login
Primes of the form 6^k + 1.
9

%I #19 Sep 15 2022 06:30:03

%S 2,7,37,1297

%N Primes of the form 6^k + 1.

%C No other terms for k < 3000. - _T. D. Noe_, Apr 25 2012

%C Apart from the first term, the exponents must be powers of two. Like Fermat primes, there are probably only finitely many terms. No more terms for k < 2^28 = 268435456. - _Charles R Greathouse IV_, Jul 16 2012

%H Wilfrid Keller, <a href="http://www.prothsearch.com/GFN06.html">Prime factors of generalized Fermat numbers F_m(6) and complete factoring status</a>

%t Select[Table[6^n + 1, {n, 0, 100}], PrimeQ] (* _T. D. Noe_, Apr 25 2012 *)

%o (PFGW) ABC2 6^(2^$a)+1

%o a: from 0 to 18

%o // _Charles R Greathouse IV_, Jul 16 2012

%Y Cf. A057735, A182330.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Apr 25 2012