Factorizations of 399...991

Table of contents

1. About 399...991
   • First ten terms
   • General term
   • Algebraic factorizations
   • Related tables
2. Prime numbers of the form 399...991
   • Last update
   • Searched up to
   • Difficulty of search
   • Results
3. Factorizations of 399...991
   • Last update
   • Completed up to
   • Range
   • Terms which have not been factored yet
   • Results
4. References

1. About 399...991

First ten terms

31, 391, 3991, 39991, 399991, 3999991, 39999991, 399999991, 3999999991, 39999999991

General term

4·10ⁿ-9

Algebraic factorizations

• 4·10^2k-9 = (2·10^k-3)(2·10^k+3)

Related tables

• Factorizations of 199...997
• Factorizations of 200...003

2. Prime numbers of the form 399...991

Last update

Aug 9, 2009

Searched up to

n≤30000

Difficulty of search

9.38%

Results

1. 4·10¹-9 = 31 is prime.
2. 4·10¹⁷-9 = 3(9)₁₆1_<18> is prime.
3. 4·10¹⁹-9 = 3(9)₁₈1_<20> is prime.
4. 4·10²⁹-9 = 3(9)₂₈1_<30> is prime.
5. 4·10⁴³-9 = 3(9)₄₂1_<44> is prime.
6. 4·10¹¹⁹-9 = 3(9)₁₁₈1_<120> is prime. (searched by Makoto Kamada / Nov 24, 2004) (certified by Makoto Kamada / PFGW / Jan 1, 2005)
7. 4·10¹⁷³-9 = 3(9)₁₇₂1_<174> is prime. (searched by Makoto Kamada / Nov 24, 2004) (certified by Makoto Kamada / PFGW / Jan 1, 2005)
8. 4·10⁹⁴⁹-9 = 3(9)₉₄₈1_<950> is prime. (searched by Makoto Kamada / PFGW / Dec 23, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / May 29, 2006)
9. 4·10¹⁶⁰⁹-9 = 3(9)₁₆₀₈1_<1610> is prime. (searched by Makoto Kamada / PFGW / Dec 23, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Aug 11, 2006)
10. 4·10⁵⁵⁷⁹-9 = 3(9)₅₅₇₈1_<5580> is PRP. (Makoto Kamada / PFGW / Dec 23, 2004)
11. 4·10¹⁹⁶⁷⁹-9 = 3(9)₁₉₆₇₈1_<19680> is PRP. (Sinkiti Sibata / PFGW / Nov 19, 2007)

3. Factorizations of 399...991

Last update

Nov 6, 2009

Completed up to

• n≤100 / Nov 24, 2004
• n≤150 / Nov 19, 2007

Range

n≤250

Terms which have not been factored yet

n=189, 191, 193, 203, 205, 207, 209, 211, 213, 221, 225, 235, 237, 239, 243, 245, 247, 249 (18/250)

Results

4·10¹-9 =

31

= definitely prime number

4·10²-9 =

391

= 17 · 23

4·10³-9 =

3991

= 13 · 307

4·10⁴-9 =

39991

= 7 · 29 · 197

4·10⁵-9 =

399991

= 53 · 7547

4·10⁶-9 =

3999991

= 1997 · 2003

4·10⁷-9 =

39999991

= 79 · 506329

4·10⁸-9 =

399999991

= 83 · 241 · 19997

4·10⁹-9 =

3999999991_<10>

= 13² · 23668639

4·10¹⁰-9 =

39999999991_<11>

= 7 · 28571 · 200003

4·10¹¹-9 =

399999999991_<12>

= 175961 · 2273231

4·10¹²-9 =

3999999999991_<13>

= 19 · 105263 · 2000003

4·10¹³-9 =

39999999999991_<14>

= 67 · 2551 · 234031723

4·10¹⁴-9 =

399999999999991_<15>

= 59 · 257 · 1319 · 20000003

4·10¹⁵-9 =

3999999999999991_<16>

= 13 · 89 · 1361 · 4243 · 598681

4·10¹⁶-9 =

39999999999999991_<17>

= 7 · 31 · 223 · 743 · 4133 · 269179

4·10¹⁷-9 =

399999999999999991_<18>

= definitely prime number

4·10¹⁸-9 =

3999999999999999991_<19>

= 17 · 53 · 211 · 233 · 2393 · 37735849

4·10¹⁹-9 =

39999999999999999991_<20>

= definitely prime number

4·10²⁰-9 =

399999999999999999991_<21>

= 43 · 79 · 337 · 1123 · 1229 · 253164557

4·10²¹-9 =

3999999999999999999991_<22>

= 13 · 347 · 2437 · 363857754541013_<15>

4·10²²-9 =

39999999999999999999991_<23>

= 7³ · 47 · 1171 · 1733 · 336463 · 3633919

4·10²³-9 =

399999999999999999999991_<24>

= 5717 · 69966765786251530523_<20>

4·10²⁴-9 =

3999999999999999999999991_<25>

= 23 · 97 · 26161 · 34267 · 2000000000003_<13>

4·10²⁵-9 =

39999999999999999999999991_<26>

= 369877 · 759263431 · 142432855693_<12>

4·10²⁶-9 =

399999999999999999999999991_<27>

= 617 · 64879 · 499621 · 19999999999997_<14>

4·10²⁷-9 =

3999999999999999999999999991_<28>

= 13 · 100197068443_<12> · 3070871358550249_<16>

4·10²⁸-9 =

39999999999999999999999999991_<29>

= 7 · 8431 · 3388854059_<10> · 199999999999997_<15>

4·10²⁹-9 =

399999999999999999999999999991_<30>

= definitely prime number

4·10³⁰-9 =

3999999999999999999999999999991_<31>

= 19 · 71 · 28169014084507_<14> · 105263157894737_<15>

4·10³¹-9 =

39999999999999999999999999999991_<32>

= 31 · 53 · 59747 · 407480025252759604989271_<24>

4·10³²-9 =

399999999999999999999999999999991_<33>

= 29 · 293 · 3067 · 767450903 · 20000000000000003_<17>

4·10³³-9 =

3999999999999999999999999999999991_<34>

= 13 · 79 · 3894839337877312560856864654333_<31>

4·10³⁴-9 =

39999999999999999999999999999999991_<35>

= 7 · 17 · 1680672268907563_<16> · 200000000000000003_<18>

4·10³⁵-9 =

399999999999999999999999999999999991_<36>

= 445668752387_<12> · 897527587154364423044093_<24>

4·10³⁶-9 =

3999999999999999999999999999999999991_<37>

= 107 · 1279 · 112957699 · 17705743103_<11> · 14614221098551_<14>

4·10³⁷-9 =

39999999999999999999999999999999999991_<38>

= 317 · 126182965299684542586750788643533123_<36>

4·10³⁸-9 =

399999999999999999999999999999999999991_<39>

= 241 · 21977 · 910042316967739_<15> · 82987551867219917_<17>

4·10³⁹-9 =

3999999999999999999999999999999999999991_<40>

= 13 · 1493 · 2166811449521_<13> · 95112086615723827961719_<23>

4·10⁴⁰-9 =

39999999999999999999999999999999999999991_<41>

= 7 · 173 · 331 · 431 · 2339 · 4877 · 81971 · 861381217 · 287456395901_<12>

4·10⁴¹-9 =

399999999999999999999999999999999999999991_<42>

= 43 · 1184658156896449_<16> · 7852328983886332499055013_<25>

4·10⁴²-9 =

3999999999999999999999999999999999999999991_<43>

= 11850947 · 50267717 · 39786967050841_<14> · 168762884518849_<15>

4·10⁴³-9 =

39999999999999999999999999999999999999999991_<44>

= definitely prime number

4·10⁴⁴-9 =

399999999999999999999999999999999999999999991_<45>

= 53 · 377358490566037735849_<21> · 20000000000000000000003_<23>

4·10⁴⁵-9 =

3999999999999999999999999999999999999999999991_<46>

= 13 · 22277 · 221071 · 45219253 · 1381671421343196669691329557_<28>

4·10⁴⁶-9 =

39999999999999999999999999999999999999999999991_<47>

= 7 · 23² · 31 · 67 · 79 · 191 · 4372157 · 174456743 · 884907301 · 510655527299_<12>

4·10⁴⁷-9 =

399999999999999999999999999999999999999999999991_<48>

= 35267 · 12227186849_<11> · 927608937918464402236039505790877_<33>

4·10⁴⁸-9 =

3999999999999999999999999999999999999999999999991_<49>

= 19 · 211 · 11471 · 43490325653166523_<17> · 2000000000000000000000003_<25>

4·10⁴⁹-9 =

39999999999999999999999999999999999999999999999991_<50>

= 83 · 2683 · 27525479 · 6525688527105038387100875841973862161_<37>

4·10⁵⁰-9 =

399999999999999999999999999999999999999999999999991_<51>

= 17 · 61 · 181 · 20563 · 809707 · 1201200837522317_<16> · 106554713181350794099_<21>

4·10⁵¹-9 =

3999999999999999999999999999999999999999999999999991_<52>

= 13 · 9533 · 11478529 · 20778496481_<11> · 346549605163_<12> · 390500219882387917_<18>

4·10⁵²-9 =

39999999999999999999999999999999999999999999999999991_<53>

= 7 · 389 · 17209 · 3793020318169_<13> · 7532632618541_<13> · 29876158840183612897_<20>

4·10⁵³-9 =

399999999999999999999999999999999999999999999999999991_<54>

= 157 · 163 · 569 · 761 · 1237 · 1665067809413_<13> · 17525652127950822486483289769_<29>

4·10⁵⁴-9 =

3999999999999999999999999999999999999999999999999999991_<55>

= 113 · 1433 · 6053 · 8860097 · 335676199 · 686898522953_<12> · 1997620911401736077_<19>

4·10⁵⁵-9 =

39999999999999999999999999999999999999999999999999999991_<56>

= 1213 · 435439 · 27926295591401_<14> · 2711805491993242645187238684535013_<34>

4·10⁵⁶-9 =

399999999999999999999999999999999999999999999999999999991_<57>

= 509 · 62658571 · 944220544009_<12> · 21181492106794667_<17> · 627092674117858723_<18>

4·10⁵⁷-9 =

3999999999999999999999999999999999999999999999999999999991_<58>

= 13 · 53 · 541999 · 15204376720919_<14> · 704488101605429696569025928135183199_<36>

4·10⁵⁸-9 =

39999999999999999999999999999999999999999999999999999999991_<59>

= 7 · 541 · 2659 · 139031879314767479609237_<24> · 28571428571428571428571428571_<29>

4·10⁵⁹-9 =

399999999999999999999999999999999999999999999999999999999991_<60>

= 79 · 89 · 14719049 · 1382642844254719_<16> · 2795459032091734897902450212049031_<34>

4·10⁶⁰-9 =

3999999999999999999999999999999999999999999999999999999999991_<61>

= 29 · 199 · 5237 · 8837 · 1632417869_<10> · 606070113479_<12> · 24023856568681_<14> · 630121869948239_<15>

4·10⁶¹-9 =

39999999999999999999999999999999999999999999999999999999999991_<62>

= 31 · 48079 · 51067383403_<11> · 525532120638669805503793461936388538314810453_<45>

4·10⁶²-9 =

399999999999999999999999999999999999999999999999999999999999991_<63>

= 43 · 11827 · 8898053 · 723962431 · 3104695253724121_<16> · 39326649113872278841672877_<26>

4·10⁶³-9 =

3999999999999999999999999999999999999999999999999999999999999991_<64>

= 13 · 5879 · 397951 · 41150327719_<11> · 201555190323689_<15> · 15856827214779275189453215813_<29>

4·10⁶⁴-9 =

39999999999999999999999999999999999999999999999999999999999999991_<65>

= 7² · 227 · 599 · 2371 · 6883 · 13326490787_<11> · 1349249466612248603_<19> · 20459445058501213949971_<23>

4·10⁶⁵-9 =

399999999999999999999999999999999999999999999999999999999999999991_<66>

= 71 · 907 · 2917 · 5335216441_<10> · 399122198972580674414039835959554050436938872399_<48>

4·10⁶⁶-9 =

3999999999999999999999999999999999999999999999999999999999999999991_<67>

= 17 · 19 · 6299 · 11813 · 376757 · 1241427542057_<13> · 1273584854099_<13> · 279392706425459492737396141_<27>

4·10⁶⁷-9 =

39999999999999999999999999999999999999999999999999999999999999999991_<68>

= 3169 · 1035361 · 7119289 · 1099261249_<10> · 1557788195773317123427567075719367853357359_<43>

4·10⁶⁸-9 =

399999999999999999999999999999999999999999999999999999999999999999991_<69>

= 23 · 47 · 241 · 10055497 · 3229088693532413_<16> · 25699991466148591_<17> · 1839927713575003331301821_<25>

4·10⁶⁹-9 =

3999999999999999999999999999999999999999999999999999999999999999999991_<70>

= 13 · 3859451384609369_<16> · 189256353195151619017207481_<27> · 421250662534968233939990563_<27>

4·10⁷⁰-9 =

39999999999999999999999999999999999999999999999999999999999999999999991_<71>

= 7 · 53 · 314663749 · 49300544393_<11> · 34750228004651_<14> · 200000000000000000000000000000000003_<36>

4·10⁷¹-9 =

399999999999999999999999999999999999999999999999999999999999999999999991_<72>

= 151 · 207997 · 1022933782794153551_<19> · 12450260872825111678178680692319362199954369403_<47>

4·10⁷²-9 =

3999999999999999999999999999999999999999999999999999999999999999999999991_<73>

= 59 · 79 · 1613 · 120943 · 3547890075714688351659371161_<28> · 1239925604463732176069435833849969_<34>

4·10⁷³-9 =

39999999999999999999999999999999999999999999999999999999999999999999999991_<74>

= 1031 · 38797284190106692531522793404461687681862269641125121241513094083414161_<71>

4·10⁷⁴-9 =

399999999999999999999999999999999999999999999999999999999999999999999999991_<75>

= 8573 · 5049497107807891_<16> · 3960790465465279655633_<22> · 2332905633967106030561063804969089_<34>

4·10⁷⁵-9 =

3999999999999999999999999999999999999999999999999999999999999999999999999991_<76>

= 13 · 373 · 401 · 8443 · 26858801 · 3713923013_<10> · 2442570608687872717356988936002096246082203654401_<49>

4·10⁷⁶-9 =

39999999999999999999999999999999999999999999999999999999999999999999999999991_<77>

= 7 · 31 · 5653633 · 348331826708401_<15> · 2645922409342926726059_<22> · 35375483339650805066405972938109_<32>

4·10⁷⁷-9 =

399999999999999999999999999999999999999999999999999999999999999999999999999991_<78>

= 6909201596477648329_<19> · 172076998829363467934536230121_<30> · 336441300962383991893868484199_<30>

4·10⁷⁸-9 =

3999999999999999999999999999999999999999999999999999999999999999999999999999991_<79>

= 211 · 2341 · 24024727 · 88033849 · 4860567927377_<13> · 17127126974796668443_<20> · 45993497522560350084477797_<26>

4·10⁷⁹-9 =

39999999999999999999999999999999999999999999999999999999999999999999999999999991_<80>

= 67 · 55843 · 155464245025206671_<18> · 3651737033218895580218723_<25> · 18831565676508989772214639824667_<32>

4·10⁸⁰-9 =

399999999999999999999999999999999999999999999999999999999999999999999999999999991_<81>

= 6770723 · 2359303200251_<13> · 9976145988074011_<16> · 1252019786340070350611_<22> · 2004782209874335297654727_<25>

4·10⁸¹-9 =

3999999999999999999999999999999999999999999999999999999999999999999999999999999991_<82>

= 13 · 719 · 769 · 556495182212521892868277729494091621088551878498180886811245042497450208637_<75>

4·10⁸²-9 =

39999999999999999999999999999999999999999999999999999999999999999999999999999999991_<83>

= 7 · 17 · 19603 · 260809 · 16954274587_<11> · 329615502427472542979_<21> · 11764705882352941176470588235294117647059_<41>

4·10⁸³-9 =

399999999999999999999999999999999999999999999999999999999999999999999999999999999991_<84>

= 43 · 53 · 173 · 4334590831_<10> · 234056903434069220367254497556350798823218530337710050465501450978683_<69>

4·10⁸⁴-9 =

3999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<85>

= 19 · 6337 · 98327 · 10311465629_<11> · 29391458183_<11> · 557414635291_<12> · 473476023375163705877_<21> · 4224078731047546560439_<22>

4·10⁸⁵-9 =

39999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<86>

= 79 · 643 · 1278163 · 124449733 · 5271060797_<10> · 11374658929_<11> · 1146546591356161409_<19> · 72013447150613939027878801921_<29>

4·10⁸⁶-9 =

399999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<87>

= 109 · 131 · 6263 · 8833091 · 23949661 · 2187467868975357653_<19> · 1459842158613772062977_<22> · 6620947236743160286544093_<25>

4·10⁸⁷-9 =

3999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<88>

= 13² · 1013 · 4853242517_<10> · 84485683303708399_<17> · 716034478303081832491184053_<27> · 79581989493293634276223487797_<29>

4·10⁸⁸-9 =

39999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<89>

= 7 · 29 · 419 · 1091 · 1201 · 218809 · 1115911 · 22068793 · 33872427605755993_<17> · 774778366537166689_<18> · 2537961573918528140906387_<25>

4·10⁸⁹-9 =

399999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<90>

= 107 · 479 · 6797351561328298574237479322906911_<34> · 1148156180270793396284227336382345195326385956160677_<52> (Makoto Kamada / GGNFS-0.54.5b)

4·10⁹⁰-9 =

3999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<91>

= 23 · 83 · 3769 · 5281 · 11125019 · 1137872495299_<13> · 126823666282673_<15> · 376099532000829380399_<21> · 174346928210271221879232893_<27>

4·10⁹¹-9 =

39999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<92>

= 31 · 723799 · 890306831 · 10009707608420736556767604383961_<32> · 200041094280928247178817127740041862433271929_<45> (Makoto Kamada / GGNFS-0.54.5b)

4·10⁹²-9 =

399999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<93>

= 601 · 647 · 10825259 · 734482643 · 6338564899_<10> · 4185387670524992598018391019_<28> · 4876798072509021078191981031219049_<34>

4·10⁹³-9 =

3999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<94>

= 13 · 12271757 · 25073207340424659020521047450035695158215103810506327032689150191965803454851029701151_<86>

4·10⁹⁴-9 =

39999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<95>

= 7 · 5443 · 40762871 · 176905403 · 987525370892477_<15> · 130400901777472032491_<21> · 1130547719902031482893713540224658938201_<40>

4·10⁹⁵-9 =

399999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<96>

= 63311 · 4783391 · 22339434383766054987787_<23> · 59125219091727708259291180183537020669016066641432440106136693_<62>

4·10⁹⁶-9 =

3999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<97>

= 53 · 6871 · 10949 · 1194151159441_<13> · 31600563093091571718561868639841689_<35> · 26584934299123232854555060648941702283057_<41>

4·10⁹⁷-9 =

39999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<98>

= 20748910387_<11> · 11947840377877_<14> · 26998259611105711237_<20> · 130854750156377789637493591_<27> · 45671999240020004544736419427_<29>

4·10⁹⁸-9 =

399999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<99>

= 17 · 79 · 241 · 311 · 2269 · 39317 · 161461 · 1089735593698011381725554998847_<31> · 253164556962025316455696202531645569620253164557_<48>

4·10⁹⁹-9 =

3999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<100>

= 13 · 26399 · 77773529 · 408808471 · 17465373185831_<14> · 95419353470123_<14> · 219969836350708990879865183829475893001854137377279_<51>

4·10¹⁰⁰-9 =

39999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999991_<101>

= 7 · 71 · 6491 · 144311 · 237151 · 1153609 · 4383461 · 8988086730774101_<16> · 243852700434495407_<18> · 1790067864550241141_<19> · 18261123537479423831_<20>

4·10¹⁰¹-9 =

3(9)₁₀₀1_<102>

= 1242505016132702919907_<22> · 321930289863134774281390210545910706737390060353248796493168385592837665658171613_<81>

4·10¹⁰²-9 =

3(9)₁₀₁1_<103>

= 19 · 197 · 159239027032849_<15> · 89342573911788731_<17> · 3355526347347494765062846183242829_<34> · 22385744135541414977650142665848487_<35>

4·10¹⁰³-9 =

3(9)₁₀₂1_<104>

= 89 · 7348321 · 545099119 · 92975796938529587_<17> · 246815893242841067_<18> · 455914728317345369_<18> · 10724566125055079702147046804421081_<35>

4·10¹⁰⁴-9 =

3(9)₁₀₃1_<105>

= 43 · 409 · 3110999 · 4335631 · 10342885269851_<14> · 140742896567473_<15> · 1062270653575649523714584464177_<31> · 1090467352009655798670870606607_<31>

4·10¹⁰⁵-9 =

3(9)₁₀₄1_<106>

= 13 · 4049 · 230177683 · 5089468623085822110371775885182959_<34> · 64868403116863325702101470038639463824085108816719708634719_<59> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 1.24 hours on Pentium 4 2.4GHz, Windows XP / Nov 18, 2007)

4·10¹⁰⁶-9 =

3(9)₁₀₅1_<107>

= 7² · 31 · 829 · 5641 · 14753 · 527513318280406704433683764738692440130410049_<45> · 723565441067403738662633995275117669829853586533_<48>

4·10¹⁰⁷-9 =

3(9)₁₀₆1_<108>

= 190125920843_<12> · 2103868837170852718371967159514240270498075443738141548131610224029698744616010054224608219061637_<97>

4·10¹⁰⁸-9 =

3(9)₁₀₇1_<109>

= 211 · 1129 · 5536417031655899_<16> · 656886980652235583190527_<24> · 14429686178846832587868560401_<29> · 319968523864926281807959061371083793_<36>

4·10¹⁰⁹-9 =

3(9)₁₀₈1_<110>

= 53 · 7969641884935205730310904257533114365615152149547_<49> · 94698982969196667127271104615127284069462500623071914214001_<59> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 0.96 hours on Cygwin on AMD XP 2700+ / Nov 18, 2007)

4·10¹¹⁰-9 =

3(9)₁₀₉1_<111>

= 61 · 463 · 947 · 36299 · 64577 · 86111 · 368453 · 60111533 · 630641640613593647_<18> · 158397422352643703820307_<24> · 33488629391928160215301711261193567_<35>

4·10¹¹¹-9 =

3(9)₁₁₀1_<112>

= 13 · 79 · 2053 · 1897145318011355363300956967527037877929133085218344826081574402956511263588896198168211338194135828964761_<106>

4·10¹¹²-9 =

3(9)₁₁₁1_<113>

= 7 · 23 · 67² · 46757 · 55243 · 169709 · 87796968481_<11> · 9368987878212461_<16> · 34734396543207627172561909369_<29> · 4418997809718205768560805948969128889_<37>

4·10¹¹³-9 =

3(9)₁₁₂1_<114>

= 7867 · 50845303165120122028727596288292868946231091902885470954620566925130291089360620312698614465488750476674717173_<110>

4·10¹¹⁴-9 =

3(9)₁₁₃1_<115>

= 17² · 47 · 617 · 3469 · 47161 · 381357863 · 1982502477023_<13> · 2551886715660056082059_<22> · 4129570129161813841531043869_<28> · 366166948392750909072952624571_<30>

4·10¹¹⁵-9 =

3(9)₁₁₄1_<116>

= 465053419121_<12> · 48540212971357_<14> · 4565203528103689_<16> · 388146190346759943944292211077936423971024540269272004873010728374421498427_<75>

4·10¹¹⁶-9 =

3(9)₁₁₅1_<117>

= 29 · 167 · 317 · 6091 · 36217 · 81839 · 133373771 · 830083951270177_<15> · 8577012162065861_<16> · 726279061919048761_<18> · 20926320650104033519325587218683355651331_<41>

4·10¹¹⁷-9 =

3(9)₁₁₆1_<118>

= 13 · 9973 · 214363 · 581922332049027043_<18> · 531991308851942132115845825480210110671439_<42> · 464912723832181683082293085018597257414298049209_<48> (Sinkiti Sibata / Msieve v. 1.28 for P42 x P48 / 7.54 hours on Pentium3 750MHz, Windows Me / Nov 18, 2007)

4·10¹¹⁸-9 =

3(9)₁₁₇1_<119>

= 7 · 24359 · 36382287863_<11> · 1715548838023451276899_<22> · 3204327551100096307916697319_<28> · 1172931096162755918903544011307055767008967058230164269_<55>

4·10¹¹⁹-9 =

3(9)₁₁₈1_<120>

= definitely prime number

4·10¹²⁰-9 =

3(9)₁₁₉1_<121>

= 19 · 97 · 3347 · 89627 · 13472671 · 195022804897_<12> · 26159207707463133368869943944733_<32> · 105263157894736842105263157894736842105263157894736842105263_<60>

4·10¹²¹-9 =

3(9)₁₂₀1_<122>

= 31 · 207550763771542349075740138245104441965655783933_<48> · 6216901143594248208194826668257714111385850652570251799400319368993225117_<73> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 1.55 hours on Cygwin on AMD 64 3200+ / Nov 18, 2007)

4·10¹²²-9 =

3(9)₁₂₁1_<123>

= 53 · 197689 · 191000601601_<12> · 493060093873981_<15> · 2608655530952645899_<19> · 78655827078856343401733_<23> · 1975692680562017890358804953016577832115900417449_<49>

4·10¹²³-9 =

3(9)₁₂₂1_<124>

= 13 · 15601 · 14877774143167099699747_<23> · 470762130228440485791543763322013994572073144603_<48> · 2815948587112211304623095233966680241651606098227_<49> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 2.60 hours on Pentium 4 2.4GHz, Windows XP / Nov 18, 2007)

4·10¹²⁴-9 =

3(9)₁₂₃1_<125>

= 7 · 79 · 67187 · 4145861 · 679928401 · 70949947126910415444647891266160232938407859977_<47> · 5382940938022136860142931615845020393406317220316048073_<55>

4·10¹²⁵-9 =

3(9)₁₂₄1_<126>

= 43 · 3271 · 9595471 · 296377134243523374156060249291119671964793449628338174285262650903842695326462431018241723161147304591463797875357_<114>

4·10¹²⁶-9 =

3(9)₁₂₅1_<127>

= 173 · 709 · 1793399 · 159075667 · 123805374165243868085316016373_<30> · 131703755921620208014649133623_<30> · 7010505260167127084147004476059947918274173937609_<49>

4·10¹²⁷-9 =

3(9)₁₂₆1_<128>

= 28597 · 1398748120432213169213553869286988145609679336993390915130957792775465957967618981011994265132706227926006224429135923348603_<124>

4·10¹²⁸-9 =

3(9)₁₂₇1_<129>

= 241 · 1746565317767_<13> · 148218399686044608087191_<24> · 77257925744689962320417057501_<29> · 82987551867219917012448132780082987551867219917012448132780083_<62>

4·10¹²⁹-9 =

3(9)₁₂₈1_<130>

= 13 · 2063359 · 149122042113033985994532365764904552386517473543046892134472143573807414176443511619794564255513610424704422404289465716973_<123>

4·10¹³⁰-9 =

3(9)₁₂₉1_<131>

= 7 · 17 · 59 · 773 · 723564791 · 250214207989_<12> · 50930050051704367752914146546619588270224810241099_<50> · 799315121261189397901309758464692809702923108613928727_<54>

4·10¹³¹-9 =

3(9)₁₃₀1_<132>

= 83 · 157 · 43427 · 89517934664444970329_<20> · 2706709430006427754108248781033420387_<37> · 2917230383237813120633073932480522042054906957099018520221291471441_<67> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 2.06 hours on Core 2 Quad Q6600 / Nov 17, 2007)

4·10¹³²-9 =

3(9)₁₃₁1_<133>

= 359 · 8423 · 1395047 · 488266873 · 5045396267_<10> · 17702820451_<11> · 120840716754001_<15> · 453907009693924437841_<21> · 269952174593306396039669287_<27> · 1468411861087106185253786003407_<31>

4·10¹³³-9 =

3(9)₁₃₂1_<134>

= 283 · 2206451413_<10> · 17745322828110113689579957_<26> · 3609900924935868884393553722022192916008376697080113513902182884643650707317688815148572213895197_<97>

4·10¹³⁴-9 =

3(9)₁₃₃1_<135>

= 23 · 163 · 3083 · 6661 · 186283 · 2907419 · 434826671 · 3754592877473_<13> · 474717736202574865914293_<24> · 20832581206768470618341726869_<29> · 594145999077637914442282147060469278819_<39>

4·10¹³⁵-9 =

3(9)₁₃₄1_<136>

= 13 · 53 · 71 · 717631 · 5476770683_<10> · 608840507813_<12> · 40266621886486270135726643_<26> · 848609592447617662992638138586825443628335178372470676088764528990820467296627_<78>

4·10¹³⁶-9 =

3(9)₁₃₅1_<137>

= 7 · 31 · 179 · 289067 · 12221768408569_<14> · 4929272942288469413_<19> · 6265355337053585617939_<22> · 6475919213812378888572319171_<28> · 1457419800611451039734374629295231356806366627_<46>

4·10¹³⁷-9 =

3(9)₁₃₆1_<138>

= 79 · 997 · 5237 · 655387 · 18609511 · 217696138293088164184518991_<27> · 365234386003280635200403386279689112427897130966004676283859706524186487861765417504363403_<90>

4·10¹³⁸-9 =

3(9)₁₃₇1_<139>

= 19 · 211 · 22783 · 473774831 · 254128194179_<12> · 58676451232029416603_<20> · 2067397236615734055061_<22> · 4112502436486078502075149_<25> · 729112006146231857757290002160431335436328591_<45>

4·10¹³⁹-9 =

3(9)₁₃₈1_<140>

= 827 · 3169 · 100185797 · 974921923 · 18849219647987_<14> · 8290159254208310080147936628003905810782930509779232189523941213775684048461272819925784127168553729081_<103>

4·10¹⁴⁰-9 =

3(9)₁₃₉1_<141>

= 193 · 1009 · 165527 · 9015029 · 318197099659911533_<18> · 4205472414155209188944371_<25> · 28730710303722801189996006104739370162441_<41> · 35802897529245969120774911383627717355267_<41>

4·10¹⁴¹-9 =

3(9)₁₄₀1_<142>

= 13 · 191 · 20359 · 195319 · 12420177806754397_<17> · 163736308730108767707475962968700893_<36> · 199209262950089812594969876563503547961581096151892699792833892052250192212997_<78> (Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona snfs / 5.44 hours on Core 2 Quad Q6600 / Nov 18, 2007)

4·10¹⁴²-9 =

3(9)₁₄₁1_<143>

= 7 · 107 · 155731 · 110242819 · 292292453 · 108873161835557496912230201617128500051561735049298977361_<57> · 97749457018750228999485760145263043889030650310456600905023807_<62>

4·10¹⁴³-9 =

3(9)₁₄₂1_<144>

= 23319815050804253_<17> · 41320276617255065999_<20> · 65592239078997416563125307_<26> · 6328768545120330781276890083775149723778473759165061794733839591210761469954001079_<82>

4·10¹⁴⁴-9 =

3(9)₁₄₃1_<145>

= 29 · 149 · 143357 · 4179362655121_<13> · 115107344774745155473488635437584064431083661453869669_<54> · 13422818791946308724832214765100671140939597315436241610738255033557047_<71>

4·10¹⁴⁵-9 =

3(9)₁₄₄1_<146>

= 67 · 11529868409241733729_<20> · 51779855951746915613207527045979455969975971369762642935411255512701536677331213503472055536703777671434517482031353309260637_<125>

4·10¹⁴⁶-9 =

3(9)₁₄₅1_<147>

= 17 · 43 · 151 · 7759 · 28481543869_<11> · 35256146990949820675155255501335850511972129326274272679_<56> · 465116279069767441860465116279069767441860465116279069767441860465116279_<72>

4·10¹⁴⁷-9 =

3(9)₁₄₆1_<148>

= 13 · 89 · 6167403400563579766175239_<25> · 9859117276170965916528849893551257536137453_<43> · 56857301497661450675385390309929156870609092238968154609890852061865551467889_<77> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs / 16.03 hours on Cygwin on AMD XP 2700+ / Nov 19, 2007)

4·10¹⁴⁸-9 =

3(9)₁₄₇1_<149>

= 7² · 53² · 673 · 847507 · 26834343679421_<14> · 23909542862637059743_<20> · 4651884471734792048380131661572294455090942337043_<49> · 170711446743697725633505677829515883121491856455923629_<54>

4·10¹⁴⁹-9 =

3(9)₁₄₈1_<150>

= 797 · 279587197 · 6930505097787449_<16> · 259011771676803216882760438429105713862269153762654978763387122923529476117102696830468777066082263142406640371598807420951_<123>

4·10¹⁵⁰-9 =

3(9)₁₄₉1_<151>

= 79 · 331 · 171077 · 73525909 · 123379312751_<12> · 10206815431870182840270817231_<29> · 7493498919620788902689385842385931447646537_<43> · 1288711252427299289691976770992371416501780989937179_<52>

4·10¹⁵¹-9 =

3(9)₁₅₀1_<152>

= 31 · 5519 · 371213 · 1158569 · 54827975693_<11> · 85431185431_<11> · 683451293547552766493247508223331705485919834283_<48> · 169811308556460662649467994337463527761352643619555931552038754243_<66> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 27.46 hours on Pentium 4 2.4GHz, Windows XP / Nov 21, 2007)

4·10¹⁵²-9 =

3(9)₁₅₁1_<153>

= 103035186006031_<15> · 1934982246763493955490755927821_<31> · 100315363558355014647859823017153_<33> · 19999999999999999999999999999999999999999999999999999999999999999999999999997_<77>

4·10¹⁵³-9 =

3(9)₁₅₂1_<154>

= 13 · 7963 · 3046082801_<10> · 2125945121483_<13> · 36758374772653_<14> · 18100935169352815275707_<23> · 42510316950321522868841089_<26> · 210957277462653394690465901462374782796266121499135809783812023957_<66>

4·10¹⁵⁴-9 =

3(9)₁₅₃1_<155>

= 7 · 7159 · 23203 · 6478104454016753760887_<22> · 4312505747417765608582777589439413779944095761779091_<52> · 1231367864992827282186416781081264122250201636487892575467458025747902057_<73>

4·10¹⁵⁵-9 =

3(9)₁₅₄1_<156>

= 1821613 · 3583357 · 4637483 · 32771932477841795426235506521_<29> · 403208254555383837372946873770549114630370766010235538732585825933608884811798208240341232025096911389953557_<108>

4·10¹⁵⁶-9 =

3(9)₁₅₅1_<157>

= 19 · 23 · 307 · 5693 · 8179 · 1237661 · 2486863 · 4822777 · 45908403975780047456872133_<26> · 8232288831717810579373722530878388597_<37> · 114139310551026338652399651844405362963557000608503422372020997_<63>

4·10¹⁵⁷-9 =

3(9)₁₅₆1_<158>

= 2306893 · 17339339102420441693654625507121483311102855659105125378593632214411331604890213807055637170861414031773471938230338381537418510524762093430427852527187_<152>

4·10¹⁵⁸-9 =

3(9)₁₅₇1_<159>

= 241 · 523 · 1571 · 4561 · 5647 · 1372638681719_<13> · 685978596651857_<15> · 32352462130214742144908089_<26> · 402766851937457023692444225437_<30> · 6392332516138127241768447324856462524373231004706954463263139_<61>

4·10¹⁵⁹-9 =

3(9)₁₅₈1_<160>

= 13 · 199 · 2130173 · 64929089 · 24131072597_<11> · 952589489681209_<15> · 74079493501806378527450601403663790436099271_<44> · 6564912794659200412500871081575072082513907943647734630671406825808638043_<73> (Sinkiti Sibata / GGNFS-0.77.1-20060513-pentium4 snfs / 77.01 hours on Pentium 4 2.4GHz, Windows XP / Nov 24, 2007)

4·10¹⁶⁰-9 =

3(9)₁₅₉1_<161>

= 7 · 47 · 1987 · 6299 · 414473453 · 16487355097_<11> · 19966584998152201_<17> · 501471938213707291_<18> · 259021994710197509542516797106845199244858179099_<48> · 548100043780603304955338234337098221979945589533507_<51>

4·10¹⁶¹-9 =

3(9)₁₆₀1_<162>

= 53 · 21806825430466113390135407080568754712841_<41> · 346092091000860392504443010316442896408178789678554842890548184933093473061870388053493738110298874615414662714544919267_<120> (Robert Backstrom / GGNFS-0.77.1-20051202-athlon snfs, Msieve 1.29 / Nov 20, 2007)

4·10¹⁶²-9 =

3(9)₁₆₁1_<163>

= 17 · 1277 · 1523 · 2530899979_<10> · 94728548632440270893171_<23> · 133940570111507996479098559_<27> · 313827973953327557599392191_<27> · 3957387137241634817201597568481_<31> · 3033556371527318787524930840338672101713_<40>

4·10¹⁶³-9 =

3(9)₁₆₂1_<164>

= 79 · 2711431 · 1507192123_<10> · 3204540690671_<13> · 248748268553561479_<18> · 227089159325096042476973_<24> · 2129679099007734476891559517_<28> · 321387735053205686267572567444278274455091556569548545847621764557_<66>

4·10¹⁶⁴-9 =

3(9)₁₆₃1_<165>

= 825611 · 1402504993_<10> · 18909138091_<11> · 8812588523511893_<16> · 2748849941029302910494614920725892417409755520329614893557061_<61> · 754143246424861575508278194050733980225970187173199288191709719_<63>

4·10¹⁶⁵-9 =

3(9)₁₆₄1_<166>

= 13² · 2488043 · 178101449 · 53413120622881228787039620154426573307960318677092493375505243684627286403897026319389625184870935049908649420094106231903695336468369821350035121077_<149>

4·10¹⁶⁶-9 =

3(9)₁₆₅1_<167>

= 7 · 31 · 113 · 229 · 24979 · 385787823329569_<15> · 5278397362612613211007287739_<28> · 1890937814311875696421686100672206606653923849_<46> · 74059954315926416227569410612850650660129447590211704312173034536059_<68>

4·10¹⁶⁷-9 =

3(9)₁₆₆1_<168>

= 43 · 443 · 3803 · 8363 · 42090948879771092306041949813824861415659616231911_<50> · 15685944386992125078642922951658875275870814395996579224833998729276744713659512994944344360612430130357121_<107> (Robert Backstrom / GGNFS-0.77.1-20050930-k8 snfs, Msieve 1.32 / Jan 5, 2008)

4·10¹⁶⁸-9 =

3(9)₁₆₇1_<169>

= 211 · 233713 · 10689751 · 30870029 · 174101240977_<12> · 27501614868292675787_<20> · 1901624710396775316537341_<25> · 1265800626727778453024504210132287247243_<40> · 21327495454449983020338735825860051020986349407972619_<53>

4·10¹⁶⁹-9 =

3(9)₁₆₈1_<170>

= 173 · 563 · 462212928665557_<15> · 61333882543515533360951_<23> · 67426291872596114148024503677_<29> · 214849165378180616457207496167989576239109216001953503018360303758200797034032319912192428035188231_<99>

4·10¹⁷⁰-9 =

3(9)₁₆₉1_<171>

= 61 · 71 · 263 · 1069 · 784009 · 730869849769_<12> · 188791641851297_<15> · 92965737425275667_<17> · 13941520301475528498949_<23> · 123958877689262908298519237788099_<33> · 18900957529184282114771140692935766432229545915707371997947_<59>

4·10¹⁷¹-9 =

3(9)₁₇₀1_<172>

= 13 · 1481551 · 2094373 · 35330951 · 23561463756765050201124699355493115971879_<41> · 28941009474935683843948897020903479139997_<41> · 4115993992441463544706180751361765698756507413749483861195184714376893_<70> (Sinkiti Sibata / GGNFS-0.77.1-20050930-nocona snfs / 96.52 hours on Core 2 Quad Q6600 2.4GHz, Windows Vista and Cygwin / Nov 4, 2008)

4·10¹⁷²-9 =

3(9)₁₇₁1_<173>

= 7 · 29 · 83 · 6271 · 161471 · 3708068388463_<13> · 803341897652669_<15> · 606376773754238324363_<21> · 1047920541237702507248025832637_<31> · 7562273344413334909707814556227561_<34> · 163788380802911156632732710348911066987517958987_<48>

4·10¹⁷³-9 =

3(9)₁₇₂1_<174>

= definitely prime number

4·10¹⁷⁴-9 =

3(9)₁₇₃1_<175>

= 19 · 53 · 1019 · 2633 · 42719 · 13351343 · 9391183921538689_<16> · 454731869459094847_<18> · 6923141487770868883_<19> · 60685815889202975701_<20> · 199478980651013971577_<21> · 1380394194751915908017_<22> · 5254035963287563578959421946859218396907_<40>

4·10¹⁷⁵-9 =

3(9)₁₇₄1_<176>

= 881 · 502411279 · 90370087395723989678725058277633153989461415339847760073141662282120456740059938920059986947649598798444671510431155920820192813041951544163357335628914648815191209_<164>

4·10¹⁷⁶-9 =

3(9)₁₇₅1_<177>

= 79 · 1031 · 9712441 · 98836273 · 160330424167_<12> · 259333214069_<12> · 636360516185020985689_<21> · 9967375987265890256911580767_<28> · 19398642095053346265761396702230843840931134820562560620756547041707080504364694471387_<86>

4·10¹⁷⁷-9 =

3(9)₁₇₆1_<178>

= 13 · 227 · 385001 · 5083123 · 1162925053_<10> · 332230023790700823439_<21> · 64657499314578118063033769725403663002679_<41> · 27726100791358863600050685537869345949466612785403199549604397338078169719410730274414575719_<92> (matsui / GGNFS-0.77.1-20060722-nocona / Apr 26, 2009)

4·10¹⁷⁸-9 =

3(9)₁₇₇1_<179>

= 7 · 17 · 23 · 67 · 293 · 52201 · 31220972566629346037_<20> · 55916398361587507836687691938105593431350598515146351210658005213_<65> · 8169177456550289517691354506398079361026545374532074621024709760357587770970084513_<82>

4·10¹⁷⁹-9 =

3(9)₁₇₈1_<180>

= 45509197 · 1874814157831_<13> · 56509686961164460509008717533_<29> · 82962091612775212635725896046171705731169425764309250070648134475290867457795804761148442726391599194995848372501717823470479622361_<131>

4·10¹⁸⁰-9 =

3(9)₁₇₉1_<181>

= 1153 · 4000853 · 14192805091_<11> · 1612351060219207303_<19> · 1075823634240573613236619945236180905716293882720442899436436921102117_<70> · 35221606618830262913343738393249032649822049079574497991150497364103099939_<74>

4·10¹⁸¹-9 =

3(9)₁₈₀1_<182>

= 31 · 587 · 12239 · 13095488550241_<14> · 4460116554200837_<16> · 3075008695410793039634658756642754100336392116486231060385034374663966161150639781687262650938183292256095536759895392902983609896041999450609681_<145>

4·10¹⁸²-9 =

3(9)₁₈₁1_<183>

= 1871 · 6709 · 14341 · 177127 · 225859 · 751763 · 1719409 · 7464124611017_<13> · 45186538905301_<14> · 94820315277907_<14> · 7391867565690931020532600599163374944095489619_<46> · 181770388080836974514656491761082559023131975054065757127548899_<63>

4·10¹⁸³-9 =

3(9)₁₈₂1_<184>

= 13 · 291521 · 175760151760128614736111330301882810113296736746728352650439858811633452129329386893_<84> · 6005184777904143133368396782495819629853737419435935288123825152255604348922994197853024855519_<94> (Serge Batalov / Msieve-1.38 snfs / 120.00 hours on Opteron-2.6GHz; Linux x86_64 / Nov 12, 2008)

4·10¹⁸⁴-9 =

3(9)₁₈₃1_<185>

= 7 · 1489 · 8233 · 9241 · 162557 · 90668547845459_<14> · 188080429537884826493_<21> · 6577596128333935936571_<22> · 169566414790523540512576421_<27> · 16314628258551292008434336517105846942520383292613380752344187754615265581346898185381_<86>

4·10¹⁸⁵-9 =

3(9)₁₈₄1_<186>

= 35063491934201_<14> · 11407876909425532766767515070105844680213096690807109262204032112482211097777055634465400185816885175799524693160422392762895179447778330591954913521449642117729318052647791_<173>

4·10¹⁸⁶-9 =

3(9)₁₈₅1_<187>

= 7321913 · 159129109 · 4211620326587_<13> · 175746623295851659_<18> · 62014234844721324719_<20> · 2319100651175680426597602137387367174469580704823_<49> · 32250659949410643441501571216321459031954131891410903461965466986948633363_<74>

4·10¹⁸⁷-9 =

3(9)₁₈₆1_<188>

= 53 · 10684013423190202598370871_<26> · 1626349888286077666713489931346081_<34> · 1156412510086878791154526581085081807094186719_<46> · 37559770618664727055350154373325301900026821932736805523253002218736318566782328163_<83> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1057010532 for P34 / Oct 26, 2008) (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 gnfs for P46 x P83 / 246.89 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Nov 11, 2008)

4·10¹⁸⁸-9 =

3(9)₁₈₇1_<189>

= 43² · 59 · 241 · 313 · 94427 · 3614470427_<10> · 19340062151882758570550401967047_<32> · 170653684700895671770239219522913_<33> · 213089577421509928559482959036656417177388199_<45> · 202503753322468777288652868121333740631106564440682715437_<57>

4·10¹⁸⁹-9 =

3(9)₁₈₈1_<190>

= 13 · 79 · 5973538769414641_<16> · [652015411336984701619618128349130445399424246532817515382372880666250037781527506634914673378585584229642458988818560670605607723797023820746604409217312171938891755704013_<171>] SUBMIT/RESERVE

4·10¹⁹⁰-9 =

3(9)₁₈₉1_<191>

= 7² · 1097 · 2777 · 323537 · 3184710803_<10> · 63716737888419215547415929687932010189450906872448170069806562750426211617_<74> · 4081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653_<94>

4·10¹⁹¹-9 =

3(9)₁₉₀1_<192>

= 89 · 305254752356293_<15> · 7425626411708544883_<19> · [1982779659046507580068781008986059634237785496432605202219397859236527888337235357678935863508303665245256247137752495383090184460311412809764459826740654001_<157>] SUBMIT/RESERVE

4·10¹⁹²-9 =

3(9)₁₉₁1_<193>

= 19² · 643 · 5743731053_<10> · 13387084763939_<14> · 6888003416488249330043_<22> · 21689554339683136588679658930304369012462798870108076460065939_<62> · 1500091411952965086038653440170200318545430389961301405134148425303374129832161763_<82>

4·10¹⁹³-9 =

3(9)₁₉₂1_<194>

= 356020398676981933_<18> · [112353112767260522359881729187375228211918910356307737254237520656808464172961169245778724482108373492206054434443907437761309852564322068419968002188716743359559719078175816627_<177>] SUBMIT/RESERVE

4·10¹⁹⁴-9 =

3(9)₁₉₃1_<195>

= 17 · 109 · 347 · 14159 · 787429 · 784377317 · 1289241992537_<13> · 38650745043061_<14> · 36454802699034857_<17> · 145923420596482481004347_<24> · 45740554784041081835936926224367892182088323307351_<50> · 5866952744783258583080885755055224630524999042809897791_<55>

4·10¹⁹⁵-9 =

3(9)₁₉₄1_<196>

= 13 · 107 · 317 · 683 · 4813 · 34945726168123_<14> · 235346907565680687670001_<24> · 84023102213882289455105713911646201_<35> · 3993335105848129845498334339702023428427294782244533437466867913637243996141634999335678685464308070534367797009_<112> (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3729024413 for P35 / Sep 23, 2008)

4·10¹⁹⁶-9 =

3(9)₁₉₅1_<197>

= 7 · 31 · 1033 · 1801 · 26891720626840241453_<20> · 425574857812513991947_<21> · 136136864578743359737953547522723_<33> · 1855514081798741393807817969446545214189_<40> · 34272964492098008972146833105500148126083732893462398747862634497615158084103_<77>

4·10¹⁹⁷-9 =

3(9)₁₉₆1_<198>

= 281910298133_<12> · 190480094567465618641014493_<27> · 7449025353749847708792163940858645078093979533400210025452931994205704095434922560694382108924013878016266620120475224815233471656885159688499655327843956585239_<160>

4·10¹⁹⁸-9 =

3(9)₁₉₇1_<199>

= 211 · 1637 · 3844549383673931497619_<22> · 79382035150980920346405340690307261392830949801_<47> · 119405769425714490171006230771951087269574666783273_<51> · 317786813596113683738897417841728349760581713829816055800984665620078724099_<75>

4·10¹⁹⁹-9 =

3(9)₁₉₈1_<200>

= 877 · 19306917307_<11> · 2362367512238169842814551460351364624763526014197834021710043197746268915212743618127338511233575062172571178528000029762748237070971655452443973681727811458036330149383339715017027238569_<187>

4·10²⁰⁰-9 =

3(9)₁₉₉1_<201>

= 23 · 29 · 53 · 197 · 379 · 3671 · 9187 · 28463 · 170547889 · 2351903621_<10> · 1221402604855740137021_<22> · 60059632438639530286975417_<26> · 107607507117527462741165517473467_<33> · 49861360773942694081325021246938997255965585182246410257045279125241288931457688087_<83>

4·10²⁰¹-9 =

3(9)₂₀₀1_<202>

= 13 · 11842799 · 1803406453_<10> · 2220194263669079_<16> · 53348426169923083_<17> · 1166568154373795165761511707_<28> · 104266778771382632137951610299920123165342937251568662918164741420036887490286230927059861854945885129398920094404223797533319_<126>

4·10²⁰²-9 =

3(9)₂₀₁1_<203>

= 7 · 79 · 383 · 617 · 2393 · 397963 · 774799 · 1690313 · 21610019 · 216954797 · 217194433913_<12> · 4359913632001_<13> · 18484717176979_<14> · 176407766384435368999_<21> · 11562800031772242924518824714175876232173_<41> · 1466104189413658796569889069140426117523998627396976056080427_<61>

4·10²⁰³-9 =

3(9)₂₀₂1_<204>

= 985938912916866838801_<21> · 49069470515507153084854289_<26> · [8267964665786356938287367844355281001398126993501074674861131857506894880016997246729292677860700547196512126677256262958971699221797075688092446705433239319_<157>] SUBMIT/RESERVE

4·10²⁰⁴-9 =

3(9)₂₀₃1_<205>

= 439 · 701 · 2317751 · 5551873 · 21897763 · 9012245475577_<13> · 322353810266010223_<18> · 3631408672796406702085696216743007169009354928263686873187008923205595863_<73> · 4372506411149619576025256338954642702426504653677338907773680184342622318497_<76>

4·10²⁰⁵-9 =

3(9)₂₀₄1_<206>

= 71 · 64845766618293547_<17> · [8688004029721909942175244154709669118988350636890249453474633452691937733425391096642439015015723799168359501222655677453767063989307255031591129889665034649016117880912025795132376173043_<187>] SUBMIT/RESERVE

4·10²⁰⁶-9 =

3(9)₂₀₅1_<207>

= 47 · 787 · 2068430377411_<13> · 1303454060208099067_<19> · 71811408358293195292411_<23> · 77125858976287579050890129854699_<32> · 37144778449564313154341134715055031_<35> · 19531312895566268888765389214062836488273_<41> · 998224205171980635252280650332109241844941_<42>

4·10²⁰⁷-9 =

3(9)₂₀₆1_<208>

= 13 · 7039 · 12973 · 493250413 · 80921269180941493_<17> · [84418010434982193986856613428889246036872582652432364034631604487131148045456398691850103682827400223806128838737018133954106283264114247435395353221360608035387161086578609_<173>] SUBMIT/RESERVE

4·10²⁰⁸-9 =

3(9)₂₀₇1_<209>

= 7 · 1499 · 397633 · 72924583 · 32500127761170009153191422527529_<32> · 81143272388834334896650363044075567399043782163_<47> · 6198620635061424030493749864953890386771151005333743_<52> · 8042133907689848374500596451675451989411649913723669050575553_<61>

4·10²⁰⁹-9 =

3(9)₂₀₈1_<210>

= 43 · 157 · 1344799 · 43219643 · 456637813 · 52186574700410202710543580507939239_<35> · [42778215758823271283365202134828897965312572658602223157505026013428737320090590105223875557676570260944693618416666386090018930911972785693795598359_<149>] (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1610337776 for P35 / Nov 4, 2008) SUBMIT/RESERVE

4·10²¹⁰-9 =

3(9)₂₀₉1_<211>

= 17 · 19 · 467 · 2333 · 3961175617793_<13> · 3347237247165798725331239871160802804281762325288903139153487422487976442557810503419931_<88> · 857265323617659665666523789112730390055722246035147878268324046292327475353621945992284612087441063009_<102>

4·10²¹¹-9 =

3(9)₂₁₀1_<212>

= 31 · 67 · 1907 · 3169 · 395448671 · [8058615637588173282347575467486607487799336802402892318644677892935480193398494054573528576268437708581307652915930605834372668524365878972744353022629470411564500027782037497755941023184376431_<193>] SUBMIT/RESERVE

4·10²¹²-9 =

3(9)₂₁₁1_<213>

= 173 · 53299 · 42876259 · 5594493493318388089_<19> · 20909268680821569816065383_<26> · 5159197730271147217349752990276548876845323_<43> · 1696335989904637732334935062814384104990952215712079_<52> · 988289716009437275446318931091762783722563293522184539500353_<60>

4·10²¹³-9 =

3(9)₂₁₂1_<214>

= 13 · 53 · 83 · 46511 · 20879639623952929785933043_<26> · [72025121798108409233842522065435116582765026496376434367204039232590046757519564170865747537195002680126761039194558857562633016243332063395673539376739329935540307771477767135041_<179>] SUBMIT/RESERVE

4·10²¹⁴-9 =

3(9)₂₁₃1_<215>

= 7 · 5237 · 34159 · 135257 · 144512707 · 255054928321_<12> · 8581253024316133683871_<22> · 70366470719053751070081322438416837323_<38> · 71688355828884849285727325871272978657_<38> · 148016327942507378622392718611581342547343863899729003040292494919737429668418883589_<84>

4·10²¹⁵-9 =

3(9)₂₁₄1_<216>

= 79 · 163 · 180953387521507871_<18> · 171663743072338266564887148567062526733640502410291091642136206963746944559806932138235194935994380010451085187744180789748032714180965121610975677058994212875151283546675512614546605870601924173_<195>

4·10²¹⁶-9 =

3(9)₂₁₅1_<217>

= 97 · 131 · 907 · 971 · 1663 · 211153 · 2334911 · 62038633 · 785013631 · 10956056139051043916590023409_<29> · 9795426399848232136433658361416964220351_<40> · 16021201316639818235833142024355288672757596038111_<50> · 5206172069618515898494220381496970287426897628124942838563_<58>

4·10²¹⁷-9 =

3(9)₂₁₆1_<218>

= 153138923096637815337324392839746144304740150626975813_<54> · 261200739767238216403031051949070797540409290687764527939818984072695012732362463527871657040814436595996243277659214477992470411020857002428756477130421386528676107_<165> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs / 201.57 hours, 62.91 hours / Jun 27, 2009)

4·10²¹⁸-9 =

3(9)₂₁₇1_<219>

= 241 · 911 · 2719 · 8543 · 430741 · 11511113 · 34640887 · 1991149621_<10> · 56507163833737820197672277_<26> · 17549207512483876748254230582091_<32> · 57204838642635824463463028377398262905391805414776179409_<56> · 4042823160116869432898157597719278823120018001928691757871030681_<64>

4·10²¹⁹-9 =

3(9)₂₁₈1_<220>

= 13 · 839 · 82467488022247679727947415497469791627336296247529111727738703553530989716089_<77> · 4447048973020707963671116712924416171932599147193348095813779150964307930192515153073852957342284283845468243469970491789991587228466841917_<139> (Robert Backstrom / GGNFS-0.77.1-20050930-k8, Msieve 1.39 snfs / 250.14 hours, 69.87 hours / May 1, 2009)

4·10²²⁰-9 =

3(9)₂₁₉1_<221>

= 7 · 1304659 · 3513431 · 22141753 · 12373930450664908843_<20> · 26184862097599361168293556342151923_<35> · 159250894289275575513806398823291602495061691198560909053340523515792467_<72> · 1091142984253028074855253881145711454222019861072878061773867745555021996423_<76>

4·10²²¹-9 =

3(9)₂₂₀1_<222>

= 151 · 1481 · 43987 · 4520901491708664102216490947309660917_<37> · [8994532558579486158422478107666038614484587159727739139328919647030809782442864806400623275472680285761731651257616798378038630894161355548480113921301545753585088558529303159_<175>] (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=3686803269 for P37 / Nov 4, 2008) SUBMIT/RESERVE

4·10²²²-9 =

3(9)₂₂₁1_<223>

= 23 · 1012147 · 1975997557667018723564857673835915138808888432213897783622339442788448713477390141945784555010290007281551_<106> · 86956521739130434782608695652173913043478260869565217391304347826086956521739130434782608695652173913043478261_<110>

4·10²²³-9 =

3(9)₂₂₂1_<224>

= 178643 · 43436879 · 162340517 · 16794970462970350799_<20> · 109702385123835820767567110173_<30> · 17234279655112338870804656441415583958437362921504443164270233279512818351598712300614757732961924029188836166061510146445768957731218168949630287526465917_<155> (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=766755851 for P30 / Nov 2, 2008)

4·10²²⁴-9 =

3(9)₂₂₃1_<225>

= 677 · 12697 · 831043 · 54670303 · 1130429630033873669_<19> · 13815806123380392068501_<23> · 137192114622451866628779759037281403166279150792129455795886714703171863952755707_<81> · 478020270900772726633696605954219944463744295928749633602720299644323342149372542277_<84>

4·10²²⁵-9 =

3(9)₂₂₄1_<226>

= 13 · 3819696010750597_<16> · [80554134890918714843219524447740449092908749517089885811728036093553440552453642999186640832559817408954172518033321888039314154346974487636600248247435391010058951132692487160606983723560130154373003279605431_<209>] SUBMIT/RESERVE

4·10²²⁶-9 =

3(9)₂₂₅1_<227>

= 7 · 17 · 31 · 53 · 1372831668613383547870044381977_<31> · 23098824314409211398591501573261950597735785754115833490357410540732332572989623_<80> · 6451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451612903225806451613_<112>

4·10²²⁷-9 =

3(9)₂₂₆1_<228>

= 687707 · 371639483 · 1515901607401889_<16> · 1032437298303243697422891016343669463744635607971675243782255307384911511456734794313424356241113953389772942272639396030992371562774622041321632359649141989935854372089845229976535638443750909120399_<199>

4·10²²⁸-9 =

3(9)₂₂₇1_<229>

= 19 · 29 · 79 · 211 · 269 · 46091 · 141642068744903728734080380860557_<33> · 66720394280058370841709380872145894939733576500903_<50> · 7477136952660057610131641830487159799848955980602003638351811_<61> · 497100539534504959831516767690043182490203130774494939527873200330969211_<72>

4·10²²⁹-9 =

3(9)₂₂₈1_<230>

= 15889 · 2517464912832777393165082761659009377556800302095789539933287179809931399081125306816036251494744791994461577191767889735036817924350179369375039335389263012146768204418150922021524325004720246711561457612184530178110642582919_<226>

4·10²³⁰-9 =

3(9)₂₂₉1_<231>

= 43 · 61 · 181 · 96497 · 829756981 · 526124351571380221566747059280628606635611899137939746959670084844353770479041712935130444030667_<96> · 20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<116>

4·10²³¹-9 =

3(9)₂₃₀1_<232>

= 13 · 2314547 · 132938457370840899885676250122511097120815566800893519253526632940401595779948433837078137669138845610958728557982321245715767408349153286715582923004936902256766575788829387481737163986001447500393082401138405185849458962081_<225>

4·10²³²-9 =

3(9)₂₃₁1_<233>

= 7² · 503 · 15031 · 3834191 · 5583119 · 6544399742820969529407841_<25> · 41493132409708849993961614871982844651028070979055904408757610584660729478322747116357_<86> · 18574254102686318016620255264499950584015414667812075794431937770191719340776172937008476822441053131_<101>

4·10²³³-9 =

3(9)₂₃₂1_<234>

= 31973 · 4142689 · 239003509289_<12> · 11355474299929_<14> · 1112716981600764213152482188294069031739505203433494550274585709542453327227562242953305068656198974213787159493188989224792626290716028485740596542143218171612651035142995380661306955934162447457163_<199>

4·10²³⁴-9 =

3(9)₂₃₃1_<235>

= 252481430303_<12> · 14233541343533_<14> · 79171895467787_<14> · 9471209741101499_<16> · 506583805706942727181861_<24> · 50068989168351494592204398161861_<32> · 8325386712283388629555879931366734094616947743_<46> · 7029372274658901576417661765722869204475035431907927006123940343512211180833331_<79>

4·10²³⁵-9 =

3(9)₂₃₄1_<236>

= 89 · 8969 · 7320037 · [6845618370199814012032272076712772767630934418703621710039114246420282863920833086102615787903068092498408661422984249572692041882395687141353951273549450747022089805372888735688390820703505261170201237276401334459506235723_<223>] SUBMIT/RESERVE

4·10²³⁶-9 =

3(9)₂₃₅1_<237>

= 191 · 8248949 · 714997972759321_<15> · 22950984299621533137884728246439_<32> · 991811671612623385550841555017839892819_<39> · 28203043059484251487882072762043305121719614244673667495654922297_<65> · 553091130404568883549143340580413178416536717655739844547962308344784263446097_<78>

4·10²³⁷-9 =

3(9)₂₃₆1_<238>

= 13 · 165953750818291137381672377369_<30> · [1854084684287800831255026300758556765515624934165962534138511682886627257448422049835732162986643665214034880887015096418780059564585634647765688001378107892556545241259313889698967281895113354080477266785803_<208>] (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=2541232610 for P30 / Nov 3, 2008) SUBMIT/RESERVE

4·10²³⁸-9 =

3(9)₂₃₇1_<239>

= 7 · 223 · 5228659514109126391498531522208323958331928046131_<49> · 38250721711810786837816564744277352704880578237524903785562032046531313_<71> · 128122998078155028827674567584881486226777706598334401024983984625240230621396540679051889814221652786675208199871877_<117>

4·10²³⁹-9 =

3(9)₂₃₈1_<240>

= 53 · 631 · 1187 · 698329 · 933649 · 1329976841_<10> · 479027965831_<12> · 59130044921610281_<17> · [410248662169011989705848636961221308898383625361767931648016616227557884046203953870267331768654827457937774615779686111326495440635952851591496964480847618998172071516834583209375281_<183>] SUBMIT/RESERVE

4·10²⁴⁰-9 =

3(9)₂₃₉1_<241>

= 71 · 15565393 · 1809720710842767815340166917761946664738252406802091186211056001325106460010448078677115659855981539067984224299_<112> · 2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003_<121>

4·10²⁴¹-9 =

3(9)₂₄₀1_<242>

= 31 · 79 · 73907 · 1255369899787_<13> · 1799396021268199_<16> · 162791655526760799733_<21> · 179194028594672986043_<21> · 333403450873810189809523_<24> · 10059152711789417434542216086430824415874405255946405117791328448907306623634891193153641412019597412820975257872969429973094920761338111235277_<143>

4·10²⁴²-9 =

3(9)₂₄₁1_<243>

= 17 · 17417 · 14488801 · 65881399 · 2194247719_<10> · 45230755231_<11> · 39243438138434903_<17> · 82493772245610301788337353942271_<32> · 3835995654100008613560231526090607813_<37> · 1148303381753459263937532296032611816041798243095825917207326175575587070103921456048688063386346672790951369351782741_<118>

4·10²⁴³-9 =

3(9)₂₄₂1_<244>

= 13² · 1620523 · 18917917748103512524609_<23> · [772048803921848523968852685498834223050085320557341912320400746405229064342749644216420133766650676394900786195206701835499585828212522135978713138512042602470850389422223271355291768401998126112123579358309582877_<213>] SUBMIT/RESERVE

4·10²⁴⁴-9 =

3(9)₂₄₃1_<245>

= 7 · 23 · 67 · 6389 · 1255591 · 1846821995548619239_<19> · 873192647167017533911_<21> · 2445409000264004985346080302093575163_<37> · 5770283446250729246099452389095675049097_<40> · 171991496996710309484092016279706178541733683213_<48> · 118110223750443992209744996157769492200408400398154132891719193722281_<69>

4·10²⁴⁵-9 =

3(9)₂₄₄1_<246>

= 17573 · 11223067 · 95091449 · 504808921 · [42250712810402420322967365346732922952127222558971055343165327692752399042566749780487338910584435190462188668674797809565360337178848708454880332778225293301790980276068136455489626282787637003305399876101859141727969_<218>] SUBMIT/RESERVE

4·10²⁴⁶-9 =

3(9)₂₄₅1_<247>

= 19 · 59 · 1559 · 13003 · 252444851578307_<15> · 1132294115524073_<16> · 1476825069370893260540808898912662128916853503986650844219312049234362445397625242702793784200603323_<100> · 416974864952176659286921762537731373167739280498222726745880301034569498329218744986251818415970890775078491_<108>

4·10²⁴⁷-9 =

3(9)₂₄₆1_<248>

= 1453 · 276239 · 2105963 · 3990001 · 10954619018073076933_<20> · [1082650708444936370588129006278800375365298729450186163329662492739819969833160015348395383059316894261095415990648775201719065324307177693102648608028023898984116103322656136559772379401228227294332778180187_<208>] SUBMIT/RESERVE

4·10²⁴⁸-9 =

3(9)₂₄₇1_<249>

= 107 · 241 · 31536909893_<11> · 807932595751_<12> · 15473661967469980997_<20> · 9336975976397637344374611852234644275771_<40> · 67921085334223439767801410472062272050391919676586092874931678368742117499_<74> · 62038450235564933442218840576529640620666357432793040061287595166043436265300664996855027_<89>

4·10²⁴⁹-9 =

3(9)₂₄₈1_<250>

= 13 · [307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307692307_<249>] SUBMIT/RESERVE

4·10²⁵⁰-9 =

3(9)₂₄₉1_<251>

= 7 · 233 · 144593 · 10817778017_<11> · 41765060149_<11> · 323601526579_<12> · 9993023712544651881405293_<25> · 397869046237867494121907980309_<30> · 70950032524214449038440162186879_<32> · 3721939007586273114581978136315755902636906895389_<49> · 1104938488904480115616998648501886905041655534575552950019302930656654642413_<76>

4. References

• A101396 (On-Line Encyclopedia of Integer Sequences)