A112245 Numbers k such that 65537*2^k+1 is prime.

287, 1695, 81359, 512895

Offset: 1

Author

T. D. Noe, Aug 30 2005, Aug 26 2007

Keywords

• nonn
• hard

Comments

Note that 65537=2^16+1 is the largest known Fermat prime. These n yield provable primes. The primes are the smallest numbers in classes 303, 1711 and 81375 of the phi iteration (see A007755).

Jacques Molne found 512895. The corresponding provable prime is the smallest number in class 512911 of the Phi iteration.

Crossrefs

Cf. A002253, A002254, A002259, A053345 (F*2^n+1 is prime, where F is a Fermat prime).

Programs

PARI

is(n)=ispseudoprime(65537*2^n+1) \\ Charles R Greathouse IV, Jun 13 2017