A139865 Primes of the form 7x^2 + 19y^2.

7, 19, 47, 83, 131, 139, 199, 251, 271, 283, 311, 367, 419, 467, 479, 503, 587, 619, 643, 647, 691, 719, 727, 859, 1151, 1223, 1259, 1279, 1483, 1487, 1531, 1543, 1559, 1567, 1783, 1811, 1847, 1867, 1879, 1907, 1987, 2063, 2099, 2239, 2243, 2267

Offset

1,1

Comments

Discriminant=-532. See A139827 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

The primes are congruent to {7, 19, 47, 55, 83, 87, 111, 115, 131, 139, 159, 187, 195, 199, 215, 251, 271, 283, 311, 327, 339, 367, 391, 419, 423, 467, 479, 495, 503} (mod 532).

Mathematica

QuadPrimes2[7, 0, 19, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(3000) | p mod 532 in {7, 19, 47, 55, 83, 87, 111, 115, 131, 139, 159, 187, 195, 199, 215, 251, 271, 283, 311, 327, 339, 367, 391, 419, 423, 467, 479, 495, 503}]; // Vincenzo Librandi, Jul 29 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=0, sqrtint(lim\7), w=7*x^2; for(y=0, sqrtint((lim-w)\19), if(isprime(t=w+19*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Mar 07 2017

Crossrefs

Sequence in context: A278403 A143128 A238730 * A146403 A000491 A097039

Adjacent sequences: A139862 A139863 A139864 * A139866 A139867 A139868

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved