Known 53-digit prime factors of googolduplex − 1

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  2. Number Theory
  3. Known 53-digit prime factors of googolduplex − 1

This is a list of known 53-digit prime factors of googolduplex − 1, i.e., 1010^(10^100) − 1.

These numbers have the form 1 + 2k × 2m × 5n, where 0 ≤ m ≤ 10100 and 0 ≤ m ≤ 10100.

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

  1. 105 5923348758 3696842193 6035156250 0000000000 0000000001 (Phil Carmody, k=1161)
  2. 115 2921504606 8469760000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  3. 115 5445352196 6934204101 5625000000 0000000000 0000000001 (Dario Alpern, k=24813)
  4. 116 5482325442 5600000000 0000000000 0000000000 0000000001 (Phil Carmody, k=53)
  5. 119 8888061873 0063000889 6021433757 5914561507 1641600001 (Phil Carmody, k=21)
  6. 121 6000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=19)
  7. 138 7778780781 4456755295 3958511352 5390625000 0000000001 (Phil Carmody, k=1)
  8. 141 0905195487 7431808000 0000000000 0000000000 0000000001 (Dario Alpern, k=3208027)
  9. 146 8658447265 6250000000 0000000000 0000000000 0000000001 (Phil Carmody, k=77)
  10. 171 2697231247 1518572699 4316333939 4163659295 9488000001 (Phil Carmody, k=3)
  11. 211 4004204496 3302042662 1474866986 0013670400 0000000001 (Phil Carmody, k=497)
  12. 307 2000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  13. 318 8915798091 3296341896 0571289062 5000000000 0000000001 (Phil Carmody, k=561)
  14. 337 7699720527 8720000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  15. 357 2718750000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=114327)
  16. 359 1189705028 9818777881 1494400000 0000000000 0000000001 (Dario Alpern, k=47529)
  17. 396 2218761444 0917968750 0000000000 0000000000 0000000001 (Phil Carmody, k=2659)
  18. 406 5758146820 6416275279 4800326228 1417846679 6875000001 (Phil Carmody, k=3)
  19. 503 8911135907 2118709493 9524136960 0000000000 0000000001 (Phil Carmody, k=159)
  20. 508 2197683525 8020344099 3500407785 1772308349 6093750001 (Phil Carmody, k=3)
  21. 523 6793518066 4062500000 0000000000 0000000000 0000000001 (Dario Alpern, k=686397)
  22. 544 4517870735 0154154139 9371890829 1383296000 0000000001 (Phil Carmody, k=1)
  23. 557 5186299632 6557853839 2956816209 0376495104 0000000001 (Phil Carmody, k=1)
  24. 560 7421875000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=2871)
  25. 605 1646778360 0091934204 1015625000 0000000000 0000000001 (Dario Alpern, k=207933)
  26. 654 7500000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=2619)
  27. 665 3024485492 3203945418 2086046785 1161956787 1093750001 (Dario Alpern, k=1534083)
  28. 794 7666063360 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=1515897)
  29. 837 5522497772 1809409558 7730407714 8437500000 0000000001 (Phil Carmody, k=943)