%I #10 Sep 08 2022 08:45:44
%S 83,97,337,65617,4294967377,18446744073709551697,
%T 340282366920938463463374607431768211537
%N Primes of the form 2^(2^k)+81.
%C Fermat primes of order 81, established by k=0,2,3,4,5,6 and 7.
%C The number of Fermat primes of order 81 exceeds the number of known Fermat primes by at least 2.
%C Next term >= 2^2^17 + 81. - _Vincenzo Librandi_, Jun 07 2016
%C Next term >= 2^2^29 + 81. - _Charles R Greathouse IV_, Jun 07 2016
%F Intersection of the primes and the set of Fermat numbers F(k,m) = 2^(2^k)+m of order m=81.
%e For n = 5, 2^32 + 81 = 4294967377 prime.
%t Select[Table[2^(2^n) + 81, {n, 0, 10}], PrimeQ] (* _Vincenzo Librandi_, Hun 07 2016 *)
%o (PARI) g(n,m) = for(x=0,n,y=2^(2^x)+m;if(ispseudoprime(y),print1(y",")))
%o (Magma) [a: n in [0..15] | IsPrime(a) where a is 2^(2^n)+81]; // _Vincenzo Librandi_, Jun 07 2016
%Y Cf. similar sequences listed in A273547.
%K nonn
%O 1,1
%A _Cino Hilliard_, Apr 30 2009, May 01 2009
%E Edited by _R. J. Mathar_, May 08 2009