A139992 Primes of the form 20x^2+20xy+47y^2.

47, 167, 383, 503, 647, 887, 983, 1223, 1487, 1823, 1847, 2063, 2663, 2687, 2903, 3023, 3167, 3407, 3527, 3863, 4007, 4583, 4703, 5087, 5927, 6047, 6263, 6863, 7103, 7607, 7703, 7727, 8447, 8543, 8783, 9623, 9743, 9887, 10223, 10247, 10463

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-3360. See A139827 for more information.

Also primes of the forms 47x^2+40xy+80y^2 and 47x^2+42xy+63y^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(12000) | p mod 840 in [47, 143, 167, 383, 503, 647]]; // Vincenzo Librandi, Aug 03 2012

Mathematica

QuadPrimes2[20, -20, 47, 10000] (* see A106856 *)

Formula

The primes are congruent to {47, 143, 167, 383, 503, 647} (mod 840).