Known 172-digit prime factors of googolduplex − 1

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  3. Known 172-digit prime factors of googolduplex − 1

This is a list of known 172-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. 10 1225560377 2219186132 3711642293 4591824568 1851617931 2424476700 0383766345 5651084770 8217841543 7337544285 8732204892 5422014027 2185986248 6217430026 9159156946 6186740531 2000000001 (Phil Carmody, k=9)
  2. 10 4900915529 2268851873 7928538803 1094692649 4114341407 1628847382 5280000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=51)
  3. 10 8701038969 5706711783 4229986099 2000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=343)
  4. 10 8935338831 9664142021 4610701464 7157844737 9306401892 9126729912 1998933206 0148126680 5117106643 3765376000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=51)
  5. 10 9755347569 0883148533 8219105066 6175987833 2153856000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=769)
  6. 20 8000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=13)
  7. 21 2941032508 4785812156 2220934218 8828423918 3673888627 1297309283 1791202916 4394720478 4947003438 8797919597 8796450018 3579431646 5215320883 2000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  8. 27 0772049000 1817611584 1667409297 7684475832 2288493187 4317907185 1300983437 8269809432 0680378203 8794215940 1527410969 2808460897 4618419097 1689531579 6136856079 1015625000 0000000001 (Phil Carmody, k=73)
  9. 37 4609826037 9190677657 9166757517 9956689831 7771197965 3810309883 5155044608 6583718744 1443673236 7619036539 1792317345 6879474745 3757081514 5942367548 2112000000 0000000000 0000000001 (Phil Carmody, k=3)
  10. 42 3779827926 7085603471 7230650403 9139537176 5772355599 0955749305 4991928393 5948790851 2455567804 8216678400 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=31)
  11. 52 2255954073 5198034730 6803200000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=27)
  12. 61 1747293874 8616743790 9007274280 1333346984 1491939656 1385237216 7700286554 1810143338 0214651189 2550151401 3376436196 2676048278 8085937500 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  13. 65 2530446799 8524526710 2941092565 4755570116 4258068966 5477586364 5546972324 4597486227 2228961268 5386828161 4268198609 3521118164 0625000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  14. 71 2883420789 1312382507 7679077655 4847294051 4465621215 5352408558 7356371013 7816206831 9832818254 0059305101 9958811914 2586731721 0737277345 2546048000 0000000000 0000000000 0000000001 (Phil Carmody, k=613)
  15. 78 9842187514 1789002343 8520762752 8242391713 2155041183 3440733233 1520000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)