Since June 16, 2000

STUDIO KAMADA

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Last update

Sequence

General term

Algebraic factorizations

Room for prime numbers

Prime numbers

1. 10³-9 = 991 is prime. (Makoto Kamada / May 29, 2003)
2. 10⁵-9 = 99991 is prime. (Makoto Kamada / May 29, 2003)
3. 10⁷-9 = 9999991 is prime. (Makoto Kamada / May 29, 2003)
4. 10³³-9 = (9)₃₂1_<33> is prime. (Makoto Kamada / May 29, 2003)
5. 10⁴⁵-9 = (9)₄₄1_<45> is prime. (Makoto Kamada / May 29, 2003)
6. 10¹⁰⁵-9 = (9)₁₀₄1_<105> is prime. (Makoto Kamada / PPSIQS / May 29, 2003)
7. 10¹⁹⁷-9 = (9)₁₉₆1_<197> is prime. (Makoto Kamada / pock 0.1.1a / May 29, 2003)
8. 10¹⁹⁹-9 = (9)₁₉₈1_<199> is prime. (Makoto Kamada / pock 0.1.1a / May 29, 2003)
9. 10²⁸¹-9 = (9)₂₈₀1_<281> is prime. (Makoto Kamada / pock 0.1.1a / May 29, 2003)
10. 10³⁰¹-9 = (9)₃₀₀1_<301> is prime. (Makoto Kamada / pock 0.1.1a / May 29, 2003)
11. 10³¹⁷-9 = (9)₃₁₆1_<317> is prime. (Makoto Kamada / pock 0.1.1a / May 29, 2003)
12. 10¹¹⁰⁷-9 = (9)₁₁₀₆1_<1107> is prime. (searched by Makoto Kamada / May 29, 2003) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Sep 13, 2006)
13. 10¹⁶⁵⁷-9 = (9)₁₆₅₆1_<1657> is prime. (searched by Makoto Kamada / May 29, 2003) (certified by Makoto Kamada / pock 0.2.1 / Aug 18, 2003)
14. 10³³⁹⁵-9 = (9)₃₃₉₄1_<3395> is PRP. (Makoto Kamada / May 29, 2003)
15. 10³⁵⁹²⁵-9 = (9)₃₅₉₂₄1_<35925> is PRP. (Jason Earls / Jan 2008)
16. 10³⁷⁵⁹⁷-9 = (9)₃₇₅₉₆1_<37597> is PRP. (Jason Earls / Jan 2008)

• 1-10000

• A056696 (On-Line Encyclopedia of Integer Sequences)
• A093177 (On-Line Encyclopedia of Integer Sequences)
• A095714 (On-Line Encyclopedia of Integer Sequences)
• Numbers b^n +/- (b-1) (Wojciech Florek)

Condition

Status

Factorization results

10¹-9 =

1

10²-9 =

91

= 7 · 13

10³-9 =

991

= definitely prime number

10⁴-9 =

9991

= 97 · 103

10⁵-9 =

99991

= definitely prime number

10⁶-9 =

999991

= 17 · 59 · 997

10⁷-9 =

9999991

= definitely prime number

10⁸-9 =

99999991

= 7 · 13 · 769 · 1429

10⁹-9 =

999999991

= 67 · 14925373

10¹⁰-9 =

9999999991_<10>

= 19² · 277 · 100003

10¹¹-9 =

99999999991_<11>

= 83 · 1289 · 934693

10¹²-9 =

999999999991_<12>

= 757 · 1321 · 1000003

10¹³-9 =

9999999999991_<13>

= 31 · 3391 · 95128471

10¹⁴-9 =

99999999999991_<14>

= 7 · 13 · 769231 · 1428571

10¹⁵-9 =

999999999999991_<15>

= 653 · 718321 · 2131907

10¹⁶-9 =

9999999999999991_<16>

= 643 · 1297 · 77101 · 155521

10¹⁷-9 =

99999999999999991_<17>

= 43 · 19387 · 119955712351_<12>

10¹⁸-9 =

999999999999999991_<18>

= 23 · 71 · 307 · 2251 · 6257 · 141623

10¹⁹-9 =

9999999999999999991_<19>

= 5441 · 1837897445322551_<16>

10²⁰-9 =

99999999999999999991_<20>

= 7 · 13 · 769230769 · 1428571429_<10>

10²¹-9 =

999999999999999999991_<21>

= 17839 · 19813 · 237877 · 11893969

10²²-9 =

9999999999999999999991_<22>

= 17 · 5882352941_<10> · 100000000003_<12>

10²³-9 =

99999999999999999999991_<23>

= 479 · 857839 · 243365325222311_<15>

10²⁴-9 =

999999999999999999999991_<24>

= 61 · 5507 · 14221 · 1152763 · 181587071

10²⁵-9 =

9999999999999999999999991_<25>

= 107 · 21569 · 390110923 · 11107033999_<11>

10²⁶-9 =

99999999999999999999999991_<26>

= 7² · 13 · 29 · 547 · 56527 · 3610339 · 48492137

10²⁷-9 =

999999999999999999999999991_<27>

= 41947 · 3192187 · 5818399 · 1283533681_<10>

10²⁸-9 =

9999999999999999999999999991_<28>

= 19 · 31 · 613 · 839 · 276964579 · 119189511323_<12>

10²⁹-9 =

99999999999999999999999999991_<29>

= 5197 · 19241870309794111987685203_<26>

10³⁰-9 =

999999999999999999999999999991_<30>

= 599 · 2131 · 3733 · 209861 · 14902357 · 67103479

10³¹-9 =

9999999999999999999999999999991_<31>

= 64332799 · 1883470517_<10> · 82529407366277_<14>

10³²-9 =

99999999999999999999999999999991_<32>

= 7 · 13 · 433 · 39323 · 45177491 · 1428571428571429_<16>

10³³-9 =

999999999999999999999999999999991_<33>

= definitely prime number

10³⁴-9 =

9999999999999999999999999999999991_<34>

= 99999999999999997_<17> · 100000000000000003_<18>

10³⁵-9 =

99999999999999999999999999999999991_<35>

= 2308769 · 13259446279_<11> · 3266586248147987441_<19>

10³⁶-9 =

999999999999999999999999999999999991_<36>

= 47 · 1283 · 949261 · 17469877 · 1000000000000000003_<19>

10³⁷-9 =

9999999999999999999999999999999999991_<37>

= 1787 · 10076191 · 555365703265382231555726123_<27>

10³⁸-9 =

99999999999999999999999999999999999991_<38>

= 7 · 13 · 17 · 43 · 103 · 9431 · 18679 · 155027 · 9486361 · 56335953419_<11>

10³⁹-9 =

999999999999999999999999999999999999991_<39>

= 757 · 22111 · 1299187 · 45985834253851859338253959_<26>

10⁴⁰-9 =

9999999999999999999999999999999999999991_<40>

= 23 · 373 · 19031 · 155773 · 859249 · 265883581 · 1721071782307_<13>

10⁴¹-9 =

99999999999999999999999999999999999999991_<41>

= 2801 · 14489 · 970867 · 192390028511_<12> · 13191864450781787_<17>

10⁴²-9 =

999999999999999999999999999999999999999991_<42>

= 67 · 1164288119_<10> · 858893931563_<12> · 14925373134328358209_<20>

10⁴³-9 =

9999999999999999999999999999999999999999991_<43>

= 31 · 89 · 163 · 631 · 1123 · 31379901759227182253273005491071_<32>

10⁴⁴-9 =

99999999999999999999999999999999999999999991_<44>

= 7 · 13 · 157 · 601 · 1031137 · 14682887281_<11> · 769230769230769230769_<21>

10⁴⁵-9 =

999999999999999999999999999999999999999999991_<45>

= definitely prime number

10⁴⁶-9 =

9999999999999999999999999999999999999999999991_<46>

= 19 · 113 · 3049 · 983513 · 2972507 · 1800293893_<10> · 290244589115247419_<18>

10⁴⁷-9 =

99999999999999999999999999999999999999999999991_<47>

= 3701884489_<10> · 27013268592563045799563304526436832319_<38>

10⁴⁸-9 =

999999999999999999999999999999999999999999999991_<48>

= 3529 · 821461 · 838069 · 411605923 · 37967337697_<11> · 26338428255901_<14>

10⁴⁹-9 =

9999999999999999999999999999999999999999999999991_<49>

= 258551 · 1542917 · 25067510989169360187582443013884314573_<38>

10⁵⁰-9 =

99999999999999999999999999999999999999999999999991_<50>

= 7 · 13 · 7668629 · 100308773475776339_<18> · 1428571428571428571428571_<25>

10⁵¹-9 =

999999999999999999999999999999999999999999999999991_<51>

= 481639 · 1001431 · 2204507 · 179488118809_<12> · 5239744793907523162973_<22>

10⁵²-9 =

9999999999999999999999999999999999999999999999999991_<52>

= 83 · 223 · 6947 · 161377320703_<12> · 2778770221987_<13> · 173430153607087049797_<21>

10⁵³-9 =

99999999999999999999999999999999999999999999999999991_<53>

= 71 · 191 · 587 · 12562329568445036102250830275767002453548588013_<47>

10⁵⁴-9 =

999999999999999999999999999999999999999999999999999991_<54>

= 17 · 29 · 1335869 · 813219713 · 1229679979486675331_<19> · 1518410537203064741_<19>

10⁵⁵-9 =

9999999999999999999999999999999999999999999999999999991_<55>

= 2701593300560063647774277_<25> · 3701519395212785560731843555083_<31>

10⁵⁶-9 =

99999999999999999999999999999999999999999999999999999991_<56>

= 7 · 13² · 109 · 199 · 571 · 89779 · 140035456540965619_<18> · 542858693881982519950057_<24>

10⁵⁷-9 =

999999999999999999999999999999999999999999999999999999991_<57>

= 10037 · 8675911 · 2086949124287147_<16> · 5502614973976617719498047337479_<31>

10⁵⁸-9 =

9999999999999999999999999999999999999999999999999999999991_<58>

= 31 · 223283 · 228859 · 5834659 · 10928153 · 335398307039_<12> · 295183134022089846821_<21>

10⁵⁹-9 =

99999999999999999999999999999999999999999999999999999999991_<59>

= 43 · 313921897407961_<15> · 7408152838496002619265064701228387953553517_<43>

10⁶⁰-9 =

999999999999999999999999999999999999999999999999999999999991_<60>

= 24551 · 1514197 · 1859827 · 26899761675796814351_<20> · 537684419034673655130289_<24>

10⁶¹-9 =

9999999999999999999999999999999999999999999999999999999999991_<61>

= 174637 · 878473364729_<12> · 31773852594137837_<17> · 2051470437966151140949832791_<28>

10⁶²-9 =

99999999999999999999999999999999999999999999999999999999999991_<62>

= 7 · 13 · 23 · 1063 · 1453 · 2089 · 17021 · 95633 · 167826727 · 40083104483_<11> · 1352315810743633261969_<22>

10⁶³-9 =

999999999999999999999999999999999999999999999999999999999999991_<63>

= 14499216344898896752959323769763_<32> · 68969244696581083712684424134557_<32>

10⁶⁴-9 =

9999999999999999999999999999999999999999999999999999999999999991_<64>

= 19 · 59 · 6271 · 4814471 · 36799991 · 9566469711577703_<16> · 839285264668608213245600047_<27>

10⁶⁵-9 =

99999999999999999999999999999999999999999999999999999999999999991_<65>

= 197 · 3319 · 12227 · 5653746453683_<13> · 2212433780585198050210908345776014868486357_<43>

10⁶⁶-9 =

999999999999999999999999999999999999999999999999999999999999999991_<66>

= 151 · 439 · 757 · 66883 · 4492009 · 5338459457_<10> · 42250012204817_<14> · 294078654564558761050369_<24>

10⁶⁷-9 =

9999999999999999999999999999999999999999999999999999999999999999991_<67>

= 1321 · 5437 · 19597 · 161831 · 20738805713683_<14> · 21169119569691551954355564217157401643_<38>

10⁶⁸-9 =

99999999999999999999999999999999999999999999999999999999999999999991_<68>

= 7² · 13 · 210019 · 971729379975436624732980913_<27> · 769230769230769230769230769230769_<33>

10⁶⁹-9 =

999999999999999999999999999999999999999999999999999999999999999999991_<69>

= 63397 · 381757 · 626947971773213_<15> · 2170339093195963_<16> · 30365832264283391654982456041_<29>

10⁷⁰-9 =

9999999999999999999999999999999999999999999999999999999999999999999991_<70>

= 17 · 2111 · 3759289 · 26793961 · 1501972065791_<13> · 8389656836773_<13> · 219540251670011409967913819_<27>

10⁷¹-9 =

99999999999999999999999999999999999999999999999999999999999999999999991_<71>

= 78881595557_<11> · 1267722835648523341138988112316740317428617451159045144870763_<61>

10⁷²-9 =

999999999999999999999999999999999999999999999999999999999999999999999991_<72>

= 103 · 1811 · 922639 · 5963471 · 69425387 · 3480881723167_<13> · 3023024732613877_<16> · 1333718356890134051_<19>

10⁷³-9 =

9999999999999999999999999999999999999999999999999999999999999999999999991_<73>

= 31 · 4341008533_<10> · 263305661205877_<15> · 282219793586905741966296113640065805999889291921_<48>

10⁷⁴-9 =

99999999999999999999999999999999999999999999999999999999999999999999999991_<74>

= 7 · 13 · 5779 · 702780737 · 40483675109_<11> · 8688593630053_<13> · 769230769230769230769230769230769231_<36>

10⁷⁵-9 =

999999999999999999999999999999999999999999999999999999999999999999999999991_<75>

= 67 · 6666551 · 49052929 · 831859001 · 54866761472622933343355173670712591013912519245187_<50>

10⁷⁶-9 =

9999999999999999999999999999999999999999999999999999999999999999999999999991_<76>

= 2399 · 34367 · 76417717 · 50954499311257_<14> · 25681678366581487_<17> · 1212908750097169152242159463709_<31>

10⁷⁷-9 =

99999999999999999999999999999999999999999999999999999999999999999999999999991_<77>

= 1111680721_<10> · 286073245559406853963_<21> · 3819624664305357584639_<22> · 82323152627172493323691403_<26>

10⁷⁸-9 =

999999999999999999999999999999999999999999999999999999999999999999999999999991_<78>

= 107 · 827 · 1093 · 187423 · 55165513569618566444754607_<26> · 1000000000000000000000000000000000000003_<40>

10⁷⁹-9 =

9999999999999999999999999999999999999999999999999999999999999999999999999999991_<79>

= 277 · 293 · 613 · 119591 · 1680713307247928623333378139199916888933751555253361302265955410357_<67>

10⁸⁰-9 =

99999999999999999999999999999999999999999999999999999999999999999999999999999991_<80>

= 7 · 13 · 43 · 661 · 4787 · 48239 · 5853526052603_<13> · 569085301052150111_<18> · 50261106447997346213579545740119923_<35>

10⁸¹-9 =

999999999999999999999999999999999999999999999999999999999999999999999999999999991_<81>

= 518729 · 2567713237_<10> · 750780443939323421019040060823110255867754708718152845260302358467_<66>

10⁸²-9 =

9999999999999999999999999999999999999999999999999999999999999999999999999999999991_<82>

= 19 · 29 · 47 · 149 · 44909 · 1046191 · 6387259 · 18348412175865138486980597873_<29> · 470659572629542911224468953859_<30>

10⁸³-9 =

99999999999999999999999999999999999999999999999999999999999999999999999999999999991_<83>

= 227 · 5678824643_<10> · 365174417962746309511512440803_<30> · 212429750392986068412353843621587493937877_<42>

10⁸⁴-9 =

999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<84>

= 23 · 61 · 1597 · 9865301191_<10> · 3369415196267_<13> · 132459430228679414184601_<24> · 101365379590466879644202035797733_<33>

10⁸⁵-9 =

9999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<85>

= 3033644667696760540431621340129571927071_<40> · 3296364965377543000577028480024125464906676521_<46> (Makoto Kamada / SNFS / 0:28:18:37)

10⁸⁶-9 =

99999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<86>

= 7 · 13 · 17 · 63473 · 71861 · 1004537 · 6948583 · 2639420403553807201_<19> · 769230769230769230769230769230769230769231_<42>

10⁸⁷-9 =

999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<87>

= 89 · 30724787 · 2408107211722250575505321_<25> · 151860663916435588509393477939479396484360673953474797_<54>

10⁸⁸-9 =

9999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<88>

= 31 · 71 · 467 · 2293 · 5113 · 13825941769007037889_<20> · 218137357234515008089_<21> · 275142993946312101483059532532768657_<36>

10⁸⁹-9 =

99999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<89>

= 12919 · 16167474982347553799533_<23> · 478772176962247587352907492838496717461481419429473558642556133_<63>

10⁹⁰-9 =

999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<90>

= 1511 · 2621 · 26190869 · 143091007 · 202758977 · 7084864849_<10> · 7665370631_<10> · 2039334898823_<13> · 35230144787557_<14> · 85164473749219_<14>

10⁹¹-9 =

9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<91>

= 1877 · 3129911 · 306588651529_<12> · 5551977068631901091589255759952253908919377717783066915271868552132757_<70>

10⁹²-9 =

99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<92>

= 7 · 13 · 44029 · 44436195239_<11> · 74716684251563_<14> · 774717324390885241_<18> · 231687279868248212917_<21> · 41881272672179231514961_<23>

10⁹³-9 =

999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<93>

= 83 · 757 · 1559760415307_<13> · 2656685632389043_<16> · 3840855484347303588648524752054204879903713883726897884305161_<61>

10⁹⁴-9 =

9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<94>

= 397 · 409 · 967 · 66977 · 230999 · 26846177 · 9450382559_<10> · 198266889049_<12> · 64414344031291_<14> · 1270455041555076682580419086613351_<34>

10⁹⁵-9 =

99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<95>

= 28002119 · 183521111 · 80159620523_<11> · 6812318414609_<13> · 35634648700779351974316488534173284861604554506730720757_<56>

10⁹⁶-9 =

999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<96>

= 8737 · 106669 · 726599 · 4378837 · 69080527 · 1127952811_<10> · 554508243299_<12> · 2663156190955741239949_<22> · 2930857126525877256434827_<25>

10⁹⁷-9 =

9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<97>

= 928307 · 90591614701069919_<17> · 2477758575530044609237440495439_<31> · 47991175334310938360645484759471530531608093_<44>

10⁹⁸-9 =

99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<98>

= 7 · 13 · 464459 · 551342479 · 5952808865209_<13> · 168557936063381_<15> · 10024665283411171_<17> · 845440161194356421_<18> · 504621641480758757819_<21>

10⁹⁹-9 =

999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<99>

= 60089 · 3663323155566124987_<19> · 5639339932759193074579906236439_<31> · 805566723873756259384442313420944670580411883_<45>

10¹⁰⁰-9 =

9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<100>

= 19 · 97 · 283 · 14627 · 3674333699_<10> · 994327748569_<12> · 61236769827829_<14> · 44848033061277421_<17> · 3148809563627188687_<19> · 41488023184722935209_<20>

10¹⁰¹-9 =

(9)₁₀₀1_<101>

= 43 · 1951013 · 1191986622000385035518638564374173230629064145436957800300259046108652989677074017088725488449_<94>

10¹⁰²-9 =

(9)₁₀₁1_<102>

= 17 · 3187 · 144203 · 1353383 · 1991177 · 273871783 · 1876732427_<10> · 6775887552190427787707_<22> · 13637925013200840085919638391816980569079_<41>

10¹⁰³-9 =

(9)₁₀₂1_<103>

= 31 · 1289 · 109811749013_<12> · 2278959357036763169790259713957172311789365105706462004361509988932771734012673210727773_<88>

10¹⁰⁴-9 =

(9)₁₀₃1_<104>

= 7 · 13 · 179 · 5290477824748729_<16> · 1947862590871197811021597_<25> · 2206202131092079878657863_<25> · 270026919286686265519817460570276301_<36>

10¹⁰⁵-9 =

(9)₁₀₄1_<105>

= definitely prime number

10¹⁰⁶-9 =

(9)₁₀₅1_<106>

= 23 · 103 · 28966193 · 4116417953254772568899_<22> · 1056215898465504263474971028839_<31> · 33517479718779992603489942082562596233732843_<44>

10¹⁰⁷-9 =

(9)₁₀₆1_<107>

= 5549373285559157092001363028537319_<34> · 18020052869794279776876644915664872171366200606040049218496910334177029489_<74> (Robert Backstrom / NFSX v1.8)

10¹⁰⁸-9 =

(9)₁₀₇1_<108>

= 67 · 21518801375655714851137_<23> · 46470989835488840363806434126781_<32> · 14925373134328358208955223880597014925373134328358209_<53>

10¹⁰⁹-9 =

(9)₁₀₈1_<109>

= 2252231 · 5021879364791_<13> · 420996486880249365031_<21> · 2100111342215991523137439256807739714502295190739810518118318630550641_<70>

10¹¹⁰-9 =

(9)₁₀₉1_<110>

= 7² · 13 · 29 · 3989 · 2290143001_<10> · 3696549175591577_<16> · 90865194024447148790098749503_<29> · 1764175903156622301759112718314562795753064064813_<49>

10¹¹¹-9 =

(9)₁₁₀1_<111>

= 311 · 19843 · 339520660770777220429931419842789373_<36> · 477272126034520940722669910353174573124220865322990922519656783471879_<69> (Robert Backstrom / NFSX v1.8)

10¹¹²-9 =

(9)₁₁₁1_<112>

= 313 · 3941689 · 19336103 · 4191836705988181479348939975589788043307_<40> · 100000000000000000000000000000000000000000000000000000003_<57>

10¹¹³-9 =

(9)₁₁₂1_<113>

= 50894932942368973_<17> · 1964832139836696397682583169637882971162304383697587052901592370317534325799462577219143296115667_<97>

10¹¹⁴-9 =

(9)₁₁₃1_<114>

= 1439 · 2448952313317_<13> · 113619994412549_<15> · 3593891055967117960201170304091_<31> · 694927032661570535093815149409312022237665045170257123_<54>

10¹¹⁵-9 =

(9)₁₁₄1_<115>

= 431 · 761 · 47521 · 117144283957_<12> · 33326319321401_<14> · 331925529497713410796178426929591703479_<39> · 495111931006187446021416144073444010100227_<42>

10¹¹⁶-9 =

(9)₁₁₅1_<116>

= 7 · 13 · 1033 · 173219 · 171132083 · 3214902282801317877541_<22> · 8071642288696029355717_<22> · 1382934587194025722583321808878440049785645138984926013_<55>

10¹¹⁷-9 =

(9)₁₁₆1_<117>

= 547 · 6987367889_<10> · 109039799172580020244441_<24> · 2399462798624315554649709206087096815106848663696985921484062707559204417437731797_<82>

10¹¹⁸-9 =

(9)₁₁₇1_<118>

= 17 · 19 · 31² · 1249 · 4345511 · 57041926629930666036665011901733531105845315401_<47> · 104058272632674297606659729448491155046826222684703433923_<57>

10¹¹⁹-9 =

(9)₁₁₈1_<119>

= 340352021759490884489_<21> · 113148498830123776919173_<24> · 713773037869037412947173769_<27> · 3638000295246258667246145912935370160176949991387_<49>

10¹²⁰-9 =

(9)₁₁₉1_<120>

= 193² · 719 · 757 · 6755603 · 3171548632838023_<16> · 33362320576752631_<17> · 253721783490136061838019_<24> · 271963805968702864258461551790513043662751795453_<48>

10¹²¹-9 =

(9)₁₂₀1_<121>

= 245669593284788565157_<21> · 40705078175497523585658176359797372933442555843803048351858849905659364452055101437395616728774464363_<101>

10¹²²-9 =

(9)₁₂₁1_<122>

= 7 · 13 · 43² · 59 · 131 · 157 · 167 · 1321 · 4656167 · 279376131961211_<15> · 247777638479293206997639471109_<30> · 6888100737095659876606563395668348970470023329997196543_<55>

10¹²³-9 =

(9)₁₂₂1_<123>

= 71 · 643 · 4523 · 1211599 · 198625207849_<12> · 31841595447419671637_<20> · 631998430051830557700888487084817052140637940611464801026449689276201645624747_<78>

10¹²⁴-9 =

(9)₁₂₃1_<124>

= 163 · 9661 · 3625031 · 603220214617_<12> · 4092282467463097_<16> · 120127553010300307_<18> · 129176073645540570328399_<24> · 45731177968650786903285932397336219226657811_<44>

10¹²⁵-9 =

(9)₁₂₄1_<125>

= 443 · 119003827 · 239025992477781293791695002659636001203014815071_<48> · 7935790893211144760583231282378683537340883150482218186749879931561_<67> (Robert Backstrom / NFSX v1.8)

10¹²⁶-9 =

(9)₁₂₅1_<126>

= 1346919923_<10> · 99582738067633474259_<20> · 259449246196264501631_<21> · 2279800480953691053649_<22> · 4404728007638875844033_<22> · 2861579460492886363697385972683569_<34>

10¹²⁷-9 =

(9)₁₂₆1_<127>

= 1279 · 4481 · 481067 · 975991 · 78121039 · 92152509519425281345483_<23> · 516211832437885012830316711233981950839391966071710578960440252992807200434681_<78>

10¹²⁸-9 =

(9)₁₂₇1_<128>

= 7 · 13 · 23 · 47 · 5676423007_<10> · 36627147032611375348033_<23> · 6871065942231129106260647628859_<31> · 711591830925780972034441044616807799046466946559453497473849_<60>

10¹²⁹-9 =

(9)₁₂₈1_<129>

= 1009 · 77477 · 13641424747_<11> · 80755181161_<11> · 362949074802653_<15> · 376154756266432204449733_<24> · 85053787774507451964167307670996633539178013275162506825756889_<62>

10¹³⁰-9 =

(9)₁₂₉1_<130>

= 613 · 34625917 · 640113583 · 168988305737_<12> · 27879282336387712355695204432176867365129339_<44> · 156222274695895650131829806836015851268070966711543754259_<57>

10¹³¹-9 =

(9)₁₃₀1_<131>

= 89 · 107 · 929 · 161985391 · 625730947759680608316517_<24> · 4173470555635270048745347_<25> · 26720812783453188342897986088256735447149625712703020502970430010797_<68>

10¹³²-9 =

(9)₁₃₁1_<132>

= 3923 · 2546962972527613_<16> · 52234229988717651520074139707847_<32> · 19144534153485086423317835475736549_<35> · 100082710942204725571854029984014199096850397403_<48>

10¹³³-9 =

(9)₁₃₂1_<133>

= 31 · 906121 · 4251769 · 305012901698475689_<18> · 274513836604759106468014028146903884058523985192147532823372067829573046278727191808481524623176990401_<102>

10¹³⁴-9 =

(9)₁₃₃1_<134>

= 7 · 13² · 17 · 83 · 4462531 · 18699520487_<11> · 1300152148179033332753_<22> · 52308679461327694413683_<23> · 143165945597753855112098594619101_<33> · 73734181764135557483526518495064769_<35>

10¹³⁵-9 =

(9)₁₃₄1_<135>

= 306763 · 8464241 · 3421887940693_<13> · 112549409303150618674183268133025591762701233598641472560443313845767714664563979024974638179818758103720133889_<111>

10¹³⁶-9 =

(9)₁₃₅1_<136>

= 19 · 181 · 8269 · 25867 · 10927079 · 1008934873_<10> · 1407477156450817_<16> · 16618414584512959499_<20> · 2161655080961323535207341_<25> · 24388450615853296712957638559087522557098904525303_<50>

10¹³⁷-9 =

(9)₁₃₆1_<137>

= 5165311746933052842465538744631_<31> · 19359915702934259182946897176045257949017142531937648447023760144426052319383724069748135763227304525002561_<107> (Robert Backstrom / GMP-ECM 5.0c)

10¹³⁸-9 =

(9)₁₃₇1_<138>

= 29 · 347 · 911 · 240347 · 797489219 · 6719463889_<10> · 9278852153_<10> · 56916658697_<11> · 724445935328640404936057_<24> · 2703789257357684025009811_<25> · 81873532684973362089980292505983625333_<38>

10¹³⁹-9 =

(9)₁₃₈1_<139>

= 2266591 · 2107924908563_<13> · 12726436311211289_<17> · 164461745696618591896009005886435914358832505722141167532684801621204516924694144596831699353270813308043_<105>

10¹⁴⁰-9 =

(9)₁₃₉1_<140>

= 7 · 13 · 103 · 2838853 · 609124139649827_<15> · 12036938568862646965703_<23> · 36956589665321881667605033_<26> · 13869625520110957004160887656033287101248266296809986130374479889043_<68>

10¹⁴¹-9 =

(9)₁₄₀1_<141>

= 67 · 151 · 7213 · 20641 · 663898341873149124755823694157220929460057755228744437893664294783209177859251794012695675122759673986348215698104475317933187831_<129>

10¹⁴²-9 =

(9)₁₄₁1_<142>

= 4957 · 390869 · 1398779 · 10900801759_<11> · 911624502096187117724092068409_<30> · 56615306657739612877438471735301_<32> · 6558317755506364692997595133084191555668163745537318023_<55>

10¹⁴³-9 =

(9)₁₄₂1_<143>

= 43 · 4987 · 8103911869384742969083926875701596043_<37> · 57543658086818917236653328425662353297036755376057033707756606095232065216600744427923471045358733757_<101> (Tetsuya Kobayashi / NFSX / 62 hours)

10¹⁴⁴-9 =

(9)₁₄₃1_<144>

= 61 · 4919 · 72103 · 349051 · 725437 · 14120947 · 928059349171_<12> · 102778173667843_<15> · 483601316311322078135288401_<27> · 280235709382592215021783942116823254062739685689808590303568199_<63>

10¹⁴⁵-9 =

(9)₁₄₄1_<145>

= 5521133 · 30320243 · 306989367187882350122759_<24> · 362929801125787433471130910799_<30> · 162964976215164129227941885578492094157_<39> · 3290022525160979923646398846777354649597_<40> (Robert Backstrom / GMP-ECM 5.0c, PPSIQS Ver 1.1)

10¹⁴⁶-9 =

(9)₁₄₅1_<146>

= 7 · 13 · 5527003 · 31820483 · 37830550701787_<14> · 3678953376089882824379299271733196192314658634813671_<52> · 44894712269811510134166455882251333879142294243975761506466492937_<65>

10¹⁴⁷-9 =

(9)₁₄₆1_<147>

= 757 · 83719 · 2529649 · 564188459973277_<15> · 1989051072783415478046060199_<28> · 5558398631776347251250612449996615477873378707620847736764219298064172335941129476440400951_<91> (Robert Backstrom / GMP-ECM 5.0c)

10¹⁴⁸-9 =

(9)₁₄₇1_<148>

= 31 · 191 · 277 · 9619 · 445792777 · 2600441047_<10> · 20025961396631_<14> · 227647200762466824679_<21> · 566498878475024033576724763236475512079_<39> · 211719305898683240805292394343293049479508278233_<48>

10¹⁴⁹-9 =

(9)₁₄₈1_<149>

= 5598934639_<10> · 24622603363924497961_<20> · 9406652544628197783013757175083_<31> · 17015077596097981289004980562402392680515791_<44> · 4532017689917763060723550614008624077237163293_<46> (Robert Backstrom / GMP-ECM 5.0c, PPSIQS Ver 1.1)

10¹⁵⁰-9 =

(9)₁₄₉1_<150>

= 17 · 23 · 593 · 3019 · 29593547 · 1228340719_<10> · 203287386737_<12> · 235122042143_<12> · 231740870573890406759791_<24> · 649616931789157865019702753163_<30> · 5461674546661760187240499608772098204986115329557_<49>

10¹⁵¹-9 =

(9)₁₅₀1_<151>

= 4065209 · 1054947908341869962347_<22> · 2331772124791830137648157620024086292452822488119665231195374868127084505089199354203662189352272288259806743791305159760717_<124>

10¹⁵²-9 =

(9)₁₅₁1_<152>

= 7² · 13 · 47843 · 695017 · 657565957 · 18660707022367378937999_<23> · 4583778702733702837221245869057_<31> · 67708151357480212958271175141825303_<35> · 1239694634341423432349916056158844097321901_<43>

10¹⁵³-9 =

(9)₁₅₂1_<153>

= 7351 · 12177173 · 4869339071_<10> · 1717538402791591_<16> · 212160165998317320103944607230187712351218102168603_<51> · 6296029889857224726698251701700348692740511088455095303322626184799_<67> (Makoto Kamada / GGNFS-0.77.1-20050930-pentium4 / 36.60 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Oct 12, 2005)

10¹⁵⁴-9 =

(9)₁₅₃1_<154>

= 19 · 9770545391_<10> · 50670908789_<11> · 492691725102017033_<18> · 21577127639648878849780469624000867189_<38> · 185554311496620532371770351611143673123_<39> · 538925768921415130739706333069119686561_<39>

10¹⁵⁵-9 =

(9)₁₅₄1_<155>

= 199 · 359 · 2820400404223072081249_<22> · 77307199863851638605347_<23> · 6419803921831371590190563637961411585509868203087940243856771169107672745149713980380003017961449703927917_<106>

10¹⁵⁶-9 =

(9)₁₅₅1_<156>

= 659 · 37657 · 82507 · 117361 · 7062049 · 1174699424012203549_<19> · 273991272661126875657939650707603352993489342536453_<51> · 1830880745642327756127708628460154103036454601740305990569843647_<64>

10¹⁵⁷-9 =

(9)₁₅₆1_<157>

= 1182138400863175552253848266595264231758705488091359346888751281045582124679_<76> · 8459246390015065347380115262012913546306699962332583936149204215042988678809171729_<82> (Makoto Kamada / GGNFS-0.54.4-k1 / 182.16596 hours / Sep 27, 2004)

10¹⁵⁸-9 =

(9)₁₅₇1_<158>

= 7 · 13 · 71 · 113 · 11273 · 66457829 · 227601541763_<12> · 13755478715667106004852653_<26> · 855791776632840528315673335967_<30> · 68236562514926748050140226135968174467243038164709414598530184443428477847_<74>

10¹⁵⁹-9 =

(9)₁₅₈1_<159>

= 557 · 787 · 66522203560881529_<17> · 463502940459739711_<18> · 5179103681557614987753607571009_<31> · 14285529639955355530391178145824057096420000669920946451104886135613114248058746965615319_<89> (Makoto Kamada / GMP-ECM 5.0.3 B1=100550, sigma=3289701478)

10¹⁶⁰-9 =

(9)₁₅₉1_<160>

= 2663 · 130960381 · 87144781633537_<14> · 4110612782962333_<16> · 3455312701687993075561_<22> · 1634764941685338629653189_<25> · 2535895350921026674019960278106110759_<37> · 5588135774935638678380176533658718987_<37>

10¹⁶¹-9 =

(9)₁₆₀1_<161>

= 37871278906453241_<17> · 21025652136804630508221938561_<29> · 125585804992968912808788945390634517801861766554822671111449018351172498773938268560062296220409535778931448185975791_<117> (Wataru Sakai / GMP-ECM B1=10000000, sigma=696853086)

10¹⁶²-9 =

(9)₁₆₁1_<162>

= 619 · 1759 · 28477 · 572435189 · 3777480038153_<13> · 82711432890473_<14> · 9232332226415328725291695187328474787743613722899413_<52> · 19531869160556511907230090805735936797585412429882883916315932831_<65>

10¹⁶³-9 =

(9)₁₆₂1_<163>

= 31 · 197 · 12803410721_<11> · 46745703973_<11> · 836469155018551_<15> · 17629888376681459284632404389201355683_<38> · 185526180890784762356394559001150584399176683003863408727544883590129373766517842415517_<87> (Patrick Keller / GMP-ECM B1=1000000, sigma=1966041121 for P38 / May 28, 2005)

10¹⁶⁴-9 =

(9)₁₆₃1_<164>

= 7 · 13 · 43 · 109 · 1151 · 12973 · 432661 · 6702143138293367_<16> · 872912117122274214886393_<24> · 26915104249006886077344416513524151206136145229903_<50> · 230472904760975218695860182014530586110889780505824741637_<57>

10¹⁶⁵-9 =

(9)₁₆₄1_<165>

= 56290473873165148381086844809790940629420103915155210253_<56> · 17764995232643102887053101422297754638281216307353274409711866004077365678936425580088372114246263483737897747_<110> (Tetsuya Kobayashi / GGNFS 0.54.4 / 4PCs*2days/sieve+1PC*0.5days/linear)

10¹⁶⁶-9 =

(9)₁₆₅1_<166>

= 17 · 29 · 6133 · 6286051 · 2384189546677451999_<19> · 23823584851228754531_<20> · 230082359474216559463433395796447020827820649934059530357_<57> · 40259743299929784472838712049504899249693041902211136407533_<59>

10¹⁶⁷-9 =

(9)₁₆₆1_<167>

= 1693 · 251081 · 235249761719633225013599965162333286462954974186008359040388274273923782742394126426981239323174861244338605681202231109681148048384561882123999429538147810827_<159>

10¹⁶⁸-9 =

(9)₁₆₇1_<168>

= 29059 · 136039691 · 152199469 · 13631181661_<11> · 21392516536095359_<17> · 16775491065354149113_<20> · 1502670426032911987830107685541_<31> · 3464655614694615820134361459503031_<34> · 65259858139040767607584620036276601603_<38>

10¹⁶⁹-9 =

(9)₁₆₈1_<169>

= 94211591202708488915524241578569786726705726654902440361_<56> · 106144051621882701124925887117325659671531292461815961898361365027825862303359296356795774245471393139352946460831_<114> (Makoto Kamada / GGNFS-0.77.1 / 168.51 hours on Pentium 4 3.06GHz, Windows XP and Cygwin / Sep 30, 2005)

10¹⁷⁰-9 =

(9)₁₆₉1_<170>

= 7 · 13 · 4073 · 19471 · 29063 · 64849 · 1848031 · 33819758330585864983_<20> · 159924045213327762917315647618256183211961766315464550981_<57> · 735561004054368499805948808599092871902963794530535645906012138636137_<69>

10¹⁷¹-9 =

(9)₁₇₀1_<171>

= 307 · 1341257227_<10> · 119089804935077063337409_<24> · 345902145520852319930047561079359_<33> · 58955144714945402926154900462795557653240056734408286929929832931465190563110621663093933530297499871449_<104> (Patrick Keller / GMP-ECM B1=1000000, sigma=3663717252 for P33 / May 29, 2005)

10¹⁷²-9 =

(9)₁₇₁1_<172>

= 19 · 23 · 997 · 967681309615663_<15> · 5455303132259154458842540374893027723704662896639359296193937202067_<67> · 4347826086956521739130434782608695652173913043478260869565217391304347826086956521739_<85>

10¹⁷³-9 =

(9)₁₇₂1_<173>

= 401 · 2528185841_<10> · 938580727415304869460365420846237262713037883_<45> · 105093292974603519781220816145515742537483095614362298755215504949519619870717052285912811121252640366779911913175797_<117> (Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4 / 255.28 hours on windows xp professional, 1 gig RAM, 3.2 ghz p4, cygwin / Sep 27, 2006)

10¹⁷⁴-9 =

(9)₁₇₃1_<174>

= 47 · 67 · 103 · 257 · 757 · 113123 · 824281 · 4632613 · 625148401 · 95226283921568354649911469910374171419599375062477580588497655609249_<68> · 616267018056359185441747698615843643683296258084651274651119987076887_<69>

10¹⁷⁵-9 =

(9)₁₇₄1_<175>

= 83 · 89 · 277590538396397099817467_<24> · 896295447371381022541530417241001_<33> · 61949583081432845501932022855183580890650237564733399_<53> · 87828944454424628608061572314719937855686216572417491650902721_<62> (Patrick Keller / GMP-ECM B1=50000, sigma=3752722861 for P33 / May 29, 2005) (Makoto Kamada / GGNFS-0.77.1-20050930-pentium4 gnfs / 54.99 hours on Pentium 4 3.06GHz, Windows XP and Cygwin for P53 x P62 / Oct 15, 2005)

10¹⁷⁶-9 =

(9)₁₇₅1_<176>

= 7 · 13 · 12097 · 302303497 · 15968813857743312100267_<23> · 7395228897021612341523232889578455213960269146595764004311471_<61> · 2544564574556572962069409237534454425346031538731320831426673073619023437129577_<79>

10¹⁷⁷-9 =

(9)₁₇₆1_<177>

= 1321 · 2376752857145462309881481_<25> · 166539912927088863044604457888822597127041055210868917788027_<60> · 1912470850607748174543437500075957519331332156283120157980757697449058309385972258440240133_<91> (matsui / GGNFS-0.77.1-20060513-prescott snfs / May 6, 2008)

10¹⁷⁸-9 =

(9)₁₇₇1_<178>

= 31 · 269 · 1663 · 3253 · 8803 · 711780703 · 751414214574205487_<18> · 50085008861179389314983865307479_<32> · 6270490382978711525333242984143695967656023_<43> · 149914670527656837997920618197642940784707574042657246252776461_<63>

10¹⁷⁹-9 =

(9)₁₇₈1_<179>

= 569 · 8951 · 944482695820147111_<18> · 546906270091264303592773419636796433846880957980999_<51> · 38010997664106318499368894010475771853596823493322466917536870017901952887416421331572081502939677862201_<104> (Wataru Sakai / GGNFS-0.77.1-20060722-nocona snfs / 378.09 hours / May 18, 2008)

10¹⁸⁰-9 =

(9)₁₇₉1_<180>

= 59 · 166303 · 1981462151_<10> · 403895669461_<12> · 5427392805973_<13> · 6775211799337_<13> · 8974986752701_<13> · 78160868906623597_<17> · 2976176599680018387033042268965119689_<37> · 1658810987591830795547164323164711490089752199766030492869341_<61>

10¹⁸¹-9 =

(9)₁₈₀1_<181>

= 613 · 4721990197_<10> · 118046288030005689138006772776064145473173086074955176614021148886231992477409_<78> · 29265915150079883819125682044728327718073357005292178916251770323960139756081440411297901759_<92> (Wataru Sakai / GGNFS-0.77.1-20060722-nocona snfs / May 12, 2008)

10¹⁸²-9 =

(9)₁₈₁1_<182>

= 7 · 13 · 17 · 1223 · 611557 · 622802562607_<12> · 541191531367411_<15> · 53040230332956067_<17> · 3920505864836767714747_<22> · 4945904653788016124568903613721692237248629_<43> · 249316864069717043485091626653147919697908905053883660187580519_<63>

10¹⁸³-9 =

(9)₁₈₂1_<183>

= 49314675241585004778040302476198275634070752715382741171333_<59> · 27179661213248372553517898319953454110361829996769269348594493_<62> · 746070354608195431221196594309881696831382401936346066887929639_<63> (Wataru Sakai / GGNFS-0.77.1-20060513-pentium4 / 693.77 hours on Pentium 4 3GHz, Windows XP and Cygwin / Oct 9, 2006)

10¹⁸⁴-9 =

(9)₁₈₃1_<184>

= 107 · 841801 · 3557017 · 211480670972866622535223234753759_<33> · 76772438105837719738754548269930764941_<38> · 3422354146951056095066841448159662200272103243_<46> · 561719994649737610867659787910638005737532777151667317_<54>

10¹⁸⁵-9 =

(9)₁₈₄1_<185>

= 43 · 68239 · 2538313576960440629507448895847540063266132079_<46> · 29377049543046125556029128856057470051512089568061282636870001_<62> · 457030771896922620319211488891391699946102749496004569879285614325665077_<72> (Wataru Sakai / GGNFS-0.77.1-20060722-nocona snfs / May 17, 2008)

10¹⁸⁶-9 =

(9)₁₈₅1_<186>

= 233 · 419 · 10744219 · 291653535584641_<15> · 52792348845059647_<17> · 5459780369426989258506416918868167807_<37> · 25943645194741155506563259922410371213134407504184593_<53> · 437130192678284489192380500009849205232710912361559391_<54>

10¹⁸⁷-9 =

(9)₁₈₆1_<187>

= 381467 · 252250919 · 573590921 · 2468421133_<10> · 28220407597_<11> · 7739992696481_<13> · 623469605000773495978145688789573442397_<39> · 538976246538898546343223750880120388579184821372415393352789944003119846089632154549645112111_<93> (Patrick Keller / GMP-ECM B1=1000000, sigma=4006704447 for P39 / May 28, 2005)

10¹⁸⁸-9 =

(9)₁₈₇1_<188>

= 7 · 13 · 151548409 · 487606042003_<12> · 1465865413328343894556166417276893_<34> · 3462670511054145557735868404409558124203646135593037_<52> · 2929765641752731346391547040207212875979805414190271980235225659141284583284855143_<82>

10¹⁸⁹-9 =

(9)₁₈₈1_<189>

= 680546965633716247679_<21> · 210016417538123401200815971279_<30> · 8147900155250040965434833800626154533552907527597_<49> · 858702947397860145236409007951942850049599814990863975327405594646045661188912043740978083_<90> (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=72668037 for P30 / Mar 12, 2005) (Wataru Sakai / GGNFS-0.77.1-20060722-nocona snfs / 1147.35 hours / Jun 14, 2008)

10¹⁹⁰-9 =

(9)₁₈₉1_<190>

= 19 · 509 · 2591 · 11279 · 37728203 · 718809580057632062928074197_<27> · 15232652842182146291582535453277_<32> · 9132939882670122379669592086842575587_<37> · 9378307897647822189773362682835304573974710330908432747151623394481317471521_<76>

10¹⁹¹-9 =

(9)₁₉₀1_<191>

= 25890181282711_<14> · 19215578593700683_<17> · 1107810740439824418721011542356263180679141608975450841_<55> · 181445361934394941929618652274442590996558678743985524419560737457231701804057845993063138605270872862639227_<108> (Tyler Cadigan / GGNFS, Msieve / 363.74 hours on Q6660 2.4 Ghz C2Q, 4 GB ram, windows vista / Aug 16, 2008)

10¹⁹²-9 =

(9)₁₉₁1_<192>

= 1861 · 38604899 · 67135031 · 3339133451_<10> · 75802272361_<11> · 1274839317373_<13> · 371370564511057_<15> · 3210299262702817_<16> · 1002960752029899359_<19> · 537345513164965072541644277270284793121977431488447071466953250940354648038688876947877485223_<93>

10¹⁹³-9 =

(9)₁₉₂1_<193>

= 31 · 71 · 397 · 31039 · 7333825763352817867_<19> · 114623516402068263048374107148074526153902078826891749923032115067_<66> · 438608874285502256844751510885066987832289149361752461518587566928513572528389208388687896598390093_<99> (Serge Batalov / Msieve-1.37; 64-bit sievers (Childers) snfs / 389.00 hours on Opteron-2.8GHz; Linux x86_64 / Sep 2, 2008)

10¹⁹⁴-9 =

(9)₁₉₃1_<194>

= 7² · 13 · 23² · 29 · 2281 · 56978387 · 24702593883547_<14> · 572041744923931_<15> · 441830682536309401_<18> · 4594143404942642691414177378188955640856825123859977753777753_<61> · 2744989966329896961448749127879070039002143600805487375898998297932229_<70>

10¹⁹⁵-9 =

(9)₁₉₄1_<195>

= 1289 · 283435121 · 190918276279_<12> · 1608873192799_<13> · 387312818354664563_<18> · 1079504646683992390751_<22> · 296827436308088224012637591_<27> · 71801525491886233491994351008708055401003967702537009426787904436648333892829264331597536123173_<95> (Wataru Sakai / GMP-ECM B1=2500000, sigma=1727198373)

10¹⁹⁶-9 =

(9)₁₉₅1_<196>

= 97 · 227 · 105199 · 135288787 · 5127030864793921_<16> · 378919599206831707_<18> · 4907420475243384479_<19> · 3616709145802705022310102159175743619073157102612973_<52> · 925441856044986409718150197395729413167764668894414882028382058169268699297_<75>

10¹⁹⁷-9 =

(9)₁₉₆1_<197>

= definitely prime number

10¹⁹⁸-9 =

(9)₁₉₇1_<198>

= 17² · 367 · 1517627 · 2113775865581_<13> · 10526423190323_<14> · 48012016357931_<14> · 3591932541314891_<16> · 80691749292003731118629647616252267832462124947404914376760456191_<65> · 20064301263767150482328850050963655988361397950026433927658752114587_<68>

10¹⁹⁹-9 =

(9)₁₉₈1_<199>

= definitely prime number

10²⁰⁰-9 =

(9)₁₉₉1_<200>

= 7 · 13 · 157 · 769 · 2593 · 596275259857_<12> · 4888946572366141_<16> · 27089835581037121_<17> · 220030935994058489226133_<24> · 4242036622639156527888055237578804493024993216233097_<52> · 47621545764299677617779790257997285086538394033923200643767527821353377_<71>

10²⁰¹-9 =

(9)₂₀₀1_<201>

= 757 · 853 · 6197 · [249904221895344556666720330266262399972283422634653609633562048234565156733954012335697729739873193504762259944825241236662567631826351956219023464231366284731238619035297496158095570410256243_<192>] SUBMIT/RESERVE

10²⁰²-9 =

(9)₂₀₁1_<202>

= 811 · 1660609 · 104506081 · 458290213 · 3490351201_<10> · 70036821437399159898409_<23> · 6342114199338576625556578199506049340359539_<43> · 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<102>

10²⁰³-9 =

(9)₂₀₂1_<203>

= 3163 · 77192849 · 409565850497209526929202144213201576993545048475612351180461631963877751744367827859151870865509939833701984037970965464400867414916162670674414788860147464394087322574642695114389620636113093_<192>

10²⁰⁴-9 =

(9)₂₀₃1_<204>

= 61 · 3607 · 167341 · 48523022783_<11> · 47195391205577821_<17> · 471886464223296562633_<21> · 239334429244078719805120829701_<30> · 17876284551980902328592233871781223_<35> · 45302831818536160855154483046504027523_<38> · 129666837065959683061728546755551575657543763_<45>

10²⁰⁵-9 =

(9)₂₀₄1_<205>

= 163 · 2924864092045432721_<19> · 20975228701525862425535472291072344362711515213362922746768134284514554516726189712322531545831813129439885126617441957274846020621653001166262173165071284981082700752728250496952368717_<185>

10²⁰⁶-9 =

(9)₂₀₅1_<206>

= 7 · 13 · 43 · 692401 · 10239241 · 7613030996929_<13> · 184181549987808479_<18> · 262672352803304881_<18> · 3901043612090232438007885999_<28> · 223958556307693271700171647119569787_<36> · 22726445496584026420510640998186677007_<38> · 492908871046517977034206424358751376938907_<42>

10²⁰⁷-9 =

(9)₂₀₆1_<207>

= 67 · 947 · 2027 · 2327680237_<10> · 20375251305794849299477_<23> · 163943867620141826091230023867229564925651296052804246141573875967454174324781673309552975541072702437827471952045422134007055607821929855776052305773848115539095966333_<168> (Wojciech Florek)

10²⁰⁸-9 =

(9)₂₀₇1_<208>

= 19 · 31 · 103 · 547 · 15887 · 458401 · 44938046971_<11> · 715368493807944331_<18> · 93738101034940412233498319251111560705584994159001501753738976257147_<68> · 13731328215929209456688791947124485531775729994561500117025176063615607948582945925408692322131_<95>

10²⁰⁹-9 =

(9)₂₀₈1_<209>

= 6199 · 1098311 · 8749770522229013046664029725719_<31> · 11779221979625493750760591465889_<32> · 142508169351112330751625366154027236299106678544471738141095195169427914114649935286029433461028125436734063605464802185882769616072838209_<138> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=3136596305 for P31 / Oct 22, 2008) (Serge Batalov / GMP-ECM 6.2.1 B1=6000000, sigma=2769882817 for P32 / Oct 24, 2008)

10²¹⁰-9 =

(9)₂₀₉1_<210>

= 1564699 · 140589838991740832020941105146256038160377_<42> · 4545851677658139202437532906827438688087706303142425442239_<58> · 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<106>

10²¹¹-9 =

(9)₂₁₀1_<211>

= 6277 · 23515656707_<11> · [67747107863082587477105411424345224422609764780486975662919251562496210922051419090545191361372504591023718788106923394075955127723744255135025064125333852948168854328720952394254817713278429554969_<197>] SUBMIT/RESERVE

10²¹²-9 =

(9)₂₁₁1_<212>

= 7 · 13² · 487 · 18217 · 157752018614917_<15> · 3004695654536743_<16> · 369038951254272125569_<21> · 56380971921971609399701_<23> · 2575673952122780047666529547878651245753_<40> · 4676160827424241349622633359482724543174987_<43> · 80213770421949436989344479680642134972992714547_<47>

10²¹³-9 =

(9)₂₁₂1_<213>

= 2671 · 832477 · 3405841 · 5328359 · 5607750409_<10> · 24831611120690827_<17> · 489257181515888972676839_<24> · [363751872966986859147527985949582795575218748140587332897669362335754803553870812649166417105950082474670291181171653500665333882601932621071_<141>] SUBMIT/RESERVE

10²¹⁴-9 =

(9)₂₁₃1_<214>

= 17 · 7968678694697845825873096579_<28> · 105268359025757399432466604657457309_<36> · 7012403690728403318908561793540433456872731_<43> · 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<108>

10²¹⁵-9 =

(9)₂₁₄1_<215>

= 1879 · 13997 · 6212923 · 21037729 · 3278149841_<10> · 470412938212506827_<18> · 2770137190923325144409_<22> · [6809795855132386932268768058797247249564627617796635589461142175629957513836174861256364231921100789981714448952536784503183037249551735551532917_<145>] SUBMIT/RESERVE

10²¹⁶-9 =

(9)₂₁₅1_<216>

= 23 · 83 · 151 · 137401213 · 1025890507_<10> · 3207480541_<10> · 15552298759_<11> · 92762470571_<11> · 12813482135218256325700577527597759817402594010431832837282926939321359468931_<77> · 415075835864390811706575139824651136151900801150981162208964016615508906209576156217481_<87>

10²¹⁷-9 =

(9)₂₁₆1_<217>

= 277 · 1597 · 209837 · 26201554231_<11> · 28091934741523_<14> · 6880830160720697642858093533_<28> · [21270794084087604016650779660527476526528382844493108281556100123577628870274924299543836954468514838537561953170556959847579919956473912494371150224629843_<155>] SUBMIT/RESERVE

10²¹⁸-9 =

(9)₂₁₇1_<218>

= 7 · 13 · 636095471381_<12> · 2307896264990110210061_<22> · 45166631624534007464908544083639_<32> · 67083924033653745174874728162417169991_<38> · 11601131675497996544648457184208378700687769_<44> · 21295287196598135831894469055861840064477475149485170209040812034482381_<71>

10²¹⁹-9 =

(9)₂₁₈1_<219>

= 89 · 172027 · 466290889 · 168664820083_<12> · 830485282648983792403171451838983520539730321241583428290887940491689756536419557446889162299575422018051080061665651474429942668263724269345073729025589308872735886582951892230252636083419031_<192>

10²²⁰-9 =

(9)₂₁₉1_<220>

= 47 · 229 · 263 · 1871 · 4443097 · 839917615309_<12> · 6714107380277349896183_<22> · 144943428069060593210324709644363984350751705174143343752073126619771304837_<75> · 519909589640850094073814039254973724161101539472144569857404667889667108322520021230643073367523_<96>

10²²¹-9 =

(9)₂₂₀1_<221>

= 2244243292414987_<16> · [44558448871375226540373951962642129976734728458907558245705265151925208084969966648536859456690150287256166432931650825893163912246227886931197577078948493557862621208139168368158344454752222607848944122693_<206>] SUBMIT/RESERVE

10²²²-9 =

(9)₂₂₁1_<222>

= 29 · 22483 · 602657779 · 28696630206070791791_<20> · 3811103616383696520035255018963138889550371472027_<49> · 11670648336895389594887395705639732998619139278066767263683_<59> · 1993886046252076663845187938068087319893076521678350863668723255877085366512385237_<82>

10²²³-9 =

(9)₂₂₂1_<223>

= 31 · 17053 · 590027 · 2761831 · 77429204016449_<14> · 2545729004258801_<16> · 3265703061602243_<16> · 18289955184503630002559_<23> · 985966656924107728080769413681833286430842191990540078718690029876670763594626381037161101860259104582075413156420630749338157475895612277_<138>

10²²⁴-9 =

(9)₂₂₃1_<224>

= 7 · 13 · 647 · 7759985029_<10> · 605811026672353_<15> · 5310320545785083_<16> · 772109420162542201_<18> · 369568082011564246318490814674287271310659910824755808150690685151322618547973_<78> · 238430728361600896205676276007090671265907651946134091671888880076349641192040039401_<84>

10²²⁵-9 =

(9)₂₂₄1_<225>

= 293 · 876607399 · 11832253617719_<14> · 10292669498837631231566729_<26> · 31969198635632808973170397736416392401304318424374034125277901682126490850491223618006814822205508423960199101378815162796713417370724734035311510268842133646517081155844442163_<176> (Wojciech Florek)

10²²⁶-9 =

(9)₂₂₅1_<226>

= 19 · 373 · 3347 · 96377 · 299261 · 1539149 · 3429445432781_<13> · 884609083918355948907037_<24> · 3775584003451138071930047_<25> · 310664096228408853908793998882075472743889042019497036205801_<60> · 2668868467392422552005114420965245432852788746018460429855287102487871476139285197_<82>

10²²⁷-9 =

(9)₂₂₆1_<227>

= 43 · 925733 · 1415114047290409_<16> · 17786640496933624840678534245662351596213_<41> · 99806868526225823221956954125006142277499588289181858360905874746351256925536418640176658497489042909882373987832308907586475427226873597370517730462039750438400917_<164> (Serge Batalov / GMP-ECM 6.2.1 B1=6000000, sigma=1970878906 for P41 / Oct 24, 2008)

10²²⁸-9 =

(9)₂₂₇1_<228>

= 71 · 757 · 336529 · 859221566249037791_<18> · 180738878352484081081720836613058416283_<39> · 356013547665340428768575295631333591720156299923_<48> · 3134188330252503582947429542915803128154373300081462177_<55> · 319061873323813867242565512269308619907572321217170192386339_<60>

10²²⁹-9 =

(9)₂₂₈1_<229>

= 179793157332153468293_<21> · 63932480430633876497881_<23> · 4392102515268294714566780119_<28> · [198076438309253561849795232365833594541374500553926506867694836215975889824525581777816943842817121367207804026565527079559475898183958538727078029585103238133_<159>] (Wojciech Florek) SUBMIT/RESERVE

10²³⁰-9 =

(9)₂₂₉1_<230>

= 7 · 13 · 17 · 149 · 643 · 16427 · 13188252227537_<14> · 2086902480830030036633784894772704335879_<40> · 279676051195225896934948823207443193519179150078386523465480944649163_<69> · 5335922447296667088377467035279126307518701118577120313195503748865958864729990739390888237574373_<97>

10²³¹-9 =

(9)₂₃₀1_<231>

= 919 · 227947037 · 237397921 · [20108219899963991178385032945756915630579944870602241047661356606913124250453411138118595381885232035113915967840276407154028434896573735056433545137633205791188008513050065381806144502965904984700952873258485557_<212>] SUBMIT/RESERVE

10²³²-9 =

(9)₂₃₁1_<232>

= 563 · 613 · 1321 · 5581 · 8774317 · 31409912863227233240324396659219_<32> · 285562837995982349446361585842661944753_<39> · 3258810312307206854209463561699139379393_<40> · 1088633633614509477084403918558191926908607051_<46> · 14076468703627736973261941485232894367607527799709257855417_<59>

10²³³-9 =

(9)₂₃₂1_<233>

= 103319 · 947719 · 457300801340671_<15> · 2233254696604262943829677849962210300232112254616557878266228978724103628169450994114477700636473130142890428587112611459892103223946927241932242143146839307787064222117699572245321291368507189184069078217961_<208>

10²³⁴-9 =

(9)₂₃₃1_<234>

= 136817541953_<12> · 12510399765769_<14> · 298112920074737523999596067065580070878142999_<45> · 1959775076019992331799342558898554074566826611021_<49> · 9127148480682127666098069205437229076855970260488284811_<55> · 109563244436806168818039119184210587861133156574721974138239127_<63>

10²³⁵-9 =

(9)₂₃₄1_<235>

= 1115363 · 5476400107084512893933_<22> · [1637150466542620463521641864646810936730159962508376375974999081043970766985055221845360455776234416343940654734610211656283611664347262318575325514391313947370826427676824204286688910344967227394380562903729_<208>] SUBMIT/RESERVE

10²³⁶-9 =

(9)₂₃₅1_<236>

= 7³ · 13 · 8461 · 89293 · 64141747 · 8460920724818143_<16> · 37627526900440243622059_<23> · 6147335446609049443147009_<25> · 232249550665794760809639124801272942935386171_<45> · 10073705259065735294499942560980394788643671299013_<50> · 101071403953684443983895115462630189568665615571767163352181_<60>

10²³⁷-9 =

(9)₂₃₆1_<237>

= 107 · 7561 · 57235347277_<11> · 672331504409_<12> · 4675438610011439_<16> · 124195659693998352897446580594911_<33> · 55317229683125179811055047825566314237250570327459404598417890762364651604901335574716743377299431025304065892097911840931358872788401832572008373559390024256489_<161> (Serge Batalov / GMP-ECM 6.2.1 B1=2000000, sigma=1344070187 for P33 / Oct 24, 2008)

10²³⁸-9 =

(9)₂₃₇1_<238>

= 23 · 31 · 59 · 7043 · 15599333329_<11> · 248188250596361555852063_<24> · 300887275512254328094763_<24> · 3025049262693665664747541346878285724445834135320710094168083527978858463925645677_<82> · 9578053105495890596842936195802739350968036547539923449027221708789738588593789339062558543_<91>

10²³⁹-9 =

(9)₂₃₈1_<239>

= 180069959 · 2481625391801_<13> · 1651544456350112110279_<22> · 46895372182244200870111_<23> · 210157492598681488168780037_<27> · 305661456410850615841673329_<27> · 44979714896150706074345874783931808634107426732167806836547470840633411076926691669415949510832232314574628364864793784477_<122>

10²⁴⁰-9 =

(9)₂₃₉1_<240>

= 67 · 1314371 · 256328913578799661_<18> · 39680844683922630781_<20> · 2968140363021126452220649514855793697359082715974543882369932510137667044124281356330082986856987_<97> · 376135469222398560079179371798099236539177092583429173601100734182099447630758605255815436349312789_<99>

10²⁴¹-9 =

(9)₂₄₀1_<241>

= 283 · 9479 · 804191 · [4635449272261294629377779703213468681518891331407530241149702094172616188345007537004333603269446014961055482551795100190895076971961332333666078422686195261794517524762612532237148044926410799595122348018765894789486716644728093_<229>] SUBMIT/RESERVE

10²⁴²-9 =

(9)₂₄₁1_<242>

= 7 · 13 · 103 · 198529 · 11787899 · 328697413420232835842838763773057913404777878180108321518328556605098171968410977813814875910384258521686461_<108> · 13869625520110957004160887656033287101248266296809986130374479889042995839112343966712898751733703190013869625520110957_<119>

10²⁴³-9 =

(9)₂₄₂1_<243>

= 191 · 2090131151_<10> · [2504915584716261518622320429705615928866391516777126140829517966298849095597766181911340323777630907153032718173656534716342455075023976067357210592911756418684539249136127860441745194251162339410637980622953565801313394779101714151_<232>] SUBMIT/RESERVE

10²⁴⁴-9 =

(9)₂₄₃1_<244>

= 19 · 749013296450169739_<18> · 71866339938008210623739_<23> · 397118863301683969907658455831_<30> · 3503918176246150929723840345375125855783997495258623504869751070595633_<70> · 7026788335642034629781710534573805278538763744803035551030475665043109854334080750234026493336617617683_<103>

10²⁴⁵-9 =

(9)₂₄₄1_<245>

= 40974399286914864833693_<23> · [2440548287231019985162221443428821790183866285693531341906864187034380567295222842170167086501911316909243011029537971246193980851646990702118681680729943453048494182626379925294396150276508253918039462146967545217138765987_<223>] SUBMIT/RESERVE

10²⁴⁶-9 =

(9)₂₄₅1_<246>

= 17 · 15739 · 89069 · 376667884978938293477936774780616434222279_<42> · 111400918951427393267751760550029690509932963494486357752363513131610869_<72> · 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<124>

10²⁴⁷-9 =

(9)₂₄₆1_<247>

= 44451761 · 1374902019013_<13> · 19945229229203232397679_<23> · [8203520121102992924527655815864204700509131223975388014600092794790532104667823841760331340262472670579150360549037086554402448433462480941173142178521283053388972682872569934752050230712834059531200108853_<205>] SUBMIT/RESERVE

10²⁴⁸-9 =

(9)₂₄₇1_<248>

= 7 · 13 · 43 · 8179 · 2569393 · 520650671 · 8152274412311_<13> · 901399309795043_<15> · 23257479000261691_<17> · 30441559635772969237_<20> · 278215836815846300810499872638251601851541_<42> · 627753020605636868785440299879864836902467148030812554348147_<60> · 2570495028748214654581797079357671705550480475040454114008023_<61>

10²⁴⁹-9 =

(9)₂₄₈1_<249>

= 121935824955601357_<18> · 8201035260671872575340203837666414392454236363272545489650445706963071219917001531557025514282235019531859106003449269923308436252722353254860723173705916722269242722881173416701360325804282168261444180657372768351173241005630948563_<232>

10²⁵⁰-9 =

(9)₂₄₉1_<250>

= 29 · 134227 · 224027 · 23220877 · 40227639590406309217166835252731879997433918357_<47> · 11096220704771508418838283142629113970847065959139563096883643429606751723_<74> · 1106326971538334438867518468448025343661281698202433005785938239861995100495925767257721870777151883601441849433_<112>