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A057002 Numbers n such that n^1024 + 1 is prime (a generalized Fermat prime). 35
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is a polynomial form (of degree 2^10) generalization of Fermat primes, whereas Fermat primes have a doubly exponential form. [From Daniel Forgues, Nov 11 2009]

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

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 *)

PROG

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

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.

Sequence in context: A252539 A033531 A088360 * A247922 A283201 A283731

Adjacent sequences:  A056999 A057000 A057001 * A057003 A057004 A057005

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Sep 09 2000

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

STATUS

approved

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Last modified July 16 23:49 EDT 2019. Contains 325092 sequences. (Running on oeis4.)