A139879 Primes of the form 12x^2+12xy+17y^2.

17, 41, 89, 257, 353, 521, 593, 761, 857, 881, 929, 1049, 1097, 1193, 1217, 1361, 1433, 1553, 1601, 1697, 1721, 1889, 2273, 2393, 2441, 2609, 2729, 2777, 2897, 3041, 3209, 3449, 3617, 3881, 4049, 4073, 4217, 4241, 4289, 4409, 4457, 4721

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-672. See A139827 for more information.

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

Links

• Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Programs

Magma

[ p: p in PrimesUpTo(6000) | p mod 168 in {17, 41, 89}]; // Vincenzo Librandi, Jul 30 2012

Mathematica

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

Formula

The primes are congruent to {17, 41, 89} (mod 168).

Extensions

Corrected and extended b-file - Ray Chandler, Jul 31 2014