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Primes of the form 8x^2+8xy+67y^2.
1

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

%S 67,83,163,227,307,587,643,683,787,827,947,1123,1163,1307,1523,1627,

%T 1723,1747,1787,1867,1987,2203,2243,2267,2347,2683,2803,3083,3187,

%U 3203,3307,3323,3347,3547,3803,3907,3947,4243,4283,4363,4483,4643

%N Primes of the form 8x^2+8xy+67y^2.

%C Discriminant=-2080. See A139827 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A139973/b139973.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 {67, 83, 123, 163, 187, 203, 227, 267, 307, 323, 427, 483} (mod 520).

%t QuadPrimes2[8, -8, 67, 10000] (* see A106856 *)

%o (Magma)[ p: p in PrimesUpTo(6000) | p mod 520 in [67, 83, 123, 163, 187, 203, 227, 267, 307, 323, 427, 483]]; // _Vincenzo Librandi_, Aug 02 2012

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 02 2008