Known 65-digit prime factors of googolduplex − 1

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  3. Known 65-digit prime factors of googolduplex − 1

This is a list of known 65-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. 10955 4865179717 3533850582 3165178298 9501953125 0000000000 0000000001 (Dario Alpern, k=394713)
  2. 11222 5199114445 3898240000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=24919)
  3. 11352 7243161826 1634866939 8576021194 4580078125 0000000000 0000000001 (Dario Alpern, k=16361)
  4. 11529 2150460684 6976000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  5. 12407 7091882954 1512307113 0381049442 8034871816 6351318359 3750000001 (Phil Carmody, k=3)
  6. 12657 6306355154 4524800000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=719503)
  7. 13738 1153909104 8743111463 7427533060 3847657659 0397440000 0000000001 (Phil Carmody, k=47)
  8. 14167 0994486089 3564108800 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  9. 14179 5703125000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=362997)
  10. 15016 6900075134 9760000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1067)
  11. 15065 0441649280 3383320589 4615698399 3986456530 6671368283 0950400001 (Phil Carmody, k=3)
  12. 18310 5468750000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  13. 18343 3463418318 3904607253 7431868755 1488000000 0000000000 0000000001 (Phil Carmody, k=69)
  14. 18859 7179662090 3098706811 8179195153 0613005161 2854003906 2500000001 (Phil Carmody, k=57)
  15. 19305 8520284862 9518830339 5166249012 1764470065 1969576960 0000000001 (Phil Carmody, k=129)
  16. 20180 6640625000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=4133)
  17. 20964 5389990453 5958234218 7331416229 6319043511 9147167776 7680000001 (Phil Carmody, k=171)
  18. 21896 3623046875 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=287)
  19. 22123 3424989477 1389712302 0800000000 0000000000 0000000000 0000000001 (Phil Carmody, k=183)
  20. 26102 8634402393 9481600000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1449)
  21. 29664 8237173964 8000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1349)
  22. 30502 8425679917 6997351442 0879360000 0000000000 0000000000 0000000001 (Phil Carmody, k=77)
  23. 34662 3210999906 4769717547 8272000000 0000000000 0000000000 0000000001 (Phil Carmody, k=7)
  24. 35324 3803944725 0705619257 7743875004 6254729789 4400000000 0000000001 (Phil Carmody, k=99)
  25. 37451 5617628488 8949190587 9367550369 3521022796 6308593750 0000000001 (Dario Alpern, k=8843)
  26. 41904 1749455516 4847073605 1523641266 7395748978 7220787200 0000000001 (Phil Carmody, k=7)
  27. 41943 0400000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  28. 43698 0374568960 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=1302303)
  29. 47022 9324228688 1280733723 5426530241 9662475585 9375000000 0000000001 (Dario Alpern, k=43371)
  30. 48704 4453620910 6445312500 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=6537)
  31. 48721 0750579833 9843750000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=204351)
  32. 52538 8935941883 9841175431 7707256234 3710160348 5643863677 9785156251 (Phil Carmody, k=813)
  33. 54931 6406250000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=9)
  34. 55751 8629963265 5785383929 5681620903 7649510400 0000000000 0000000001 (Phil Carmody, k=1)
  35. 60699 5737811892 0298629208 3722418134 2437097771 4796721373 9704320001 (Phil Carmody, k=967)
  36. 64865 1123046875 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=4251)
  37. 66408 2786653543 8581760000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=9)
  38. 67108 8640000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  39. 70983 6109111765 1264920107 5788596426 7188683152 1987915039 0625000001 (Dario Alpern, k=536337)
  40. 94283 8592529296 8750000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=6178987)
  41. 95780 9713041180 5364739668 9196894323 9761711951 3647513600 0000000001 (Phil Carmody, k=1)
  42. 97398 7840000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=23779)