Known 35-digit prime factors of Googolplex - 1

  1. Alpertron
  2. Number Theory
  3. Known 35-digit prime factors of Googolplex − 1

This is a list of known 35-digit prime factors of googolplex − 1, i.e., 1010^100 − 1.

These numbers have the form 1 + 2k × 2m × 5n, where 0 ≤ m ≤ 100 and 0 ≤ n ≤ 100.

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

  1. 10808 6391056891 9040000000 0000000001 (Phil Carmody, k=3)
  2. 10986 2412500660 8664989471 4355468751 (Dario Alpern, k=24159)
  3. 11138 6718750000 0000000000 0000000001 (Dario Alpern, k=5703)
  4. 11605 6878683004 4007717928 9600000001 (Phil Carmody, k=3)
  5. 12288 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  6. 12676 5060022822 9401496703 2053760001 (Phil Carmody, k=1)
  7. 13411 0353817600 0000000000 0000000001 (Phil Carmody, k=1249)
  8. 14293 6511610880 0000000000 0000000001 (Phil Carmody, k=13)
  9. 14560 0000000000 0000000000 0000000001 (Phil Carmody, k=91)
  10. 15113 5027408599 8535156250 0000000001 (Dario Alpern, k=4057)
  11. 15136 0000000000 0000000000 0000000001 (Phil Carmody, k=473)
  12. 16132 1622726973 1462001800 5371093751 (Phil Carmody, k=1419)
  13. 16355 3280000000 0000000000 0000000001 (Dario Alpern, k=3993)
  14. 17053 0256582424 0446090698 2421875001 (Phil Carmody, k=3)
  15. 18310 5468750000 0000000000 0000000001 (Phil Carmody, k=3)
  16. 18915 1184349560 8320000000 0000000001 (Phil Carmody, k=21)
  17. 19036 2334251403 8085937500 0000000001 (Phil Carmody, k=511)
  18. 21110 6232532992 0000000000 0000000001 (Phil Carmody, k=3)
  19. 24354 0256329388 8380928000 0000000001 (Dario Alpern, k=16899)
  20. 26074 2184960000 0000000000 0000000001 (Dario Alpern, k=397861)
  21. 27809 0095804809 2160000000 0000000001 (Dario Alpern, k=8093487)
  22. 28037 5465082880 0000000000 0000000001 (Phil Carmody, k=51)
  23. 29491 2000000000 0000000000 0000000001 (Phil Carmody, k=9)
  24. 33971 7551816704 0000000000 0000000001 (Dario Alpern, k=2531093)
  25. 34033 2296825867 6029059834 0920344577 (Dario Alpern, k=1718239)
  26. 35258 9971456000 0000000000 0000000001 (Phil Carmody, k=2627)
  27. 38866 9596846226 5609326485 5716331521 (Dario Alpern, k=49057)
  28. 39813 1200000000 0000000000 0000000001 (Phil Carmody, k=243)
  29. 42333 6345600000 0000000000 0000000001 (Dario Alpern, k=16149)
  30. 46611 9241854550 5748197518 0820480001 (Dario Alpern, k=120489)
  31. 47697 3000294400 0000000000 0000000001 (Dario Alpern, k=4548769)
  32. 47867 9687500000 0000000000 0000000001 (Dario Alpern, k=61271)
  33. 54043 1955284459 5200000000 0000000001 (Phil Carmody, k=3)
  34. 65865 1445502935 0400000000 0000000001 (Phil Carmody, k=117)
  35. 70368 7441776640 0000000000 0000000001 (Phil Carmody, k=1)
  36. 72662 8800000000 0000000000 0000000001 (Dario Alpern, k=454143)
  37. 74506 9451673600 0000000000 0000000001 (Dario Alpern, k=6939)
  38. 85006 4679980278 0151367187 5000000001 (Dario Alpern, k=3651)
  39. 91878 3622907118 1727766937 6000000001 (Phil Carmody, k=19)
  40. 96845 4063869751 4598400000 0000000001 (Phil Carmody, k=21)
  41. 97656 2500000000 0000000000 0000000001 (Phil Carmody, k=1)