Known 44-digit prime factors of googolduplex − 1

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  2. Number Theory
  3. Known 44-digit prime factors of googolduplex − 1

This is a list of known 44-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. 1140 8855402054 0646134703 2884838400 0000000001 (Phil Carmody, k=9)
  2. 1144 4091796875 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  3. 1160 5152394622 5643157958 9843750000 0000000001 (Phil Carmody, k=319)
  4. 1195 9968566894 5312500000 0000000000 0000000001 (Dario Alpern, k=1567617)
  5. 1324 0356989263 8104527527 6563951124 4800000001 (Phil Carmody, k=51)
  6. 1464 2253004800 0000000000 0000000000 0000000001 (Dario Alpern, k=4468461)
  7. 1467 3941598482 3689225835 6428800000 0000000001 (Dario Alpern, k=6069)
  8. 1501 2011863291 2635803222 6562500000 0000000001 (Dario Alpern, k=644761)
  9. 1507 0252038457 7552882073 6000000000 0000000001 (Phil Carmody, k=2553)
  10. 1521 1807202738 7528179604 3846451200 0000000001 (Phil Carmody, k=3)
  11. 1533 3033246720 0000000000 0000000000 0000000001 (Phil Carmody, k=357)
  12. 1562 0571502950 0424861907 9589843750 0000000001 (Phil Carmody, k=687)
  13. 1584 3280000000 0000000000 0000000000 0000000001 (Dario Alpern, k=198041)
  14. 1589 8885685206 8919338545 9712000000 0000000001 (Dario Alpern, k=10521)
  15. 1766 4000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=69)
  16. 1823 0571291595 7678080000 0000000000 0000000001 (Phil Carmody, k=253)
  17. 1847 7439880371 0937500000 0000000000 0000000001 (Phil Carmody, k=31)
  18. 2249 3042051792 1447753906 2500000000 0000000001 (Dario Alpern, k=603793)
  19. 2457 6000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  20. 2886 2180229120 0000000000 0000000000 0000000001 (Phil Carmody, k=21)
  21. 3102 4000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1939)
  22. 3145 0960775911 8371232153 6000000000 0000000001 (Phil Carmody, k=333)
  23. 3239 6083200000 0000000000 0000000000 0000000001 (Dario Alpern, k=19773)
  24. 3288 1791412364 6914958953 8574218750 0000000001 (Dario Alpern, k=4519239)
  25. 3690 4000000000 0000000000 0000000000 0000000001 (Dario Alpern, k=4613)
  26. 3712 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=29)
  27. 4294 9672960000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  28. 4877 4837547843 9828310254 9442560000 0000000001 (Phil Carmody, k=197)
  29. 5300 7812500000 0000000000 0000000000 0000000001 (Phil Carmody, k=1357)
  30. 5479 2014486568 9600000000 0000000000 0000000001 (Dario Alpern, k=637863)
  31. 6047 3139527680 0000000000 0000000000 0000000001 (Phil Carmody, k=11)
  32. 6399 1576736563 2000000000 0000000000 0000000001 (Phil Carmody, k=291)
  33. 6485 1834634135 1424000000 0000000000 0000000001 (Phil Carmody, k=9)
  34. 6617 1361331913 5747581279 0732062720 0000000001 (Phil Carmody, k=261)
  35. 9348 9231766831 9183603818 6139648000 0000000001 (Phil Carmody, k=59)