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Primes of the form 2^(2^k)+81.
5

%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