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A057002
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Numbers n such that n^1024 + 1 is prime (a generalized Fermat prime).
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14
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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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
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MATHEMATICA
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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} ]
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PROG
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(PARI) isA057002(n) = isprime(n^1024+1) [From Michael B. Porter, Apr 03 2010]
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CROSSREFS
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Other sequences of numbers n such that n^(2^k)+1 is prime for fixed k: A088362, A088361, A057465, A056995, A056994, A006316, A006315, A006313, A006314, A000068, A005574, A006093.
Sequence in context: A189121 A033531 A088360 * A051989 A104375 A066946
Adjacent sequences: A056999 A057000 A057001 * A057003 A057004 A057005
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v, Sep 09 2000
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EXTENSIONS
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More terms from Jeppe Stig Nielsen (mail(AT)jeppesn.dk), Sep 27 2003
Edited by N. J. A. Sloane, May 14 2008 at the suggestion of T. D. Noe
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STATUS
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approved
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