Known 262-digit prime factors of googolduplex − 1

  1. Alpertron
  2. Number Theory
  3. Known 262-digit prime factors of googolduplex − 1

This is a list of known 262-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 1279573647 1900812837 6964247527 1522015606 3540459369 9509122067 2905702348 5239258655 0526870199 6370989115 9746312450 0961839657 9753607511 5203857421 8750000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=651)
  2. 10 5696460800 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=63)
  3. 11 8341757557 6353070006 4587244946 2459030655 7365693151 9508361816 4062500000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=293)
  4. 13 7753244236 9868173400 8631295573 1915369374 8699342290 0642680684 0579502022 5923508405 6854248046 8750000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  5. 18 4467440737 0955161600 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
  6. 22 3247636177 5463409315 1918397502 8502997517 4211358535 1034998893 7377929687 5000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=283)
  7. 30 5873646937 4308371895 4503637140 0666673492 0745969828 0692618608 3850143277 0905071669 0107325594 6275075700 6688218098 1338024139 4042968750 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
  8. 52 3218105140 2015604625 4740065246 9311272541 8067120965 5512167015 5286086716 8762534465 0670533227 2417616111 3814030548 2819895884 1190198799 4012837796 2141116792 6593917319 0387158593 4189229851 0606209728 7745488063 7856926561 8239114701 2822329998 0163574218 7500000000 0000000001 (Phil Carmody, k=3)
  9. 61 5940607784 8180499513 8683715225 2267080043 6279880333 8657792000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=157)
  10. 82 8149876086 5114168140 7051531151 8746971383 7087326169 2395317368 2093620300 2929687500 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=43)
  11. 88 3636823753 5907795572 3895189752 9615735538 7922499009 2172007884 1093678945 8499088541 6281761912 6719751409 8930428817 2373813237 0225349876 4494025053 5266833961 3421405558 9836027751 4713700952 5977191515 2668952941 8945312500 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=9)