A139656 - OEIS

%I #22 Sep 08 2022 08:45:33

%S 313,337,433,601,673,937,1153,1249,1297,1609,1777,1873,1993,2089,2161,

%T 2473,2521,2617,2713,2833,2857,3121,3169,3433,3457,3769,3793,4057,

%U 4177,4273,4657,4729,4801,4969,4993,5113,5209,5281,5521,5641,5737

%N Primes of the form x^2 + 312*y^2.

%C Discriminant=-1248. See A139643 for more information.

%C The primes are congruent to {1, 25, 49, 121, 217, 289} (mod 312).

%H Vincenzo Librandi and Ray Chandler, <a href="/A139656/b139656.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Vincenzo Librandi).

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

%t QuadPrimes2[1, 0, 312, 10000] (* see A106856 *)

%o (Magma) [ p: p in PrimesUpTo(7000) | p mod 312 in {1, 25, 49, 121, 217, 289}]; // _Vincenzo Librandi_, Jul 29 2012

%o (Magma) k:=312; [p: p in PrimesUpTo(6000) | NormEquation(k, p) eq true]; // _Bruno Berselli_, Jun 01 2016

%K nonn,easy

%O 1,1

%A _T. D. Noe_, Apr 29 2008