A107144 Primes of the form 5x^2 + 8y^2.

5, 13, 37, 53, 157, 173, 197, 277, 293, 317, 373, 397, 557, 613, 653, 677, 733, 757, 773, 797, 853, 877, 997, 1013, 1093, 1117, 1213, 1237, 1277, 1373, 1453, 1493, 1597, 1613, 1637, 1693, 1733, 1877, 1933, 1973, 1997, 2053, 2213, 2237, 2293

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -160. See A107132 for more information.

Except for 5, also primes of the form 13x^2 + 8xy + 32y^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)

Crossrefs

Cf. A139827.

Programs

Magma

[5] cat [ p: p in PrimesUpTo(3000) | p mod 40 in {13, 37} ]; // Vincenzo Librandi, Jul 24 2012

Mathematica

QuadPrimes2[5, 0, 8, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List([5]),t); forprime(p=13,lim, t=p%40; if(t==13||t==37, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Formula

Except for 5, the primes are congruent to {13, 37} (mod 40). - T. D. Noe, May 02 2008