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Primes of the form 6x^2+6xy+17y^2.
1

%I #17 Sep 08 2022 08:45:33

%S 17,29,53,89,137,197,269,353,389,401,449,461,509,557,569,641,677,761,

%T 773,797,809,821,881,929,941,953,1013,1049,1097,1109,1181,1193,1277,

%U 1301,1481,1553,1697,1877,1889,1913,1949,1997,2069,2129,2213,2297

%N Primes of the form 6x^2+6xy+17y^2.

%C Discriminant=-372. See A139827 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A139840/b139840.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)

%F The primes are congruent to {17, 29, 53, 65, 77, 89, 137, 161, 185, 197, 209, 269, 305, 353, 365} (mod 372).

%t QuadPrimes2[6, -6, 17, 10000] (* see A106856 *)

%o (Magma) [ p: p in PrimesUpTo(3000) | p mod 372 in {17, 29, 53, 65, 77, 89, 137, 161, 185, 197, 209, 269, 305, 353, 365}]; // _Vincenzo Librandi_, Jul 29 2012

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 02 2008