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Primes of the form 6x^2+6xy+31y^2.
2

%I #17 Sep 08 2022 08:45:34

%S 31,43,67,103,151,211,283,367,463,571,691,739,751,811,823,859,919,967,

%T 991,1123,1171,1279,1291,1399,1447,1459,1471,1483,1531,1567,1627,1663,

%U 1699,1783,1831,1867,1879,1987,1999,2083,2179,2239,2311,2371,2383

%N Primes of the form 6x^2+6xy+31y^2.

%C Discriminant=-708. See A139827 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A139883/b139883.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 {31, 43, 55, 67, 91, 103, 115, 151, 187, 211, 235, 247, 259, 283, 319, 367, 391, 415, 427, 451, 463, 511, 571, 583, 655, 667, 679, 691, 703} (mod 708).

%t QuadPrimes2[6, -6, 31, 10000] (* see A106856 *)

%o (Magma) [ p: p in PrimesUpTo(4000) | p mod 708 in {31, 43, 55, 67, 91, 103, 115, 151, 187, 211, 235, 247, 259, 283, 319, 367, 391, 415, 427, 451, 463, 511, 571, 583, 655, 667, 679, 691, 703}]; // _Vincenzo Librandi_, Jul 30 2012

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 02 2008