>

9·10¹⁹⁷-1 =: 8(9)₁₉₇_<198>; = 31 · 277 · 27450632285963828291729_<23> · [3818112268196165689479781790439330543302891662224712896124961773277885163454921823655935042268853704582463791302464990137598241649983644542032759069272259846593508442000013_<172>] (Wataru Sakai / GMP-ECM B1=2500000, sigma=2672822829) SUBMIT/RESERVE

9·10¹⁹⁸-1 =: 8(9)₁₉₈_<199>; = 29 · 643 · 345221647 · 477752776081611404646500077456166023_<36> · 18189468758616411279538180668857592713662364213329197479_<56> · 160883788276934627554030138896337212420228454979353247171126722797232798841636724406070681610983_<96>

9·10¹⁹⁹-1 =: 8(9)₁₉₉_<200>; = 311 · 18816601 · 7199849885356048147_<19> · 8780607192536057363_<19> · 6189868364159015753089_<22> · 653013029588688183402047290771742842951_<39> · 60185198005340312093913851920027593244762401225251579516624254991791230274129125334702673471_<92> (Sander Hoogendoorn / GMP-ECM) (Robert Backstrom / GMP-ECM 6.0.1 B1=1174000, sigma=378789720 for P39 / Feb 5, 2008)

9·10²⁰⁰-1 =: 8(9)₂₀₀_<201>; = 103 · 163 · 313 · 30908839729_<11> · 52687875503_<11> · 271975894534095225991176221835439_<33> · 20990446375297618944778008551499605099634313008134910244350187_<62> · 18421621929042446518945642871526259144172571872058046358421612697832167819925377_<80>

9·10²⁰¹-1 =: 8(9)₂₀₁_<202>; = 2294564964667_<13> · 12476080853161_<14> · [314386559271698519584061601157869811128821047924431956774433715499124059666742739281031965973650393840664177630046844462551572393688094746377808784846090573075736991148271572677_<177>] SUBMIT/RESERVE

9·10²⁰²-1 =: 8(9)₂₀₂_<203>; = 7 · 13 · 17 · 23 · 461 · 42703 · 112455688781_<12> · 608906393745935368545043_<24> · 14652714986922379314736190545012031169061014220429491786130421653_<65> · 128060437587372995319339355138356780636701102819820530493717889157422282840645351747588735187_<93>

9·10²⁰³-1 =: 8(9)₂₀₃_<204>; = 359 · 397 · 1090121453_<10> · [5792721746949381263246555450843623097856424498764256327126681154950325860138087923320433963121060453434022738399576909614780205538350127610792728900999389072499561154212711073600190303340321_<190>] SUBMIT/RESERVE

9·10²⁰⁴-1 =: 8(9)₂₀₄_<205>; = 757 · 341667013 · 3184685509_<10> · 4357048548962608484941710525445154377541575699_<46> · 216203292699210532299880330172360087254034249311_<48> · 11599047429948021078058597960005614850022606973185675972655317149495105361550724254328327239_<92>

9·10²⁰⁵-1 =: 8(9)₂₀₅_<206>; = 2162664653_<10> · 1845200848424553733_<19> · 82971532256549192147_<20> · [271819476241130488854244811473304787120760686166422968499959671891667747982590140078636166672507855834935987267464074607706966958908419130245794145257266592933_<159>] SUBMIT/RESERVE

9·10²⁰⁶-1 =: 8(9)₂₀₆_<207>; = 19 · 60083 · 83301251819_<11> · 1141870773049_<13> · 5959534140575605571563_<22> · 23917741750007011930592110720920008759435096557_<47> · 1098742369919843494185783706649927078558709517031491_<52> · 52922512935658165935800313758093233844200674356148904094417_<59>

9·10²⁰⁷-1 =: 8(9)₂₀₇_<208>; = 31178093 · 437355437 · 8818647100342200893_<19> · 1128079654607137676707_<22> · [66346298944020392603484497612666103081441614843048626911193836751881822551731135061069119296731745472582789384820074691840937730214159201572718886363889_<152>] SUBMIT/RESERVE

9·10²⁰⁸-1 =: 8(9)₂₀₈_<209>; = 7 · 13 · 347 · 1321 · 32089 · 133881109 · 2813505323_<10> · 15058978723753_<14> · 8380200882966911_<16> · 32926128941294964210169_<23> · 32165325017020156619259454561_<29> · 1335571157005293313685597645833240585336319076853216277941261580514907200064107415536254079056908687_<100>

9·10²⁰⁹-1 =: 8(9)₂₀₉_<210>; = 11071883 · 3100246223387_<13> · 791281198830680471_<18> · [33135535049229488781040884212467119901094781857415840762237304072012875122435194733406492095949063832373172602677412408866006391964302517946107655743986314896662058905677489_<173>] SUBMIT/RESERVE

9·10²¹⁰-1 =: 8(9)₂₁₀_<211>; = 167 · 3851 · 69233 · 2172689417_<10> · 522970842054278052596796307_<27> · 4105406260953967323411421624379333441658282336124257972514962287_<64> · 43331937082027356896277786604653850042609738130660234281339823494576285875232909161815897043317493103_<101>

9·10²¹¹-1 =: 8(9)₂₁₁_<212>; = 922059280500261049_<18> · [97607607128221426357377013488961714417672649880576719570712379297973765260634609757666743202155071041935920974507857219886770282749305052414640900808516085867306486791876528928802932236198738551_<194>] SUBMIT/RESERVE

9·10²¹²-1 =: 8(9)₂₁₂_<213>; = 31 · 218279 · 4744051332993243749733574090207_<31> · 203990612149063181178190673768547952947112612321147898789683681650672394753_<75> · 137438782475638975806192991538352292249827056198718154288777207152314240032252300954283279655853288681_<102>

9·10²¹³-1 =: 8(9)₂₁₃_<214>; = 293 · 31517 · 297630677 · 653240602737601_<15> · 2763180643414756163_<19> · 1880839632718006855987957867_<28> · 240517498236320119968635920027_<30> · 179481389251375241524195452694409_<33> · 22343541377353884509643293353805591669647127166940550303134256458298751571009_<77> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3144849970 for P33 / Nov 23, 2008) (Sinkiti Sibata / Msieve 1.38 for P30 x P77 / 46.3 hours / Nov 25, 2008)

9·10²¹⁴-1 =: 8(9)₂₁₄_<215>; = 7 · 13 · 43 · 149 · 35491 · 132967 · 319469 · 406859 · 3286888271596093_<16> · 2762969980683717258321223144209234268699368337958266176306842668501370570391151817_<82> · 27710893469268378687085304936496533197645542536668954891993497757911796495887926681123282141_<92>

9·10²¹⁵-1 =: 8(9)₂₁₅_<216>; = 1594837 · 3084860091146129_<16> · [182932443168146329536107439965379476609018081738136475800750573255026519004566909056500589766164538310841930793505582466992062465914156687385003217573278263261011693459436670795419625561766346963_<195>] SUBMIT/RESERVE

9·10²¹⁶-1 =: 8(9)₂₁₆_<217>; = 61 · 479 · 1537022713_<10> · 12042349012118749379843_<23> · 5580815161537522052816552016371_<31> · 60631261945090711190778038575214536541054929_<44> · 2050264538747272760451120621063903142800302077_<46> · 23987308437233184406133324376083302948918445967347350246327033_<62>

9·10²¹⁷-1 =: 8(9)₂₁₇_<218>; = 4283 · 9437 · [2226693698068400121320169087202298165617568177835436499136747964820515746299525781043122372826162443589498526559668426505166387088778846785932174761510589994411246228259212184388744498798587415207194714541702769_<211>] SUBMIT/RESERVE

9·10²¹⁸-1 =: 8(9)₂₁₈_<219>; = 17 · 941 · 60259 · 78121 · 470317 · 524086391 · 11861956980462821_<17> · 14770997282202389_<17> · 4194875121286899383_<19> · 2554805335672876431983_<22> · 26506062415929309987997152493_<29> · 33005323977166274796073777418225748488133943_<44> · 29515385542052210711260544097911301044937947161_<47>

9·10²¹⁹-1 =: 8(9)₂₁₉_<220>; = 136523 · 3275933 · [20123414623063055102118571087903749096571159337618260154664291160939792032690128124998976228268348411190796072598184524509069267467017885465416230112288285628875789971268498264586927034423866579944092570018561_<209>] SUBMIT/RESERVE

9·10²²⁰-1 =: 8(9)₂₂₀_<221>; = 7 · 13 · 7482121 · 228966966455977967620471917769017793_<36> · 25016448656495401004069927663455363536577225267399577915957403823231_<68> · 23076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923_<110>

9·10²²¹-1 =: 8(9)₂₂₁_<222>; = 89 · 106488463511_<12> · 551029570561_<12> · [172335614263112567179081867466993970765225540021715938315260756668337285450737775572869450031393778581870591318194452990592879792164909246568202384476242199160419692269526807699774717892321366997121_<198>] SUBMIT/RESERVE

9·10²²²-1 =: 8(9)₂₂₂_<223>; = 67 · 6883 · 50769977 · 966767341958861_<15> · 822533722631126307625175578433_<30> · 1934766413697553399092247719779_<31> · 80515494338141194672046088158648781419_<38> · 3103125095145859264337050293405093023943285127966189415280642637135368146774978576169338417355259_<97>

9·10²²³-1 =: 8(9)₂₂₃_<224>; = 6997 · 633790652387_<12> · 20294801406914642962244218873248543299149735371441537563178842213852148072109436983033892161885256828504303661989445893971612432873129501966448138296925307809568065372164387244393430943718879147664031493401441_<209>

9·10²²⁴-1 =: 8(9)₂₂₄_<225>; = 19 · 23 · 181 · 3407 · 127103 · 3483791461_<10> · 7807361641_<10> · 8118226003_<10> · 954027040968047_<15> · 10210034882989784864647209757_<29> · 2439916668000842264184198385585361045416127281052552280029060389_<64> · 5006959449134196242766265868072792925075855906976643628238419170429812879439_<76>

9·10²²⁵-1 =: 8(9)₂₂₅_<226>; = 853 · 1049 · 55157579569_<11> · 133538941942257663803_<21> · 49761553125602982208933121512742791_<35> · [27441694944874738547985333891331430219518293144909937468780274729274695337974413869161834959704177482590200454318554050429898051581550176667766086127396391_<155>] (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=894971310 for P35 / Oct 28, 2008) SUBMIT/RESERVE

9·10²²⁶-1 =: 8(9)₂₂₆_<227>; = 7² · 13 · 29 · 59 · 10243 · 8139497 · 47825881 · 319042484686421_<15> · 8860269191229929657_<19> · 831972291458432430035984753_<27> · 339493482302125699689696823651386878401_<39> · 183196997235114666313664862887412748867877758421_<48> · 141583048280838478129901762617470802340141205501351431287_<57>

9·10²²⁷-1 =: 8(9)₂₂₇_<228>; = 31 · 71 · 401 · 613 · 5279 · 9710839 · 1506283955768878297951559_<25> · 21542810126742033377137661884795289035742458338164984788784814332187585460966303502744555308850123798452119220786033876609974398994353793852854006302730531280828689067948109292411408837_<185>

9·10²²⁸-1 =: 8(9)₂₂₈_<229>; = 919 · 967 · 295357 · 171141301 · 5078181337_<10> · 3451900116240059527310349962515641788338540306292431489892874508205404626512683628520178446569627_<97> · 11429625511698592200629533241927411979327821030913432739903978629728413991676984595399531610900916380341_<104>

9·10²²⁹-1 =: 8(9)₂₂₉_<230>; = 197 · 208440677 · 1189638653569_<13> · 1894742524089853_<16> · 81036479966432843_<17> · 49931612314311537707693_<23> · [240310297661166400485936362786332361583251738596432632828490772305058814102347092398830258825622814264893962996338765698926236641973725988355663176866797_<153>] SUBMIT/RESERVE

9·10²³⁰-1 =: 8(9)₂₃₀_<231>; = 832033003 · 403233877351_<12> · 1577831737746491_<16> · 66935581832507131_<17> · 5185040008134360225023375060014351_<34> · 10929766662867956939358630793031023525224309137_<47> · 448192115145409256752005959887688729242511151091393953380282171310853902822633424231824418287457229_<99>

9·10²³¹-1 =: 8(9)₂₃₁_<232>; = 757 · 72043 · 267413919813067483_<18> · 8396785017878813402797147_<25> · [73495000374915762859216129340875350621606641556304628851630109938131596023912677555409049768864357258781866352609555924461782303651497588176040351979174743012122623433649443058580049_<182>] SUBMIT/RESERVE

9·10²³²-1 =: 8(9)₂₃₂_<233>; = 7 · 13 · 191 · 419 · 176989 · 342803 · 3080389672652381470662675187786673261869_<40> · 805614854347532273657889152825813219506231_<42> · 273073929335371915922432805053316071687914686044309883829457031841_<66> · 300572659388749176537866923029182472055638130513953259347940318716277_<69>

9·10²³³-1 =: 8(9)₂₃₃_<234>; = 1163 · 20690127509876948541763_<23> · 37402413528078313225157455296433627979815209705817642004489823300246185036042952351622004569082719963544966038837562863463991077653816853769655709533603986694498817862617509179644966975536274976215393981970271_<209>

9·10²³⁴-1 =: 8(9)₂₃₄_<235>; = 17 · 103 · 151 · 787 · 983 · 7717 · 1343893 · 5364595726158023_<16> · 698810987349616407838127758561787_<33> · 236408012483724037920438356017353423704940485863994051049626928720839267_<72> · 4787172289684415190372122785770632962010454236261129833023534339757976679455179640719536246397_<94>

9·10²³⁵-1 =: 8(9)₂₃₅_<236>; = 43 · 83 · 2689483 · 5892443 · [1591225639153431768007566049477746705340043319419634665441039537722729376906742965530026725645981701242485147321836891990824496168048939599558565575212435906471000156733361990942820845793699204418087878684415916429628759_<220>] SUBMIT/RESERVE

9·10²³⁶-1 =: 8(9)₂₃₆_<237>; = 229 · 1801 · 2322347 · 269136729617782632743_<21> · 525337354976588234359540934329_<30> · 50730503927128935534261432720820845779278829698082773940411_<59> · 131004366812227074235807860262008733624454148471615720524017467248908296943231441048034934497816593886462882096069869_<117>

9·10²³⁷-1 =: 8(9)₂₃₇_<238>; = 2038378317634843_<16> · 16458968745184537055041_<23> · [268259492009414780158612424935774837377983696944818400310056859744318788116949812279242159327330296092443080358232178746828802771544827213961454818642680738119122592804385242229650438777035387599027373_<201>] SUBMIT/RESERVE

9·10²³⁸-1 =: 8(9)₂₃₈_<239>; = 7 · 13 · 1553 · 438721 · 7141775796359_<13> · 642459091110046921_<18> · 2909223957003733935959638857517450326431467_<43> · 18121551992896711422356563612737888923327762681447_<50> · 6000908468590146007802970302085578213299657647019234436854511092567500093029441038440754743913961970037423_<106>

9·10²³⁹-1 =: 8(9)₂₃₉_<240>; = 719 · 3714202444243_<13> · 337014081628848980650804962314582987701723478832378345683527803207293332544866460706041453711708004510945624606887985056689566478244464427440359623860252710513541727202497061662621374053508032473519582460497645264664094703947_<225>

9·10²⁴⁰-1 =: 8(9)₂₄₀_<241>; = 47 · 107 · 587 · 129457 · 97356367 · 23194910287_<11> · 44209021499_<11> · 11890818970927053203_<20> · 2047296729179266187110579273833644931841_<40> · 944274051192262206631103925845322418206838969_<45> · 14024472877652688033418848086042342088954204619_<47> · 731732109565129767405444811518543619679358772542643_<51>

9·10²⁴¹-1 =: 8(9)₂₄₁_<242>; = 199 · 17921668997152761272351_<23> · [25235445794948821739748678732191479860646613915310649971905671891079318635081668702935911295793325871652144818294111071512155813738294274363970467769114647418288047846110437398740880356716473955611500403122023243195351_<218>] SUBMIT/RESERVE

9·10²⁴²-1 =: 8(9)₂₄₂_<243>; = 19 · 31 · 695084724889_<12> · 2533733441819_<13> · 5680551281721563208659_<22> · 67236972872290888335676434473866511834711951165578089027465183928012262948453258565151_<86> · 2271589796011125260933021182971065840770325771072812443357936760347860632353214061224348430869129003298879789_<109>

9·10²⁴³-1 =: 8(9)₂₄₃_<244>; = 21874481 · [411438333096908676370424514300476431875115117016947739240076141692230320801668391583782033502874879637144305275174300135395212348123825200698476000413449809392049118788235478592612094430949013144586150409694291718281224592254325942636079_<237>] SUBMIT/RESERVE

9·10²⁴⁴-1 =: 8(9)₂₄₄_<245>; = 7 · 13 · 43711 · 2655233370133_<13> · 92771425356838998606541_<23> · 2294796717664213509541276266917758467689777187014509_<52> · 10056194912293669804719011098323636255061719884507348567986171070655047_<71> · 3980297609513933332382807187105798139082232720008215213498031449569053628602395321_<82>

9·10²⁴⁵-1 =: 8(9)₂₄₅_<246>; = 32111117 · 172807608592522667_<18> · 477686215192476748920251227_<27> · [339532637756691064099979297959976382666189473964798133778656689443265687015691551665577564600322675698680258500385768470772877278355959799098195918708103977987748420059618510280852951228327296483_<195>] SUBMIT/RESERVE

9·10²⁴⁶-1 =: 8(9)₂₄₆_<247>; = 23 · 19553 · 2990366970937067399_<19> · 166235481615022500575018646587621550923191_<42> · 40128811045536569808228286660052417775119260016039979721737391386749724030769_<77> · 1003221353484891513387954898308810381727983558088177158306275171844453418150696067538783658365482703827401_<106>

9·10²⁴⁷-1 =: 8(9)₂₄₇_<248>; = 547 · 27920471 · 466553086942912739773_<21> · [12630815039449560205963291928005946973269477358319164351123083186295835583586818232098279066553124847974445214981296311324549796426364058808409578975294269836041018310628409790287918526397585938651600317651381893456399_<218>] SUBMIT/RESERVE

9·10²⁴⁸-1 =: 8(9)₂₄₈_<249>; = 2767 · 5449 · 17167 · 57571 · 158941 · 64072783 · 2602864396977816164601828457_<28> · 197691309554911543479077660268414631217739335706830786585014015880624021918384268676142039645857_<96> · 11525763706642949500110430345615582532053120160077139973457388941551304686760716557918497750074407_<98>

9·10²⁴⁹-1 =: 8(9)₂₄₉_<250>; = 1239961 · 17567289930891241_<17> · 2211131180516999698877_<22> · 132852679081112049264025722783994751_<36> · 173971508153106043979381596158458837_<36> · [8084753086520734729835410115388355154353484488692121661133313572891265091227154991684283911329904836521257457036748584838069340122707201_<136>] (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=1540395319 for P36 / Oct 31, 2008) (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=2491863350 for P36 / Nov 2, 2008) SUBMIT/RESERVE

9·10²⁵⁰-1 =: 8(9)₂₅₀_<251>; = 7 · 13 · 17 · 1471 · 7673 · 600701 · 3599650081_<10> · 31612646761_<11> · 634218826805839667438296844687_<30> · 19233942138039946177234105344928717_<35> · 3876544332029444008036492867365402990466431683_<46> · 16412899871082734672605658515241235597824962933_<47> · 97153246083586305759374376504412500632762391535023918322219_<59>

Factorizations

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