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Primes of the form x^2 + 56y^2.
2

%I #18 Feb 09 2017 17:26:16

%S 137,233,281,449,673,953,977,1033,1129,1409,1481,1873,2017,2081,2129,

%T 2137,2377,2417,2657,2713,2753,2857,2969,3313,3529,3593,3697,3833,

%U 4001,4561,4649,4657,4673,4729,4817,4993,5657,5737,5849,6217,6329

%N Primes of the form x^2 + 56y^2.

%C Discriminant = -224. See A107132 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A107164/b107164.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[1, 0, 56, 10000] (* see A106856 *)

%o (PARI) list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\1), w=x^2; for(y=1, sqrtint((lim-w)\56), if(isprime(t=w+56*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