cp's OEIS Frontend

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

%I A057002 #35 Feb 16 2025 08:32:43
%S A057002 1,824,1476,1632,2462,2484,2520,3064,3402,3820,4026,6640,7026,7158,
%T A057002 9070,12202,12548,12994,13042,15358,17646,17670,18336,19564,20624,
%U A057002 22500,24126,26132,26188,26240,29074,29658,30778,31126,32244,33044,34016
%N A057002 Numbers n such that n^1024 + 1 is prime (a generalized Fermat prime).
%C A057002 This sequence is infinite under Bunyakovsky's conjecture. - _Charles R Greathouse IV_, Apr 26 2012
%H A057002 T. D. Noe, <a href="/A057002/b057002.txt">Table of n, a(n) for n = 1..1000</a> (from Yves Gallot)
%H A057002 Yves Gallot, <a href="http://yves.gallot.pagesperso-orange.fr/primes/">Generalized Fermat Prime Search</a>
%H A057002 Jeppe Stig Nielsen, <a href="http://jeppesn.dk/generalized-fermat.html">Generalized Fermat Primes sorted by base</a>.
%H A057002 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GeneralizedFermatNumber.html">Generalized Fermat Number</a>
%t A057002 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} ]
%t A057002 Do[If[PrimeQ[n^1024 + 1], Print[n], ## &[]], {n, 1, 100}] (* Includes first term and runs faster, _Daniel Jolly_, Nov 04 2014 *)
%o A057002 (PARI) isA057002(n) = isprime(n^1024+1) \\ _Michael B. Porter_, Apr 03 2010
%Y A057002 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.
%Y A057002 Cf. A006093.
%K A057002 nonn
%O A057002 1,2
%A A057002 _Robert G. Wilson v_, Sep 09 2000
%E A057002 More terms from _Jeppe Stig Nielsen_, Sep 27 2003
%E A057002 Edited at the suggestion of _T. D. Noe_ by _N. J. A. Sloane_, May 14 2008