A106889 Primes of the form 2x^2 + 5y^2.

2, 5, 7, 13, 23, 37, 47, 53, 103, 127, 157, 167, 173, 197, 223, 263, 277, 293, 317, 367, 373, 383, 397, 463, 487, 503, 557, 607, 613, 647, 653, 677, 727, 733, 743, 757, 773, 797, 823, 853, 863, 877, 887, 967, 983, 997, 1013, 1063, 1087, 1093, 1103, 1117

Offset: 1

Author

T. D. Noe, May 09 2005

Keywords

• nonn
• easy

Comments

Discriminant = -40.

Links

• 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. Primes in A020674.

Programs

Mathematica

QuadPrimes2[2, 0, 5, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\5), if(isprime(t=w+5*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

Formula

The primes are congruent to {2, 5, 7, 13, 23, 37} (mod 40). - T. D. Noe, May 02 2008