1,1

All terms are primes. Largest currently known prime of the form (2^n + 1)/257 is (256^23029 + 1)/257 found by Donovan Johnson 03/2005. The only currently known prime of the form (2^n + 1)/65537 is (65536^239 + 1)/65537.

H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.

H. Lifchitz, Mersenne and Fermat primes field

Do[n=8*Prime[k]; f=2^n+1; If[PrimeQ[f/257], Print[{n, n/8}]], {k, 1, 2570}]

Cf. A000978 = numbers n such that (2^n + 1)/3 is prime. Cf. A057182 = numbers n such that (16^n + 1)/17 is a prime.

Sequence in context: A121228 A012173 A009143 this_sequence A139079 A049506 A069524

Adjacent sequences: A127314 A127315 A127316 this_sequence A127318 A127319 A127320

bref,hard,more,nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Mar 29 2007