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Generalized Fermat numbers 32n+1 div 2

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Factorizations and statistics of Generalized Fermat numbers GF(3,1) = 32n+1 div 2 and their factors k•2n+1.

Currently there are 120 factors known.

Count of factors according to difference n - m

n-m 2 3 4 5 6 7 8 9 10 11 12
Frequency 23 18 15 6 7 2 1 1 0 1 0

Factorizations

There are 15 General Fermat numbers:

m State Factorization
0 PR 2
1 PR 5
2 PR 41
3 FF 17 * 193
4 PR 21523361
5 PR 926510094425921
6 PR 1716841910146256242328924544641
7 FF 257 * 275201 * 138424618868737<15> * 3913786281514524929<19> * 153849834853910661121<21>
8 FF 12289 * 8972801 * 891206124520373602817<21>
9 FF 134382593 * 22320686081<11> * 12079910333441<14> * 100512627347897906177<21>
15 CF 65537 * 786433 * 3041503300933451777<19> * 951901181416549122049<21> * C<15584>
207 UF 2468256835981809063232453773836025757474103798450369795022913537<64>
34346 UF P<10341>
42290 UF P<12733>
16408814 UF P<4939547>
Generalized Fermat numbers
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