A107135 Primes of the form 5x^2 + 6y^2.

5, 11, 29, 59, 101, 131, 149, 179, 251, 269, 389, 419, 461, 491, 509, 659, 701, 821, 941, 971, 1019, 1061, 1091, 1109, 1181, 1229, 1259, 1301, 1451, 1499, 1571, 1619, 1709, 1811, 1901, 1931, 1949, 1979, 2069, 2099, 2141, 2309, 2339, 2381, 2411

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -120. See A107132 for more information.

Except for 5, also primes of the form 11x^2 + 4xy + 14y^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

[ p: p in PrimesUpTo(3000) | p mod 120 in {5, 11, 29, 59, 101} ]; // Vincenzo Librandi, Jul 23 2012

Mathematica

QuadPrimes2[5, 0, 6, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List([5]),s=[11,29,59,101]); forprime(p=11,lim, if(setsearch(s,p%120), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Formula

The primes are congruent to {5, 11, 29, 59, 101} (mod 120). - T. D. Noe, May 02 2008