A139841 Primes of the form 2x^2 + 51y^2.

2, 53, 59, 83, 101, 149, 179, 251, 293, 389, 443, 461, 467, 491, 509, 557, 563, 587, 659, 701, 773, 797, 971, 1019, 1109, 1181, 1259, 1277, 1283, 1301, 1307, 1373, 1427, 1613, 1619, 1667, 1709, 1733, 1787, 1811, 1973, 1997, 2027, 2099, 2141

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant = -408. 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)

Programs

Magma

[ p: p in PrimesUpTo(3000) | p mod 408 in {2, 35, 53, 59, 77, 83, 101, 149, 155, 179, 203, 251, 293, 341, 365, 389, 395}]; // Vincenzo Librandi, Jul 29 2012

Mathematica

QuadPrimes2[2, 0, 51, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List([2]), s=[35, 53, 59, 77, 83, 101, 149, 155, 179, 203, 251, 293, 341, 365, 389, 395]); forprime(p=53, lim, if(setsearch(s, p%408), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Formula

The primes are congruent to {2, 35, 53, 59, 77, 83, 101, 149, 155, 179, 203, 251, 293, 341, 365, 389, 395} (mod 408).