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Primes of the form 3x^2 + 20y^2.
4

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

%S 3,23,47,83,107,167,227,263,347,383,443,467,503,563,587,647,683,743,

%T 827,863,887,947,983,1103,1163,1187,1223,1283,1307,1367,1427,1487,

%U 1523,1583,1607,1667,1787,1823,1847,1907,2003,2027,2063,2087,2207

%N Primes of the form 3x^2 + 20y^2.

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

%C Except for 3, also primes of the forms 2x^2 + 2xy + 23y^2 (A139831) and 8x^2 + 4xy + 23y^2. See A140633. - _T. D. Noe_, May 19 2008

%H Vincenzo Librandi and Ray Chandler, <a href="/A107169/b107169.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 3, the primes are congruent to {23, 47} (mod 60). - _T. D. Noe_, May 02 2008

%t QuadPrimes2[3, 0, 20, 10000] (* see A106856 *)

%o (Magma) [3] cat [p: p in PrimesUpTo(3000) | p mod 60 in [23, 47]]; // _Vincenzo Librandi_, Jul 25 2012

%o (PARI) list(lim)=my(v=List([3]),t); forprime(p=23,lim, t=p%60; if(t==23||t==47, 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