A123646 Smallest generalized Fermat prime of the form a^(2^n) + b^(2^n), where bases a,b>1; or -1 if no such prime exists.

5, 13, 97, 2070241, 4338014017, 3512911982806776822251393039617, 4457915690803004131256192897205630962697827851093882159977969339137, 1638935311392320153195136107636665419978585455388636669548298482694235538906271958706896595665141002450684974003603106305516970574177405212679151205373697500164072550932748470956551681

Offset: 0

Author

Alexander Adamchuk, Nov 14 2006

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Generalized Fermat Number.

Crossrefs

Cf. A000215 (Fermat numbers: 2^(2^n) + 1), A019434 (Fermat primes of the form 2^(2^n) + 1).

Cf. A111635 (allows one of a,b to be 1).

Programs

Mathematica

Do[f=Min[Select[Take[Union[ Flatten[ Table[ i^(2^n) + j^(2^n), {i, 2, 300}, {j, 2, 300} ] ] ],500],PrimeQ]];Print[{n,f}],{n,0,7}]

Extensions

Offset corrected by Jeppe Stig Nielsen, Nov 14 2019