A139897 Primes of the form 3*x^2+80*y^2.

3, 83, 107, 227, 347, 443, 467, 563, 587, 683, 827, 947, 1163, 1187, 1283, 1307, 1427, 1523, 1667, 1787, 1907, 2003, 2027, 2243, 2267, 2843, 2963, 3083, 3203, 3323, 3347, 3467, 3803, 3923, 3947, 4283, 4523, 4547, 4643, 4787, 5003, 5147

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-960. See A139827 for more information.

Except for 3, also primes of the form 27*x^2+24*x*y+32*y^2. See A140633. - T. D. Noe, May 19 2008

Excepting for the first term, 3, the members of this sequence seem to be terms of A123239 which are prime in k(i), k(rho) & k(sqrt(5)). [From A.K. Devaraj, Nov 30 2009]

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

[3] cat [p: p in PrimesUpTo(6000) | p mod 120 in [83, 107]]; // Vincenzo Librandi, Jul 31 2012

Mathematica

QuadPrimes2[3, 0, 80, 10000] (* see A106856 *)

Formula

Except for 3, primes congruent to 83 or 107 (mod 120).