|
%I #14 Mar 30 2012 17:22:27
%S 17,97,257,337,881,3697,10657,16561,49297,65537,66977,89041,149057,
%T 847601,988417,1146097,1972097,2070241,2522257,2836961,3553777,
%U 3959297,4398577,5385761,7166897,11073217,17653681,32530177,41532497,44048497
%N Generalized Fermat primes of the form (k+1)^2^m + k^2^m, with m>1.
%C For k=1, these are the Fermat primes A019434. Is the set of generalized Fermat primes infinite? Conjecture that there are only a finite number of generalized Fermat primes for each value of k. See A077659, which shows that in cases such as k=11, there appear to be no primes. See A078901 for generalized Fermat numbers.
%C See A080131 for the conjectured number of primes for each k. See A080208 for the least k such that (k+1)^2^n + k^2^n is prime. The largest probable prime of this form discovered to date is the 10217-digit 312^2^12 + 311^2^12.
%H T. D. Noe, <a href="/A078902/b078902.txt">Table of n, a(n) for n = 1..525</a> (terms < 10^14)
%H T. D. Noe, <a href="http://www.sspectra.com/math/GenFermatPrimes.txt">Table of generalized Fermat primes of the form (k+1)^2^m + k^2^m</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GeneralizedFermatNumber.html">Generalized Fermat Number</a>
%t lst3=Select[lst2, PrimeQ[ # ]&] (* lst2 is from A078901 *)
%Y Cf. A019434, A077659, A078900, A078901.
%Y Cf. A080131, A080208, A019434, A078902, A080134, A153504, A152913, A194185.
%K nonn
%O 1,1
%A _T. D. Noe_, Dec 12 2002
|
