Known 302-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 302-digit prime factors of googolduplex − 1

This is a list of known 302-digit prime factors of googolduplex − 1, i.e., 10^{10^(10^100)} − 1.

These numbers have the form 1 + 2k × 2^m × 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. 14 9098156604 1605363462 8482766204 7076368219 8706156612 7811495206 5405873771 1977755679 9817830324 1729736328 1250000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=133)
2. 61 1258337820 8030848068 6555213492 5945196070 8558743918 2779682650 5070646339 0050170452 4491837300 7364671713 1417896525 3925350177 2084468945 9447351964 6271597594 0227508544 9218750000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=27)
3. 71 7464813734 3063403129 4954664443 7059215494 1142407760 7513961896 1351573034 3351606279 6115875244 1406250000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)
4. 82 7180612553 0276748714 0869206996 2853565812 1109008789 0625000000 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)