A107200 Primes of the form 2x^2 + 43y^2.

2, 43, 61, 331, 389, 419, 587, 691, 1093, 1109, 1187, 1237, 1637, 1723, 2069, 2179, 2221, 2269, 2309, 2557, 2699, 2837, 3253, 3259, 3491, 3533, 3571, 3581, 3821, 3907, 4093, 4259, 4283, 4451, 4603, 4651, 4733, 5051, 5189, 5387, 5531, 5653

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -344. See A107132 for more information.

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. A107132.

Programs

Mathematica

QuadPrimes2[2, 0, 43, 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)\43), if(isprime(t=w+43*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 10 2017