A107169 Primes of the form 3x^2 + 20y^2.

3, 23, 47, 83, 107, 167, 227, 263, 347, 383, 443, 467, 503, 563, 587, 647, 683, 743, 827, 863, 887, 947, 983, 1103, 1163, 1187, 1223, 1283, 1307, 1367, 1427, 1487, 1523, 1583, 1607, 1667, 1787, 1823, 1847, 1907, 2003, 2027, 2063, 2087, 2207

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -240. See A107132 for more information.

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

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)

Crossrefs

Cf. A139827.

Programs

Magma

[3] cat [p: p in PrimesUpTo(3000) | p mod 60 in [23, 47]]; // Vincenzo Librandi, Jul 25 2012

Mathematica

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

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

Formula

Except for 3, the primes are congruent to {23, 47} (mod 60). - T. D. Noe, May 02 2008