Known 43-digit prime factors of googolduplex − 1

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  2. Number Theory
  3. Known 43-digit prime factors of googolduplex − 1

This is a list of known 43-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. 104 3528318405 1513671875 0000000000 0000000001 (Dario Alpern, k=7003)
  2. 105 2249033392 5732336642 5559040000 0000000001 (Phil Carmody, k=17)
  3. 114 1071319580 0781250000 0000000000 0000000001 (Phil Carmody, k=2393)
  4. 120 8925819614 6291747061 7600000000 0000000001 (Phil Carmody, k=1)
  5. 121 6000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=19)
  6. 129 0240000000 0000000000 0000000000 0000000001 (Phil Carmody, k=63)
  7. 150 1464843750 0000000000 0000000000 0000000001 (Phil Carmody, k=123)
  8. 155 4312234475 2191565930 8433532714 8437500001 (Phil Carmody, k=7)
  9. 165 1507200000 0000000000 0000000000 0000000001 (Phil Carmody, k=63)
  10. 172 3178491334 1689947020 2119389184 0000000001 (Dario Alpern, k=556789)
  11. 173 5680000000 0000000000 0000000000 0000000001 (Phil Carmody, k=339)
  12. 204 0062320599 6867323166 7200000000 0000000001 (Phil Carmody, k=27)
  13. 233 0481131520 0000000000 0000000000 0000000001 (Dario Alpern, k=55563)
  14. 266 4535259100 3756970167 1600341796 8750000001 (Phil Carmody, k=3)
  15. 362 6777458843 8875241185 2800000000 0000000001 (Phil Carmody, k=3)
  16. 371 9247132494 2744104191 6608810424 8046875001 (Phil Carmody, k=67)
  17. 405 1391601562 5000000000 0000000000 0000000001 (Dario Alpern, k=33189)
  18. 415 3445635951 7421568000 0000000000 0000000001 (Dario Alpern, k=4721921)
  19. 446 4804063288 2239146621 7739124736 0000000001 (Dario Alpern, k=45083)
  20. 479 7811916800 0000000000 0000000000 0000000001 (Dario Alpern, k=91511)
  21. 485 6970068532 4945981440 0000000000 0000000001 (Dario Alpern, k=16851)
  22. 498 4604984193 4345233892 7647605129 2160000001 (Phil Carmody, k=3)
  23. 531 2662293228 3508654080 0000000000 0000000001 (Phil Carmody, k=9)
  24. 537 4703881695 0068183040 0000000000 0000000001 (Dario Alpern, k=74589)
  25. 547 3702368991 8352510156 8000000000 0000000001 (Dario Alpern, k=29673)
  26. 547 9989795276 1966735124 5880126953 1250000001 (Dario Alpern, k=19281)
  27. 674 4827330112 4572753906 2500000000 0000000001 (Dario Alpern, k=4526377)
  28. 681 0296326875 6866455078 1250000000 0000000001 (Phil Carmody, k=117)
  29. 723 4375000000 0000000000 0000000000 0000000001 (Phil Carmody, k=463)
  30. 781 5970093361 1020445823 6694335937 5000000001 (Phil Carmody, k=11)
  31. 798 9484629433 7185099720 9548950195 3125000001 (Dario Alpern, k=56221)
  32. 824 2790400000 0000000000 0000000000 0000000001 (Dario Alpern, k=5031)
  33. 824 6337208320 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  34. 840 2601480484 0087890625 0000000000 0000000001 (Dario Alpern, k=7048613)
  35. 850 7059173023 4615865843 6518579420 5286400001 (Phil Carmody, k=1)
  36. 928 4550294640 3520617434 3168000000 0000000001 (Phil Carmody, k=3)
  37. 952 0595519809 4599396735 1806925796 8025600001 (Phil Carmody, k=573)
  38. 967 0901768700 9997619200 0000000000 0000000001 (Dario Alpern, k=6871589)
  39. 980 0132167323 0277477451 8869403492 4489932801 (Phil Carmody, k=9)