Known 92-digit prime factors of Googolplex + 10

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  2. Number Theory
  3. Known 92-digit prime factors of Googolplex + 10

This is a list of known 92-digit prime factors of googolplex + 10, i.e., 1010^100 + 10.

These numbers have the form 1 + 2k ∏i piei, where pi is a prime factor of 10100 − 1 and ei is zero or one.

The list of prime factors of 10100 − 1 is: 3, 3, 11, 41, 101, 251, 271, 3541, 5051, 9091, 21401, 25601, 27961, 60101, 7019801, 18 2521213001, 1410 3673319201, 7887 5943472201 and 168058 8011350901.

In the list you can see the prime factors, their discoverer and their corresponding value of k.

  1. 10 1394757845 4569299052 1589034158 9318283549 3465122856 7929634998 8034421898 8123911312 2783406397 (Patrick Demichel, k=157766)
  2. 10 2044019574 1533626795 6880688463 8051250252 0000000010 2044019574 1533626795 6880688463 8051250253 (Patrick Demichel, k=153814)
  3. 10 3382048833 0547327079 7997168095 2703904266 2178217832 1203831011 2725544901 5818950273 4882122089 (David Broadhurst, k=76)
  4. 10 4895766919 7493663288 9422667780 5055417926 4119758153 5889567619 2649177908 6393740072 8398483503 (Patrick Demichel, k=757039)
  5. 12 2015607073 6481256563 6732500303 3780802328 3027903042 1012295980 6546646490 6295402750 9247100727 (David Broadhurst, k=1)
  6. 12 5447441730 0971917212 6755791807 1963926931 8475804890 6971636851 9447722090 8279986929 0439731811 (Patrick Demichel, k=1017055)
  7. 13 1229025555 3924693241 7920706663 0741953994 8597839746 2631185822 2522532974 9322866929 9339793729 (Patrick Demichel, k=134176)
  8. 13 2738962289 4145436398 7289392480 0540017809 1667359957 3680044800 5208480274 8707671710 0168975731 (David Broadhurst, k=35)
  9. 14 2123896706 7034267016 8456583967 4837960980 2574257439 9549639280 9608524442 5882326541 7412218407 (Patrick Demichel, k=286531)
  10. 16 3362783465 8581817688 8805144745 1313021246 1188118828 2174664653 9769936500 7617025933 2501140059 (Phil Carmody, k=2891)
  11. 16 6791255490 1105425585 9928242326 5622436640 2485173696 4306081810 3590599265 7443068646 8107610321 (Phil Carmody, k=840)
  12. 16 9823137473 1403205474 6712067896 9522919506 7257836786 2565300703 8661042243 9454231127 6780756277 (Patrick Demichel, k=475586)
  13. 17 8075345134 7717667296 4294633443 8221944473 1022495636 7052849515 8740162915 3272137824 9244440093 (Patrick Demichel, k=1570234)
  14. 19 5204490166 6533864561 3531183393 7450199222 7077000126 8127490059 3610864668 6454183286 4527199331 (Phil Carmody, k=685)
  15. 21 2614275859 6373863111 7622238465 7561699373 1313188386 1301087494 7687051476 6309050100 8874887739 (Patrick Demichel, k=583291)
  16. 22 9455965513 3526536245 6750550790 7175876500 1483494890 7972470645 5010031113 5267055922 8659371369 (Patrick Demichel, k=2819188)
  17. 23 1685291331 7370517951 4553817228 1513944246 2760988542 8924302812 0131506471 1792828708 4274932767 (David Broadhurst, k=1)
  18. 23 3431011292 5174524578 2704409731 8427176323 5159902465 8271108850 0334427020 7544507289 3587078767 (Patrick Demichel, k=101397)
  19. 23 6239451293 9930935556 8819248912 0735336247 5265923114 0973528203 5196858647 3553325821 6001259339 (Patrick Demichel, k=145141)
  20. 26 1311219424 1673306799 0394884762 8127490065 9717593926 1593625524 1390900699 0677290862 7845083967 (Patrick Demichel, k=94411)
  21. 26 3515240452 8936146473 6914573358 1772974480 5742574283 7772666195 4678720731 1171999100 7515548739 (Patrick Demichel, k=262103)
  22. 27 8113212245 3067729111 4766598699 4900398434 1858232165 6254980107 4925961249 2908366561 6758630573 (Phil Carmody, k=1382)
  23. 29 7790851935 6949366543 1603049745 8607803869 2326537491 4535685585 5377170978 0723487775 3718733653 (Patrick Demichel, k=1055774)
  24. 30 2391856996 7416996039 6042627878 9660070209 5643564386 6748292640 3060560396 0399063522 5303634567 (Phil Carmody, k=251)
  25. 31 8858419543 2868247365 9743541218 2213976048 4476950069 4381469505 7345197403 5266591180 6690926087 (Paul Leyland, k=38041)
  26. 32 9493014312 1747581921 6460913008 4973599397 4649782687 4843231657 6397364576 1811130353 9623382053 (Patrick Demichel, k=352574)
  27. 34 1432819172 3254988118 8122226209 3798420668 6930693103 4502126103 0185681188 1191533140 0729113739 (David Broadhurst, k=1)
  28. 34 6488296322 1861017654 9220428573 2254999044 7458401251 9029895104 9319418872 1762027355 9713400263 (Patrick Demichel, k=2021921)
  29. 43 5313292241 8725099645 1249547221 9521912394 1289387859 4023904426 0014487460 9960159406 0811300211 (Phil Carmody, k=595)
  30. 49 3000288359 1026474743 9031098050 7708970614 5437623685 8652474818 2937045405 6047959947 3425864277 (Patrick Demichel, k=1780558)
  31. 53 5824265092 1801422222 2216863979 5713004208 0000000053 5824265092 1801422222 2216863979 5713004209 (Patrick Demichel, k=1901864)
  32. 56 0506372902 4252623298 9728309152 6727380772 7404016933 3102356025 1656640176 2324292275 4131397651 (Patrick Demichel, k=45275)
  33. 69 8435877278 9478760159 3632482366 7409169688 0000000069 8435877278 9478760159 3632482366 7409169689 (Phil Carmody, k=748)
  34. 74 8721088141 0516239948 0514991577 0089828406 5403110420 2993643815 2166617131 9546602386 7825655877 (Patrick Demichel, k=120658)
  35. 75 0408844717 1708136475 9627234623 8150853557 3267326807 7141517984 4975463208 6359907891 1418180291 (Paul Leyland, k=32545)

Phil Carmody is organizing a distributed computing project in order to find more factors of Googolplex + 10. If you like these pages I would appreciate that you donate some idle cycles of your computer. You will be cited as the discoverer of the factors you find.