A139857 Primes of the form 8x^2 + 15y^2.

23, 47, 167, 263, 383, 503, 647, 743, 863, 887, 983, 1103, 1223, 1367, 1487, 1583, 1607, 1823, 1847, 2063, 2087, 2207, 2423, 2447, 2543, 2663, 2687, 2903, 2927, 3023, 3167, 3407, 3527, 3623, 3767, 3863, 4007, 4127, 4463, 4583, 4703, 4943

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 12x^2 + 12xy + 23y^2, which has discriminant = -960. - T. D. Noe, May 07 2008

Also primes of the forms 23x^2 + 22xy + 47y^2 and 23x^2 + 8xy + 32y^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 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 {23, 47}]; // Vincenzo Librandi, Jul 29 2012

Mathematica

QuadPrimes2[8, 0, 15, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\8), w=8*x^2; for(y=1, sqrtint((lim-w)\15), if(isprime(t=w+15*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 22 2017

Formula

The primes are congruent to {23, 47} (mod 120).