Known 304-digit prime factors of googolduplex − 1

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2. Number Theory
3. Known 304-digit prime factors of googolduplex − 1

This is a list of known 304-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. 5597 1055019306 5531618230 9899671680 4046913324 2600801804 7775282376 1618517531 0993674609 0595416728 4976595936 7691690544 9816365496 9119829186 3131540335 0307584920 6329722708 7558631405 0832890055 4612291367 7187291417 6516908937 7619920318 5241591141 4127415023 5234874362 0780169294 4485694169 9981689453 1250000000 0000000001 (Phil Carmody, k=37)
2. 6219 8967865060 0870236565 8690249311 2145488772 1559741945 4545880184 8138051316 7215815942 7721468565 2466475472 6916922391 1500881624 8881575083 6004547762 7232012041 1585264719 1786672919 9886322021 4843750000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=59)
3. 7174 6481373430 6340312949 5466444370 5921549411 4240776075 1396189613 5157303433 5160627961 1587524414 0625000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=1)