### Peter Luschnymoderator

Discussion - For n>0, f(n) = 2^(2^n)+2^(2^(n-1))+1 has at least n+1 distinct prime factors, hence, the # of primes is infinite

http://www.cut-the-knot.org/proofs/InfinitudeOfPrimesViaPowersOfTwo.shtml

http://www.cut-the-knot.org/proofs/InfinitudeOfPrimesViaPowersOfTwo.shtml

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7 comments

Will do (in a couple of days). Still exploring. I'll point out that the first differences (1, 1, 1, 2, 2, 1, 2, 2, 4, 2, 2, ...) are of course the number of new factors at each step. Those new factors are the factors of http://oeis.org/A220294 . :)

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