A139858 Primes of the form 8x^2+8xy+17y^2.

17, 113, 137, 233, 257, 353, 593, 617, 857, 953, 977, 1097, 1193, 1217, 1433, 1553, 1697, 1913, 2153, 2273, 2297, 2393, 2417, 2633, 2657, 2753, 2777, 2897, 3137, 3257, 3593, 3617, 3833, 4073, 4217, 4337, 4457, 4673, 4793, 4817, 4937, 5153

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-480. See A139827 for more information.

Also primes of the form 17x^2+14xy+17y^2, which has discriminant=-960. - T. D. Noe, May 07 2008

Also primes of the forms 17x^2+16xy+32y^2 and 17x^2+6xy+57y^2. See A140633. - T. D. Noe, May 19 2008

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
• William C. Jagy and Irving Kaplansky, Positive definite binary quadratic forms that represent the same primes [Cached copy] See Item 15 of Table II.
• 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 120 in {17, 113}]; // Vincenzo Librandi, Jul 29 2012

Mathematica

QuadPrimes2[8, -8, 17, 10000] (* see A106856 *)

Formula

The primes are congruent to {17, 113} (mod 120).