A107202 Primes of the form x^2 + 88y^2.

89, 97, 113, 137, 257, 313, 353, 401, 433, 449, 521, 577, 617, 641, 881, 929, 977, 1049, 1153, 1193, 1321, 1409, 1433, 1489, 1609, 1697, 1721, 1753, 1873, 2017, 2113, 2137, 2161, 2281, 2297, 2377, 2473, 2633, 2689, 2729, 2753, 2777, 2897

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -352. See A107132 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)

Crossrefs

Cf. A139643.

Programs

Magma

[ p: p in PrimesUpTo(4000) | p mod 88 in {1, 9, 25, 49, 81}]; // Vincenzo Librandi, Jul 28 2012

Mathematica

QuadPrimes2[1, 0, 88, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List(), s=[1, 9, 25, 49, 81]); forprime(p=89, lim, if(setsearch(s, p%88), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Formula

The primes are congruent to {1, 9, 25, 49, 81} (mod 88). - T. D. Noe, Apr 29 2008