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Primes of the form 12x^2+12xy+17y^2.
2

%I #19 Sep 08 2022 08:45:34

%S 17,41,89,257,353,521,593,761,857,881,929,1049,1097,1193,1217,1361,

%T 1433,1553,1601,1697,1721,1889,2273,2393,2441,2609,2729,2777,2897,

%U 3041,3209,3449,3617,3881,4049,4073,4217,4241,4289,4409,4457,4721

%N Primes of the form 12x^2+12xy+17y^2.

%C Discriminant=-672. See A139827 for more information.

%C Also primes of the forms 17x^2+10xy+41y^2 and 17x^2+4xy+20y^2. See A140633. - _T. D. Noe_, May 19 2008

%H Vincenzo Librandi and Ray Chandler, <a href="/A139879/b139879.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, 41, 89} (mod 168).

%t QuadPrimes2[12, -12, 17, 10000] (* see A106856 *)

%o (Magma) [ p: p in PrimesUpTo(6000) | p mod 168 in {17, 41, 89}]; // _Vincenzo Librandi_, Jul 30 2012

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 02 2008

%E Corrected and extended b-file - _Ray Chandler_, Jul 31 2014