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

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

Offset

1,1

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

Links

Table of n, a(n) for n=1..7.

Formula

Intersection of the primes and the set of Fermat numbers F(k,m) = 2^(2^k)+m of order m=81.

Example

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

Mathematica

Select[Table[2^(2^n) + 81, {n, 0, 10}], PrimeQ] (* Vincenzo Librandi, Hun 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)+81]; // Vincenzo Librandi, Jun 07 2016

Crossrefs

Cf. similar sequences listed in A273547.

Sequence in context: A220121 A335916 A158719 * A115258 A316970 A139965

Adjacent sequences: A160025 A160026 A160027 * A160029 A160030 A160031

Keyword

nonn

Author

Cino Hilliard, Apr 30 2009, May 01 2009

Extensions

Edited by R. J. Mathar, May 08 2009

Status

approved