A139830 Primes of the form 7x^2+6xy+7y^2.

7, 23, 47, 103, 127, 167, 223, 263, 367, 383, 463, 487, 503, 607, 647, 727, 743, 823, 863, 887, 967, 983, 1063, 1087, 1103, 1223, 1303, 1327, 1367, 1423, 1447, 1487, 1543, 1567, 1583, 1607, 1663, 1783, 1823, 1847, 2063, 2087, 2143, 2207, 2287

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-160. See A139827 for more information.

Also primes of the forms 7x^2+2xy+23y^2 and 7x^2+4xy+12y^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(3000) | p mod 40 in {7, 23}]; // Vincenzo Librandi, Jul 29 2012

Mathematica

Union[QuadPrimes2[7, 6, 7, 10000], QuadPrimes2[7, -6, 7, 10000]] (* see A106856 *)

Formula

The primes are congruent to {7, 23} (mod 40).