Known 362-digit prime factors of googolduplex − 1

1. Alpertron
2. Number Theory
3. Known 362-digit prime factors of googolduplex − 1

This is a list of known 362-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. 30 4553020477 8779067928 8294669966 5225618834 2619641314 6979272723 8548737203 7467159368 7188889148 6694114347 5597509269 3010750159 2248561093 2352043336 8476292114 1573412645 9799682834 0802591905 8480189256 8209143392 6169368532 6165935665 6497303628 1394058732 9852860420 9423065185 5468750000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=3)
2. 46 3273935126 0170785353 6010993904 1114577492 0420175555 4787329195 3432315432 2675454401 3249860712 7865515743 3955556222 4162331403 6061971559 1434703627 7730586429 2417256150 7988238672 1028853312 9590540925 1719962378 2879954144 9240435151 2850817223 9745311374 3501099466 8482808833 6871587671 3395118713 3789062500 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000001 (Phil Carmody, k=49)
3. 70 3857338150 3089187447 7605219641 7518031478 3914278640 6336108864 4698409590 7512955934 5450790696 8886708590 3840351806 0324363258 5233429766 1070266269 7466951189 1481770918 9064909812 6515195699 9664020146 0046681235 9709111335 4015308045 0414968997 7049114379 0568456120 4669138168 7774806576 8356184364 4134359200 6959860969 0765533830 6142311921 5760380029 6783447265 6250000000 0000000001 (Phil Carmody, k=9)