A107133 Primes of the form 4x^2 + 7y^2.

7, 11, 23, 43, 67, 71, 79, 107, 127, 151, 163, 179, 191, 211, 239, 263, 331, 347, 359, 379, 431, 443, 463, 487, 491, 499, 547, 571, 599, 631, 659, 683, 739, 743, 751, 823, 827, 863, 883, 907, 911, 919, 947, 967, 991, 1019, 1031, 1051, 1087, 1103, 1163

Offset

1,1

Comments

Discriminant = -112. 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)

Formula

Except for 7, the primes are congruent to {11, 15, 23} (mod 28). - T. D. Noe, May 02 2008

Mathematica

QuadPrimes2[4, 0, 7, 10000] (* see A106856 *)

Prog

(PARI) list(lim)=my(v=List(), w, t); for(x=0, sqrtint(lim\4), w=4*x^2; for(y=1, sqrtint((lim-w)\7), if(isprime(t=w+7*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017

Crossrefs

Cf. A139827.

Sequence in context: A210001 A294074 A228227 * A079138 A163848 A111671

Adjacent sequences: A107130 A107131 A107132 * A107134 A107135 A107136

Keyword

nonn,easy

Author

T. D. Noe, May 13 2005

Status

approved