Factorizations of 688...883

Table of contents

1. About 688...883
   • First ten terms
   • General term
2. Prime numbers of the form 688...883
   • Last update
   • Searched up to
   • Difficulty of search
   • Results
3. Factorizations of 688...883
   • Last update
   • Completed up to
   • Range
   • Results
4. References

1. About 688...883

First ten terms

63, 683, 6883, 68883, 688883, 6888883, 68888883, 688888883, 6888888883, 68888888883

General term

(62·10ⁿ-53)/9

2. Prime numbers of the form 688...883

Last update

Aug 9, 2009

Searched up to

n≤10000

Difficulty of search

17.98%

Results

1. (62·10²-53)/9 = 683 is prime.
2. (62·10³-53)/9 = 6883 is prime.
3. (62·10⁸-53)/9 = 688888883 is prime.
4. (62·10⁵⁰-53)/9 = 6(8)₄₉3_<51> is prime.
5. (62·10⁵⁶-53)/9 = 6(8)₅₅3_<57> is prime.
6. (62·10⁷²-53)/9 = 6(8)₇₁3_<73> is prime.
7. (62·10¹⁰⁸-53)/9 = 6(8)₁₀₇3_<109> is prime. (searched by Makoto Kamada / Dec 6, 2004) (certified by Makoto Kamada / PFGW / Jan 5, 2005)
8. (62·10¹³²-53)/9 = 6(8)₁₃₁3_<133> is prime. (searched by Makoto Kamada / Dec 6, 2004) (certified by Makoto Kamada / PFGW / Jan 5, 2005)
9. (62·10¹⁸²-53)/9 = 6(8)₁₈₁3_<183> is prime. (searched by Makoto Kamada / Dec 6, 2004) (certified by Makoto Kamada / PFGW / Jan 5, 2005)
10. (62·10¹¹⁰⁰-53)/9 = 6(8)₁₀₉₉3_<1101> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Makoto Kamada / PFGW / Jan 5, 2005)
11. (62·10¹³⁶⁸-53)/9 = 6(8)₁₃₆₇3_<1369> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Makoto Kamada / PFGW / Jan 5, 2005)
12. (62·10¹⁶⁰⁵-53)/9 = 6(8)₁₆₀₄3_<1606> is prime. (searched by Makoto Kamada / PFGW / Dec 17, 2004) (certified by Tyler Cadigan / PRIMO 2.2.0 beta 6 / Aug 10, 2006)
13. (62·10⁵¹³²-53)/9 = 6(8)₅₁₃₁3_<5133> is PRP. (Makoto Kamada / PFGW / Dec 21, 2004)

3. Factorizations of 688...883

Last update

Nov 5, 2009

Completed up to

• n≤100 / Jan 5, 2005
• n≤150 / Nov 4, 2009

Range

n≤150

Results

(62·10¹-53)/9 =

63

= 3² · 7

(62·10²-53)/9 =

683

= definitely prime number

(62·10³-53)/9 =

6883

= definitely prime number

(62·10⁴-53)/9 =

68883

= 3 · 22961

(62·10⁵-53)/9 =

688883

= 13 · 19 · 2789

(62·10⁶-53)/9 =

6888883

= 569 · 12107

(62·10⁷-53)/9 =

68888883

= 3 · 7 · 3280423

(62·10⁸-53)/9 =

688888883

= definitely prime number

(62·10⁹-53)/9 =

6888888883_<10>

= 373 · 18468871

(62·10¹⁰-53)/9 =

68888888883_<11>

= 3³ · 29 · 87980701

(62·10¹¹-53)/9 =

688888888883_<12>

= 13 · 23² · 100172879

(62·10¹²-53)/9 =

6888888888883_<13>

= 5209 · 1322497387_<10>

(62·10¹³-53)/9 =

68888888888883_<14>

= 3 · 7 · 17² · 47 · 149 · 263 · 6163

(62·10¹⁴-53)/9 =

688888888888883_<15>

= 8719 · 79010080157_<11>

(62·10¹⁵-53)/9 =

6888888888888883_<16>

= 389 · 1097 · 16143323551_<11>

(62·10¹⁶-53)/9 =

68888888888888883_<17>

= 3 · 22962962962962961_<17>

(62·10¹⁷-53)/9 =

688888888888888883_<18>

= 13 · 52991452991452991_<17>

(62·10¹⁸-53)/9 =

6888888888888888883_<19>

= 43661 · 44171 · 3572056093_<10>

(62·10¹⁹-53)/9 =

68888888888888888883_<20>

= 3² · 7 · 1093474426807760141_<19>

(62·10²⁰-53)/9 =

688888888888888888883_<21>

= 191 · 98401753 · 36653291221_<11>

(62·10²¹-53)/9 =

6888888888888888888883_<22>

= 197 · 541 · 64637669374150979_<17>

(62·10²²-53)/9 =

68888888888888888888883_<23>

= 3 · 68564641 · 334909694385521_<15>

(62·10²³-53)/9 =

688888888888888888888883_<24>

= 13 · 19 · 14347 · 194397702770991887_<18>

(62·10²⁴-53)/9 =

6888888888888888888888883_<25>

= 282479945017_<12> · 24387178666699_<14>

(62·10²⁵-53)/9 =

68888888888888888888888883_<26>

= 3 · 7 · 6977 · 7057 · 110913973 · 600696059

(62·10²⁶-53)/9 =

688888888888888888888888883_<27>

= 22713665380633_<14> · 30329269950251_<14>

(62·10²⁷-53)/9 =

6888888888888888888888888883_<28>

= 107 · 4063407109_<10> · 15844373310735941_<17>

(62·10²⁸-53)/9 =

68888888888888888888888888883_<29>

= 3² · 7654320987654320987654320987_<28>

(62·10²⁹-53)/9 =

688888888888888888888888888883_<30>

= 13 · 17 · 71 · 1553 · 28270084195195866702121_<23>

(62·10³⁰-53)/9 =

6888888888888888888888888888883_<31>

= 83 · 547 · 151734298559258361905880683_<27>

(62·10³¹-53)/9 =

68888888888888888888888888888883_<32>

= 3 · 7 · 331 · 479 · 20690280483782807985420427_<26>

(62·10³²-53)/9 =

688888888888888888888888888888883_<33>

= 199 · 4110800131859_<13> · 842111778597088663_<18>

(62·10³³-53)/9 =

6888888888888888888888888888888883_<34>

= 23 · 16142997765256123_<17> · 18553983130518527_<17>

(62·10³⁴-53)/9 =

68888888888888888888888888888888883_<35>

= 3 · 981349556125307_<15> · 23399371630256138723_<20>

(62·10³⁵-53)/9 =

688888888888888888888888888888888883_<36>

= 13 · 163 · 419 · 5122981 · 71594911 · 2115433130282533_<16>

(62·10³⁶-53)/9 =

6888888888888888888888888888888888883_<37>

= 1778033 · 1162547297_<10> · 3332719266703114444483_<22>

(62·10³⁷-53)/9 =

68888888888888888888888888888888888883_<38>

= 3³ · 7² · 13217671 · 28610237 · 137693342577403029323_<21>

(62·10³⁸-53)/9 =

688888888888888888888888888888888888883_<39>

= 29 · 109 · 7172791 · 30383409544818927068471236333_<29>

(62·10³⁹-53)/9 =

6888888888888888888888888888888888888883_<40>

= 125921944020413_<15> · 54707612263134552622230191_<26>

(62·10⁴⁰-53)/9 =

68888888888888888888888888888888888888883_<41>

= 3 · 173 · 439231979 · 302195414508567659038883479583_<30>

(62·10⁴¹-53)/9 =

688888888888888888888888888888888888888883_<42>

= 13² · 19 · 617 · 7604131 · 3652884427_<10> · 12518093427570952657_<20>

(62·10⁴²-53)/9 =

6888888888888888888888888888888888888888883_<43>

= 86877392549_<11> · 236845372261117_<15> · 334793870849570051_<18>

(62·10⁴³-53)/9 =

68888888888888888888888888888888888888888883_<44>

= 3 · 7 · 14461 · 900937 · 251789222144630940403467313285339_<33>

(62·10⁴⁴-53)/9 =

688888888888888888888888888888888888888888883_<45>

= 359 · 3023 · 634770279195516719900345161458427717019_<39>

(62·10⁴⁵-53)/9 =

6888888888888888888888888888888888888888888883_<46>

= 17 · 885201223 · 3201641299_<10> · 142983386841933139670128487_<27>

(62·10⁴⁶-53)/9 =

68888888888888888888888888888888888888888888883_<47>

= 3² · 2593 · 63352646911_<11> · 46595007843065431713874036587269_<32>

(62·10⁴⁷-53)/9 =

688888888888888888888888888888888888888888888883_<48>

= 13 · 1009 · 2383 · 3037 · 73602601941461_<14> · 98594493391281167300929_<23>

(62·10⁴⁸-53)/9 =

6888888888888888888888888888888888888888888888883_<49>

= 1543 · 44381 · 1664324917_<10> · 60443284400319324369978996307253_<32>

(62·10⁴⁹-53)/9 =

68888888888888888888888888888888888888888888888883_<50>

= 3 · 7 · 23599 · 2105543814697_<13> · 675493376658173_<15> · 97735177681028917_<17>

(62·10⁵⁰-53)/9 =

688888888888888888888888888888888888888888888888883_<51>

= definitely prime number

(62·10⁵¹-53)/9 =

6888888888888888888888888888888888888888888888888883_<52>

= 61 · 353627 · 71049884730142177_<17> · 4494801847221898674970552157_<28>

(62·10⁵²-53)/9 =

68888888888888888888888888888888888888888888888888883_<53>

= 3 · 1201 · 1619 · 75600448033216621217_<20> · 156211750787662605576532507_<27>

(62·10⁵³-53)/9 =

688888888888888888888888888888888888888888888888888883_<54>

= 13 · 1487 · 605261961533837_<15> · 79961000159771161_<17> · 736331297799904349_<18>

(62·10⁵⁴-53)/9 =

6888888888888888888888888888888888888888888888888888883_<55>

= 59 · 227 · 2313017449537_<13> · 2038569116819730619_<19> · 109085483649008156377_<21>

(62·10⁵⁵-53)/9 =

68888888888888888888888888888888888888888888888888888883_<56>

= 3² · 7 · 23 · 34610698093_<11> · 1373632113839435035489696536948475657616519_<43>

(62·10⁵⁶-53)/9 =

688888888888888888888888888888888888888888888888888888883_<57>

= definitely prime number

(62·10⁵⁷-53)/9 =

6888888888888888888888888888888888888888888888888888888883_<58>

= 837947203 · 8221149094149895848377083119029026568501940436561_<49>

(62·10⁵⁸-53)/9 =

68888888888888888888888888888888888888888888888888888888883_<59>

= 3 · 131² · 1338090027560338148299222828679154068117415241708697801_<55>

(62·10⁵⁹-53)/9 =

688888888888888888888888888888888888888888888888888888888883_<60>

= 13 · 19 · 47 · 18371 · 19753 · 2032559 · 80453575012214577292045939899286609253311_<41>

(62·10⁶⁰-53)/9 =

6888888888888888888888888888888888888888888888888888888888883_<61>

= 5807 · 19750517 · 60064640987045223926285021712313935973880003599657_<50>

(62·10⁶¹-53)/9 =

68888888888888888888888888888888888888888888888888888888888883_<62>

= 3 · 7 · 17 · 1709 · 2134981549_<10> · 203116173618272447419_<21> · 260375590921886092526756461_<27>

(62·10⁶²-53)/9 =

688888888888888888888888888888888888888888888888888888888888883_<63>

= 229 · 787 · 7732169 · 494353516335165059624262241580125720944474116571109_<51>

(62·10⁶³-53)/9 =

6888888888888888888888888888888888888888888888888888888888888883_<64>

= 2069 · 3825439 · 3934739 · 28234088972815587705097_<23> · 7834615715371670147103211_<25>

(62·10⁶⁴-53)/9 =

68888888888888888888888888888888888888888888888888888888888888883_<65>

= 3⁴ · 71 · 647 · 142555111 · 102980470961_<12> · 1261141640595630227114719008741571884709_<40>

(62·10⁶⁵-53)/9 =

688888888888888888888888888888888888888888888888888888888888888883_<66>

= 13 · 26393 · 579497069 · 3865616401391_<13> · 417584725733899_<15> · 2146359506019722698397047_<25>

(62·10⁶⁶-53)/9 =

6888888888888888888888888888888888888888888888888888888888888888883_<67>

= 29 · 157 · 28657163 · 51436637782069802237_<20> · 1026468823245519892064620574115840581_<37>

(62·10⁶⁷-53)/9 =

68888888888888888888888888888888888888888888888888888888888888888883_<68>

= 3 · 7 · 1481 · 44357633 · 225542503 · 13197422338212103202213_<23> · 16776020671643781281151109_<26>

(62·10⁶⁸-53)/9 =

688888888888888888888888888888888888888888888888888888888888888888883_<69>

= 5231 · 129517 · 79070197 · 38807119194910741_<17> · 331370206450897416159979345544057977_<36>

(62·10⁶⁹-53)/9 =

6888888888888888888888888888888888888888888888888888888888888888888883_<70>

= 40800169 · 20792268281939080627_<20> · 8120548188093404426046140088978702809058841_<43>

(62·10⁷⁰-53)/9 =

68888888888888888888888888888888888888888888888888888888888888888888883_<71>

= 3 · 51287 · 2157247 · 1574945037540922871_<19> · 131781775109571426194603295077816596697119_<42>

(62·10⁷¹-53)/9 =

688888888888888888888888888888888888888888888888888888888888888888888883_<72>

= 13 · 83 · 1973 · 138829 · 29614607982235139081_<20> · 78707200707824039829899075519246070957901_<41>

(62·10⁷²-53)/9 =

6888888888888888888888888888888888888888888888888888888888888888888888883_<73>

= definitely prime number

(62·10⁷³-53)/9 =

68888888888888888888888888888888888888888888888888888888888888888888888883_<74>

= 3² · 7 · 1399 · 16631 · 182047 · 15937307 · 1023810591613_<13> · 106208941064055737_<18> · 148968138408381071628661_<24>

(62·10⁷⁴-53)/9 =

688888888888888888888888888888888888888888888888888888888888888888888888883_<75>

= 136271238067760495311652321_<27> · 5055277244537404135576352891786464407693922725523_<49>

(62·10⁷⁵-53)/9 =

6888888888888888888888888888888888888888888888888888888888888888888888888883_<76>

= 14816318669204676246814930759_<29> · 464952802561358306481127059360693172990386061237_<48>

(62·10⁷⁶-53)/9 =

68888888888888888888888888888888888888888888888888888888888888888888888888883_<77>

= 3 · 1787 · 4007 · 97903172029119381571_<20> · 32755728848923300288820536641372331942228999433399_<50>

(62·10⁷⁷-53)/9 =

688888888888888888888888888888888888888888888888888888888888888888888888888883_<78>

= 13 · 17 · 19 · 23 · 7133053303466548856237912638504912027593411359732533510969370439016420979_<73>

(62·10⁷⁸-53)/9 =

6888888888888888888888888888888888888888888888888888888888888888888888888888883_<79>

= 393541 · 1029859 · 9208040947747687_<16> · 296134144780363111_<18> · 6233410087154544802515325092290701_<34>

(62·10⁷⁹-53)/9 =

68888888888888888888888888888888888888888888888888888888888888888888888888888883_<80>

= 3 · 7³ · 66947413886189396393478026131087355577151495518842457617967822049454702515927_<77>

(62·10⁸⁰-53)/9 =

688888888888888888888888888888888888888888888888888888888888888888888888888888883_<81>

= 107 · 45707 · 9861274892544445473573260897115212579_<37> · 14283992711523566845460794559071971673_<38> (Makoto Kamada / msieve 0.83)

(62·10⁸¹-53)/9 =

6888888888888888888888888888888888888888888888888888888888888888888888888888888883_<82>

= 233 · 16649 · 99901 · 332569 · 21670283 · 2466544315669749020570156001418395654869717278527528949637_<58>

(62·10⁸²-53)/9 =

68888888888888888888888888888888888888888888888888888888888888888888888888888888883_<83>

= 3² · 601 · 6959 · 146767 · 12469726984451398366975393120716668491092276113308865378877916574013779_<71>

(62·10⁸³-53)/9 =

688888888888888888888888888888888888888888888888888888888888888888888888888888888883_<84>

= 13 · 173 · 77412482604441049453_<20> · 3956842185185719793189387847208666389094800303739022726934439_<61>

(62·10⁸⁴-53)/9 =

6888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<85>

= 1423969 · 1527371 · 452370929 · 7001795415873796831703769577023972444363717762541536189537079273_<64>

(62·10⁸⁵-53)/9 =

68888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<86>

= 3 · 7 · 1123 · 123637 · 6671642647557059_<16> · 3541350351458451334561014845933392598567313503515632973592947_<61>

(62·10⁸⁶-53)/9 =

688888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<87>

= 2621 · 3545377463341816741_<19> · 74134383340183313187651217467528934812742155451666696925942190403_<65>

(62·10⁸⁷-53)/9 =

6888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<88>

= 3209 · 818603 · 24863434432389575156041_<23> · 105473901927475322169708028459122398806654333879675874569_<57>

(62·10⁸⁸-53)/9 =

68888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<89>

= 3 · 169866421 · 10597100729740439987680169_<26> · 12756552664003686031147049547720691901814509532962340389_<56>

(62·10⁸⁹-53)/9 =

688888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<90>

= 13 · 9811 · 3387621940172231_<16> · 4114871208943246244069_<22> · 387472931317328958422167807381830973464732293879_<48>

(62·10⁹⁰-53)/9 =

6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<91>

= 422445855460927997483_<21> · 33556672148916735676465680323_<29> · 485958565647795068214767734140618990559987_<42>

(62·10⁹¹-53)/9 =

68888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<92>

= 3³ · 7 · 68147 · 115741 · 456475591771_<12> · 5142932518265017644167_<22> · 19684528537336160259425730358782206832838792973_<47>

(62·10⁹²-53)/9 =

688888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<93>

= 4241 · 6163 · 26356560813489638111539324454224598971855218803304417252890780150671700990837069365201_<86>

(62·10⁹³-53)/9 =

6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<94>

= 17 · 18948525347_<11> · 21385767533307912170737843380813672786944484717236250941811611079590302210813696417_<83>

(62·10⁹⁴-53)/9 =

68888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<95>

= 3 · 29 · 97 · 8163157825440086371476346591881607878763939908625297889428710616055088148938131163513317797_<91>

(62·10⁹⁵-53)/9 =

688888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<96>

= 13 · 19 · 307 · 21997 · 34142503 · 332176439323_<12> · 1204375671856677769_<19> · 121716805655290953857_<21> · 248412642307416152548425223783_<30>

(62·10⁹⁶-53)/9 =

6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<97>

= 937 · 325667092395508138920526121_<27> · 95741090263364731118422293703_<29> · 235796494159920180143575982409661253093_<39>

(62·10⁹⁷-53)/9 =

68888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<98>

= 3 · 7 · 2389 · 17733347 · 42195566902351_<14> · 1835085050439015562773556017271007487632716806458061157715139913869059831_<73>

(62·10⁹⁸-53)/9 =

688888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<99>

= 857 · 12974534799727_<14> · 61955028758851972754801279504243920904718883494662475413412520183041869675512332997_<83>

(62·10⁹⁹-53)/9 =

6888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<100>

= 23 · 71 · 5593080827_<10> · 68812692541_<11> · 10960827636837620453177242450207825113387293750786123288655106395484748103293_<77>

(62·10¹⁰⁰-53)/9 =

68888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888883_<101>

= 3² · 2273 · 3367497134911711829148403426156762423077131978730453580138284640411051908338900566499921244018619_<97>

(62·10¹⁰¹-53)/9 =

6(8)₁₀₀3_<102>

= 13 · 23251728891511_<14> · 2279032808214089446136663768676020052224253621621430501322238301048550088272902351394681_<88>

(62·10¹⁰²-53)/9 =

6(8)₁₀₁3_<103>

= 461 · 971 · 5234821 · 608238767329856403231492542029_<30> · 4833403936780460989909255914993332444536391473076934345986077_<61> (Sinkiti Sibata / Msieve 1.42 for P30 x P61 / 1.08 hours / Oct 19, 2009)

(62·10¹⁰³-53)/9 =

6(8)₁₀₂3_<104>

= 3 · 7 · 44789 · 633596467349_<12> · 20489869764516817636841_<23> · 2091306858961996157313463337_<28> · 2697669937496756913918572268363832079_<37>

(62·10¹⁰⁴-53)/9 =

6(8)₁₀₃3_<105>

= 98429 · 7996135078594847_<16> · 875277944546341190501520024739394283833575466620771222205201228044176432994191333041_<84>

(62·10¹⁰⁵-53)/9 =

6(8)₁₀₄3_<106>

= 47 · 159137420172433_<15> · 127349145601808743_<18> · 7232408921599725180800609070286806649010270554344988224191954532781365131_<73>

(62·10¹⁰⁶-53)/9 =

6(8)₁₀₅3_<107>

= 3 · 113 · 11116067 · 16672547 · 1917905057249_<13> · 12503923897550914363542721328779_<32> · 45721761051315303484508810863903696812464253643_<47> (Makoto Kamada / Msieve 1.42 for P32 x P47 / Oct 19, 2009)

(62·10¹⁰⁷-53)/9 =

6(8)₁₀₆3_<108>

= 13 · 68437349759_<11> · 1347694514561_<13> · 17440928299500689_<17> · 32942123214583773758603846951008151653988352373057305386999827045681_<68>

(62·10¹⁰⁸-53)/9 =

6(8)₁₀₇3_<109>

= definitely prime number

(62·10¹⁰⁹-53)/9 =

6(8)₁₀₈3_<110>

= 3² · 7 · 17 · 418506778607605679698237_<24> · 153694105792841950610308704181948371281200956788920544448114129738875533761346121729_<84>

(62·10¹¹⁰-53)/9 =

6(8)₁₀₉3_<111>

= 147231400776881_<15> · 194515565010121_<15> · 1269732347255548376022933253021410325919_<40> · 18944458379391368190158730640812933874910357_<44> (Makoto Kamada / Msieve 1.42 for P40 x P44 / Oct 19, 2009)

(62·10¹¹¹-53)/9 =

6(8)₁₁₀3_<112>

= 61 · 1090221497_<10> · 3656180389_<10> · 28331984073498917684990407501443101367648701591939978165821491850382196930949575909973436891_<92>

(62·10¹¹²-53)/9 =

6(8)₁₁₁3_<113>

= 3 · 59 · 83 · 17404799 · 269419365580029272816469820042457166241927262577106032305707202073074092564490696377105633844112460687_<102>

(62·10¹¹³-53)/9 =

6(8)₁₁₂3_<114>

= 13 · 19 · 673 · 992223307 · 1063435579931_<13> · 3927503237224680430799420758807540851530004146936072957722555668752201408524687623994429_<88>

(62·10¹¹⁴-53)/9 =

6(8)₁₁₃3_<115>

= 23667079 · 291074740946649516355139934627711720947434573099996365791016664493699830422203301425109912756402633755052277_<108>

(62·10¹¹⁵-53)/9 =

6(8)₁₁₄3_<116>

= 3 · 7 · 191 · 148808921 · 219472177828399_<15> · 326879794344541_<15> · 56504568025147639_<17> · 28471899502391722241004336164699174066481470191138989340093_<59>

(62·10¹¹⁶-53)/9 =

6(8)₁₁₅3_<117>

= 163 · 2801 · 6679840150123809044106204970050911_<34> · 225882401828618911503033856318130927193899656636246403015114140502544786702431_<78> (Serge Batalov / Msieve v. 1.44 SVN130 snfs / 0.77 hours / Oct 20, 2009)

(62·10¹¹⁷-53)/9 =

6(8)₁₁₆3_<118>

= 4127 · 9804449 · 112984010357_<12> · 433521166879_<12> · 4608165234450536482751_<22> · 754286236810225754980964124189472516279084936145442818965837657_<63>

(62·10¹¹⁸-53)/9 =

6(8)₁₁₇3_<119>

= 3³ · 105854887097_<12> · 871160852814744599_<18> · 27667897063121991567755689674535080368402932407969012863115472346723885927831927099976343_<89>

(62·10¹¹⁹-53)/9 =

6(8)₁₁₈3_<120>

= 13² · 197 · 2851 · 254046508858892934445411_<24> · 28568392292101461750289899904624360936012816605149302252813563353697973068997920223361671_<89>

(62·10¹²⁰-53)/9 =

6(8)₁₁₉3_<121>

= 401 · 781400782447_<12> · 482405308064170957733903050853_<30> · 45574182575106151558337843101685805891290347589926937888473827782420994639913_<77> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=578454154 / Oct 18, 2009)

(62·10¹²¹-53)/9 =

6(8)₁₂₀3_<122>

= 3 · 7² · 23 · 547 · 135607 · 79958873 · 180710756350297_<15> · 508257390153719_<15> · 270003465424968056889793715401_<30> · 138525863661582180904788443560115323359340453_<45> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3755067476 / Oct 18, 2009)

(62·10¹²²-53)/9 =

6(8)₁₂₁3_<123>

= 29 · 132334703 · 1890862439_<10> · 75758258119039_<14> · 3240072375431047797243291826273_<31> · 386752213777628326595914391950321943476350166705076893653673_<60> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=3333449080 / Oct 18, 2009)

(62·10¹²³-53)/9 =

6(8)₁₂₂3_<124>

= 942637 · 1099236740404454597537_<22> · 8226127289692476371319524848640942547201787_<43> · 808198493369811057446035929143293359486982523771510861_<54> (Markus Tervooren / Oct 19, 2009)

(62·10¹²⁴-53)/9 =

6(8)₁₂₃3_<125>

= 3 · 370427 · 3404473 · 3712531 · 19489374341863_<14> · 417074852550523729196087_<24> · 603383466319532700227327603801040621865461260628911158942828904849881_<69>

(62·10¹²⁵-53)/9 =

6(8)₁₂₄3_<126>

= 13 · 17 · 167 · 59160769 · 315505274995743914984956426899490556694173360011994704697871343228215432290850910613819476890592283648873710547801_<114>

(62·10¹²⁶-53)/9 =

6(8)₁₂₅3_<127>

= 173 · 12758567 · 1078536023989751339_<19> · 78386413610940286599153430380427_<32> · 36916942752550184917976993403193051422617760309595195906576668662321_<68> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=932430793 for P32 / Oct 25, 2009)

(62·10¹²⁷-53)/9 =

6(8)₁₂₆3_<128>

= 3² · 7 · 4373075016167159_<16> · 5453325435685665821475301936816985008441_<40> · 45852211565333095184206412202116635585191607632222241319520518384375539_<71> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 5.22 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Oct 29, 2009)

(62·10¹²⁸-53)/9 =

6(8)₁₂₇3_<129>

= 172687 · 22708380787_<11> · 1664032005959132837_<19> · 105570284492663064648265419065370629172920373840590904570432516259965058815168484742069636127811_<96>

(62·10¹²⁹-53)/9 =

6(8)₁₂₈3_<130>

= 617 · 1861 · 5999535713349150818941463207411787713589519314295645314415829562092920615594941539846642190496290303211696617413381461221759_<124>

(62·10¹³⁰-53)/9 =

6(8)₁₂₉3_<131>

= 3 · 827 · 209767934901885224303739917497_<30> · 27526445632823402801555781212943586751_<38> · 4808760820477327944086801289662261340494201135301405931889669_<61> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=2956527615 for P30 / Oct 25, 2009) (Sinkiti Sibata / Msieve 1.42 snfs / 1 hour 55 min, 0.12 hours / Oct 29, 2009)

(62·10¹³¹-53)/9 =

6(8)₁₃₀3_<132>

= 13 · 19 · 199 · 10513 · 81899 · 2213322253356502762971124059611562807329201224533739_<52> · 7354433687504421692647292079401137480439947289067440673701943894427_<67> (Erik Branger / GGNFS, Msieve snfs / 4.98 hours / Oct 29, 2009)

(62·10¹³²-53)/9 =

6(8)₁₃₁3_<133>

= definitely prime number

(62·10¹³³-53)/9 =

6(8)₁₃₂3_<134>

= 3 · 7 · 107² · 907 · 2289278554181_<13> · 10629282830317033_<17> · 12982323887859053141836442058860516271892144890733669593843149985590879207139602590362457211468657_<98>

(62·10¹³⁴-53)/9 =

6(8)₁₃₃3_<135>

= 71 · 571 · 809 · 115867212779005898579_<21> · 181278225569940150941649364303135152541764323902040493556058134308053901415553431944915617174967727188376333_<108>

(62·10¹³⁵-53)/9 =

6(8)₁₃₄3_<136>

= 9909859 · 695155086352781496577185294855243539679917634437471702562961681784664028911903679849419541578632843200785085730169207138960189937_<129>

(62·10¹³⁶-53)/9 =

6(8)₁₃₅3_<137>

= 3² · 578104135471_<12> · 13240384418662045941713420453405509639020876312665516990963682494522248197955446359879964795876883961046756121198300812309397_<125>

(62·10¹³⁷-53)/9 =

6(8)₁₃₆3_<138>

= 13 · 379 · 9913338693829_<13> · 92016598929517614098722805673273505224217_<41> · 153278236964167015210420723223931171496148765949262538905208174029503679220103953_<81> (Erik Branger / GGNFS, Msieve snfs / 7.17 hours / Oct 30, 2009)

(62·10¹³⁸-53)/9 =

6(8)₁₃₇3_<139>

= 302791 · 77761357942084376053452253_<26> · 2598917760441813104579654155912123_<34> · 112577044979171717082980452895774413486489534296882540558515482893898057627_<75> (Sinkiti Sibata / Msieve 1.40 snfs / 9.15 hours / Oct 31, 2009)

(62·10¹³⁹-53)/9 =

6(8)₁₃₈3_<140>

= 3 · 7 · 5717 · 369255581 · 3244926862035919103_<19> · 12636939835943186520877_<23> · 37895513352668306014971617488552871788751731109376651729794467042011975520632901402429_<86>

(62·10¹⁴⁰-53)/9 =

6(8)₁₃₉3_<141>

= 179 · 363896476067_<12> · 477963635654411_<15> · 515803180255627489616321311_<27> · 3198418875632240379011137191604877_<34> · 13412325599365541821859014592804644094125132239526043_<53> (Makoto Kamada / GMP-ECM 6.2.3 B1=1e6, sigma=1421997904 for P34 / Oct 25, 2009)

(62·10¹⁴¹-53)/9 =

6(8)₁₄₀3_<142>

= 17 · 181 · 331 · 463 · 467 · 1021 · 30638681807566461462919885196044510986136259558136175448658999084484164495809884125398011160038816268609139303816519666065813149_<128>

(62·10¹⁴²-53)/9 =

6(8)₁₄₁3_<143>

= 3 · 38231 · 1897221955530729728636794936489_<31> · 316587764021525936138950181020917122053434327967423987470819925009163201030651339553471066974369806252970879_<108> (Sinkiti Sibata / GGNFS-0.77.1-20060513-k8 snfs / 23.85 hours on Core 2 Duo E6300 1.86GHz, Windows Vista / Oct 31, 2009)

(62·10¹⁴³-53)/9 =

6(8)₁₄₂3_<144>

= 13 · 23 · 292091 · 74147646382470298060152019_<26> · 106380602604511725887126673097311669286262122133484516816013481015102211017312688860991935996157347924033590073_<111>

(62·10¹⁴⁴-53)/9 =

6(8)₁₄₃3_<145>

= 157 · 853 · 13313 · 3863888312822091934139397758040765803700634631758344271862483198868677034331932153005183224132654679017865104976591506082488391526991571_<136>

(62·10¹⁴⁵-53)/9 =

6(8)₁₄₄3_<146>

= 3⁴ · 7 · 4444002491_<10> · 286154403651761_<15> · 20277487323458673341622013549649441909_<38> · 4711695927599623445659927588915785695966831005489230458903957349220464530717361011_<82> (Sinkiti Sibata / Msieve 1.40 snfs / 12.36 hours / Nov 2, 2009)

(62·10¹⁴⁶-53)/9 =

6(8)₁₄₅3_<147>

= 109 · 3546785903202467_<16> · 185105741159841547_<18> · 7988310259462790706409802227377510746398133_<43> · 1205071721783088836806307130889214158089504203258137865788043317649411_<70> (Jo Yeong Uk / GGNFS/Msieve v1.39 snfs / 6.61 hours on Core 2 Quad Q6700 / Nov 4, 2009)

(62·10¹⁴⁷-53)/9 =

6(8)₁₄₆3_<148>

= 193 · 219617649126448594971647_<24> · 162526668302257112767437795342548863672511004342028746709172958330130367000256356604124098219985106041988658778251712783373_<123>

(62·10¹⁴⁸-53)/9 =

6(8)₁₄₇3_<149>

= 3 · 2957 · 554396173829032040309_<21> · 80618323734034493160877932323_<29> · 15649311336687670483003413809050773543817_<41> · 11102668729253886618598862637858746443379270194714314067_<56> (Sinkiti Sibata / Msieve 1.40 gnfs for P41 x P56 / 7.06 hours / Oct 30, 2009)

(62·10¹⁴⁹-53)/9 =

6(8)₁₄₈3_<150>

= 13 · 19 · 822023080792100030591391359_<27> · 3392877775363584697805171775862103569436144633173086246241031082098722262200960904407656867216320866003121887562551735771_<121>

(62·10¹⁵⁰-53)/9 =

6(8)₁₄₉3_<151>

= 29 · 9210591331619_<13> · 661875852763457366391885680418340090691973432419556589889316841_<63> · 38966117144008027984903360062825590816642015961644316334865082860882091613_<74> (Dmitry Domanov / GGNFS/msieve snfs / 14.57 hours / Nov 4, 2009)

4. References

• A103045 (On-Line Encyclopedia of Integer Sequences)