A160028 Primes of the form 2^(2^k)+81.

83, 97, 337, 65617, 4294967377, 18446744073709551697, 340282366920938463463374607431768211537

Offset: 1

Author

Cino Hilliard, Apr 30 2009, May 01 2009

Keywords

• nonn

Comments

Fermat primes of order 81, established by k=0,2,3,4,5,6 and 7.

The number of Fermat primes of order 81 exceeds the number of known Fermat primes by at least 2.

Next term >= 2^2^17 + 81. - Vincenzo Librandi, Jun 07 2016

Next term >= 2^2^29 + 81. - Charles R Greathouse IV, Jun 07 2016

Examples

			For n = 5, 2^32 + 81 = 4294967377 prime.
		

Crossrefs

Cf. similar sequences listed in A273547.

Programs

Magma

[a: n in [0..15] | IsPrime(a) where a is 2^(2^n)+81]; // Vincenzo Librandi, Jun 07 2016

Mathematica

Select[Table[2^(2^n) + 81, {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=81.

Extensions

Edited by R. J. Mathar, May 08 2009