[math-fun] Question about Fermat primes
20 Dec
2006
20 Dec
'06
noon
Define 2[0] :=1, 2[n+1] := 2^(2[n]) for n >= 0. Is it known whether any Fermat number of the form 2[n] + 1 is composite? The sequence begins 2, 3, 5, 17, 65537, 2^65536 + 1. Is 2^65536 + 1 known to be composite? --Dan
20 Dec
20 Dec
12:05 p.m.
On Wed, 20 Dec 2006, Daniel Asimov wrote:
Define 2[0] :=1, 2[n+1] := 2^(2[n]) for n >= 0.
Is it known whether any Fermat number of the form 2[n] + 1 is composite?
The sequence begins 2, 3, 5, 17, 65537, 2^65536 + 1.
Is 2^65536 + 1 known to be composite?
Wikipedia says "the only known Fermat primes are F_0..F_4.": http://en.wikipedia.org/wiki/Fermat_number
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