Known 93-digit prime factors of Googolplex - 10

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  2. Number Theory
  3. Known 93-digit prime factors of Googolplex − 10

This is a list of known 93-digit prime factors of googolplex − 10, i.e., 1010^100 − 10.

These numbers have the form 1 + 2k ∏i piei, where pi is a prime factor of 10100 − 1 and ei is zero or one.

The list of prime factors of 10100 − 1 is: 3, 3, 11, 41, 101, 251, 271, 3541, 5051, 9091, 21401, 25601, 27961, 60101, 7019801, 18 2521213001, 1410 3673319201, 7887 5943472201 and 168058 8011350901.

In the list you can see the prime factors, their discoverer and their corresponding value of k.

  1. 134 5191742692 0000000134 5191742692 0000000134 5191742692 0000000134 5191742692 0000000134 5191742693 (Phil Carmody, k=294)
  2. 137 0745004987 2846529397 9390846841 1657368996 1579341578 9806251888 3345522759 1144395035 0393829289 (Phil Carmody, k=116)
  3. 171 4353593519 2872698646 9847555111 0512769920 0000000171 4353593519 2872698646 9847555111 0512769921 (Phil Carmody, k=320)
  4. 171 5814690331 9457533333 3316175186 4300138758 0000000171 5814690331 9457533333 3316175186 4300138759 (Phil Carmody, k=13)
  5. 217 5960314267 8284442231 5798601834 7203625076 0000000217 5960314267 8284442231 5798601834 7203625077 (Dario Alpern, k=1142)
  6. 220 6211475893 5931409149 9598452964 8012968464 0491386834 5720089279 6422795763 9107066350 8504355079 (Phil Carmody, k=1)
  7. 272 9673242690 1961623197 6200738106 1145277914 7627826765 0390036087 9765653080 6503062526 6732539359 (Phil Carmody, k=21)
  8. 589 8217943949 0173818658 0470011330 1633274977 9009901579 9208042958 9183719648 1460110340 0643175969 (Phil Carmody, k=16)
  9. 733 9475800992 5474786875 1139407882 9033241622 9753524518 9722277207 5228310660 1385884097 8786765409 (Phil Carmody, k=336)
  10. 892 3178981154 5698408572 7225502843 0608809397 9999999107 6821018845 4301591427 2774497156 9391190603 (Phil Carmody, k=959)