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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.
0

%I #8 Nov 14 2019 12:59:20

%S 5,13,97,2070241,4338014017,3512911982806776822251393039617,

%T 4457915690803004131256192897205630962697827851093882159977969339137,

%U 1638935311392320153195136107636665419978585455388636669548298482694235538906271958706896595665141002450684974003603106305516970574177405212679151205373697500164072550932748470956551681

%N 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.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GeneralizedFermatNumber.html">Generalized Fermat Number</a>.

%t 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}]

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

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

%K nonn

%O 0,1

%A _Alexander Adamchuk_, Nov 14 2006

%E Offset corrected by _Jeppe Stig Nielsen_, Nov 14 2019