A139868 Primes of the form 3x^2 + 55y^2.

3, 67, 103, 163, 223, 367, 463, 487, 643, 727, 823, 883, 907, 1087, 1123, 1303, 1423, 1483, 1543, 1567, 1747, 1783, 2083, 2143, 2203, 2347, 2467, 2707, 2803, 2887, 3067, 3463, 3547, 3727, 3943, 4027, 4327, 4423, 4447, 4603, 4723, 4783, 4987

Offset

1,1

Comments

Discriminant = -660. See A139827 for more information.

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)

Formula

The primes are congruent to {3, 67, 103, 163, 223, 247, 367, 427, 463, 487, 643} (mod 660).

Mathematica

QuadPrimes2[3, 0, 55, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(6000) | p mod 660 in {3, 67, 103, 163, 223, 247, 367, 427, 463, 487, 643}]; // Vincenzo Librandi, Jul 30 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=1, sqrtint(lim\3), w=3*x^2; for(y=0, sqrtint((lim-w)\55), if(isprime(t=w+55*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Mar 07 2017

Crossrefs

Sequence in context: A105443 A065425 A096482 * A110716 A142035 A142926

Adjacent sequences: A139865 A139866 A139867 * A139869 A139870 A139871

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved