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

17, 19, 31, 271, 65551, 4294967311

Offset

1,1

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

Links

Table of n, a(n) for n=1..6.

Formula

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

Example

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

Mathematica

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

Prog

(PARI) g(n, m) = for(x=0, n, y=2^(2^x)+m; if(ispseudoprime(y), print1(y", ")))
(Magma) [a: n in [0..15] | IsPrime(a) where a is 2^(2^n)+15]; // Vincenzo Librandi, Jun 07 2016

Crossrefs

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

Cf. similar sequences listed in A273547.

Sequence in context: A292237 A085106 A079592 * A288407 A286611 A144213

Adjacent sequences: A160024 A160025 A160026 * A160028 A160029 A160030

Keyword

nonn

Author

Cino Hilliard, Apr 30 2009

Extensions

Edited by R. J. Mathar, May 08 2009

Status

approved