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

%I #18 Feb 09 2017 14:36:56

%S 2,19,37,173,179,181,269,307,509,547,563,683,971,1093,1123,1171,1229,

%T 1381,1523,1571,1579,1627,1637,1667,1877,1931,1933,2083,2339,2371,

%U 2389,2621,2731,2749,2789,2909,3061,3067,3109,3181,3221,3229,3371

%N Primes of the form 2x^2 + 19y^2.

%C Discriminant = -152. See A107132 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A107143/b107143.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi]

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

%t QuadPrimes2[2, 0, 19, 10000] (* see A106856 *)

%o (PARI) list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\2), w=2*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_, Feb 09 2017

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 13 2005