[math-fun] Question about Fermat primes

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