A056874 Primes of form x^2+xy+3y^2, discriminant -11.

3, 5, 11, 23, 31, 37, 47, 53, 59, 67, 71, 89, 97, 103, 113, 137, 157, 163, 179, 181, 191, 199, 223, 229, 251, 257, 269, 311, 313, 317, 331, 353, 367, 379, 383, 389, 397, 401, 419, 421, 433, 443, 449, 463, 467, 487, 499, 509, 521, 577, 587, 599

Offset: 1

Author

N. J. A. Sloane, Sep 02 2000

Keywords

• nonn
• easy

Comments

Also, primes of form (x^2+11*y^2)/4.

Also, primes of the form x^2-xy+3y^2 with x and y nonnegative. - T. D. Noe, May 07 2005

Primes congruent to 0, 1, 3, 4, 5 or 9 (mod 11). As this discriminant has class number 1, all binary quadratic forms ax^2+bxy+cy^2 with b^2-4ac=-11 represent these primes. - Rick L. Shepherd, Jul 25 2014

Also, primes which are squares (mod 11) (or, (mod 22), cf. A191020). - M. F. Hasler, Jan 15 2016

Also, primes p such that Legendre(-11,p) = 0 or 1. - N. J. A. Sloane, Dec 25 2017

Links

• Vincenzo Librandi, N. J. A. Sloane and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi, next 4000 terms from N. J. A. Sloane]
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A002346 and A002347 for values of x and y.

Primes in A028954.

Programs

Mathematica

QuadPrimes2[1, 1, 3, 100000] (* see A106856 *)

PARI

{ fc2(a,b,c,M) = my(p,t1,t2,n);
m = 0;
for(n=1,M, p = prime(n);
t2 = qfbsolve(Qfb(a,b,c),p); if(t2 == 0,, m++; print(m," ",p )));
}
fc2(1,-1,3,10703);

Extensions

Edited by N. J. A. Sloane, Jun 01 2014 and Jun 16 2014