A057002 Numbers n such that n^1024 + 1 is prime (a generalized Fermat prime).

1, 824, 1476, 1632, 2462, 2484, 2520, 3064, 3402, 3820, 4026, 6640, 7026, 7158, 9070, 12202, 12548, 12994, 13042, 15358, 17646, 17670, 18336, 19564, 20624, 22500, 24126, 26132, 26188, 26240, 29074, 29658, 30778, 31126, 32244, 33044, 34016

Offset: 1

Author

Robert G. Wilson v, Sep 09 2000

Keywords

• nonn

Comments

This sequence is infinite under Bunyakovsky's conjecture. - Charles R Greathouse IV, Apr 26 2012

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000 (from Yves Gallot)
• Yves Gallot, Generalized Fermat Prime Search
• Jeppe Stig Nielsen, Generalized Fermat Primes sorted by base.
• Eric Weisstein's World of Mathematics, Generalized Fermat Number

Crossrefs

Other sequences of numbers n such that n^(2^k)+1 is prime for fixed k: A005574, A000068, A006314, A006313, A006315, A006316, A056994, A056995, A057465, A088361, A088362, A226528, A226529, A226530, A251597, A253854, A244150, A243959, A321323.

Cf. A006093.

Programs

Mathematica

Do[ k = 1; While[ PowerMod[ n, 1024, 2*k*1024 + 1 ] != 2*k*1024 && k < 2*10^6, k++ ]; If[ k == 2*10^6 && PrimeQ[ n^1024 + 1 ], Print[ n ] ], {n, 2, 13954, 2} ]
Do[If[PrimeQ[n^1024 + 1], Print[n], ## &[]], {n, 1, 100}] (* Includes first term and runs faster, Daniel Jolly, Nov 04 2014 *)

PARI

isA057002(n) = isprime(n^1024+1) \\ Michael B. Porter, Apr 03 2010

Extensions

More terms from Jeppe Stig Nielsen, Sep 27 2003

Edited at the suggestion of T. D. Noe by N. J. A. Sloane, May 14 2008