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Primes of the form 5x^2 + 12y^2.
3

%I #21 Sep 08 2022 08:45:18

%S 5,17,53,113,137,173,197,233,257,293,317,353,557,593,617,653,677,773,

%T 797,857,953,977,1013,1097,1193,1217,1277,1373,1433,1493,1553,1613,

%U 1637,1697,1733,1877,1913,1973,1997,2153,2213,2237,2273,2297,2333

%N Primes of the form 5x^2 + 12y^2.

%C Discriminant = -240. See A107132 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A107167/b107167.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)

%F Except for 5, the primes are congruent to {17, 53} (mod 60). - _T. D. Noe_, May 02 2008

%t QuadPrimes2[5, 0, 12, 10000] (* see A106856 *)

%o (Magma) [5] cat [p: p in PrimesUpTo(3000) | p mod 60 in [17, 53]]; // _Vincenzo Librandi_, Jul 25 2012

%o (PARI) list(lim)=my(v=List([5]),t); forprime(p=17,lim, t=p%60; if(t==17||t==53, listput(v,p))); Vec(v) \\ _Charles R Greathouse IV_, Feb 10 2017

%Y Cf. A139827.

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 13 2005