A078902 Generalized Fermat primes of the form (k+1)^2^m + k^2^m, with m>1.

17, 97, 257, 337, 881, 3697, 10657, 16561, 49297, 65537, 66977, 89041, 149057, 847601, 988417, 1146097, 1972097, 2070241, 2522257, 2836961, 3553777, 3959297, 4398577, 5385761, 7166897, 11073217, 17653681, 32530177, 41532497, 44048497

Offset: 1

Author

T. D. Noe, Dec 12 2002

Keywords

• nonn

Comments

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.

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.

Links

• T. D. Noe, Table of n, a(n) for n = 1..525 (terms < 10^14)
• T. D. Noe, Table of generalized Fermat primes of the form (k+1)^2^m + k^2^m
• Eric Weisstein's World of Mathematics, Generalized Fermat Number

Crossrefs

Cf. A019434, A077659, A078900, A078901.

Cf. A080131, A080208, A019434, A078902, A080134, A153504, A152913, A194185.

Programs

Mathematica

lst3=Select[lst2, PrimeQ[ # ]&] (* lst2 is from A078901 *)