Known 109-digit prime factors of googolduplex − 1

  1. Alpertron
  2. Number Theory
  3. Known 109-digit prime factors of googolduplex − 1

This is a list of known 109-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. 103079215 1040000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  2. 112444385 8936636319 6201820200 0197674490 0410553303 5968103511 4952804361 8477469361 8618132353 5155200000 0000000001 (Phil Carmody, k=69)
  3. 120520353 3194242706 6564715692 5587195189 1652245337 0946264760 3200000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  4. 145519152 2836685180 6640625000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  5. 150589112 5402009600 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=107)
  6. 189995212 8530173793 6647902825 3116792555 2712305868 8000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=13)
  7. 211758236 8135750847 6708062516 9910490512 8479003906 2500000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  8. 220273663 0793438522 4698661344 8735061818 4039038680 2981690078 8665806666 4092211285 5672111796 5215334400 0000000001 (Phil Carmody, k=33)
  9. 318719115 1307836756 9772421908 8233570621 0198720319 9164020537 5473472788 9842914795 1923200000 0000000000 0000000001 (Phil Carmody, k=21)
  10. 419430400 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  11. 494271864 6337554513 5069433917 1209862609 1924933115 2736104399 9917455948 8892555236 8164062500 0000000000 0000000001 (Phil Carmody, k=657)
  12. 545237961 3964545392 0734571311 9885010743 6376088014 6053785783 9413680144 3840000000 0000000000 0000000000 0000000001 (Phil Carmody, k=79)
  13. 546812681 1957529810 9312555677 9405341338 2923577233 0310910644 2651602488 2497998439 8080587829 4255763456 0000000001 (Phil Carmody, k=1)
  14. 588922669 7619660414 9233700514 8345084587 1514439428 1584827588 4604845487 0469868183 1359863281 2500000000 0000000001 (Phil Carmody, k=501)
  15. 687194767 3600000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  16. 790273982 4640000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=23)
  17. 868440669 2798714656 7678238756 5159308899 5248849923 0423029593 1880059348 4722995200 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  18. 935361047 8917778676 5035829293 8421132579 7968275046 4000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  19. 961779215 6454575931 5797946679 2772971217 5732856849 2084741592 4072265625 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=381)