A160027 Primes of the form 2^(2^k)+15.

17, 19, 31, 271, 65551, 4294967311

Offset: 1

Author

Cino Hilliard, Apr 30 2009

Keywords

• nonn

Comments

Fermat primes of order 15.

The number of Fermat primes of order 15 exceeds the number of known Fermat primes.

Terms given correspond to n= 0, 1, 2, 3, 4 and 5.

Next term >= 2^2^16 + 15. - Vincenzo Librandi, Jun 07 2016

Next term >= 2^2^17 + 15. - Charles R Greathouse IV, Jun 07 2016

Examples

			For k = 5, 2^32 + 15 = 4294967311 is prime.
		

Crossrefs

Cf. A019434 (order 1), A104067 (superset for order 13), A160028 (order 81).

Cf. similar sequences listed in A273547.

Programs

Magma

[a: n in [0..15] | IsPrime(a) where a is 2^(2^n)+15]; // Vincenzo Librandi, Jun 07 2016

Mathematica

Select[Table[2^(2^n) + 15, {n, 0, 10}], PrimeQ] (* Vincenzo Librandi, Jun 07 2016 *)

PARI

g(n,m) = for(x=0,n,y=2^(2^x)+m;if(ispseudoprime(y),print1(y",")))

Formula

Intersection of the primes and the set of Fermat numbers F(k,m) = 2^(2^k)+m of order m=15.

Extensions

Edited by R. J. Mathar, May 08 2009