A107181 Primes of the form 8x^2 + 9y^2.

17, 41, 89, 113, 137, 233, 257, 281, 353, 401, 449, 521, 569, 593, 617, 641, 761, 809, 857, 881, 929, 953, 977, 1049, 1097, 1193, 1217, 1289, 1361, 1409, 1433, 1481, 1553, 1601, 1697, 1721, 1889, 1913, 2081, 2129, 2153, 2273, 2297, 2393, 2417

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -288. See A107132 for more information.

Also primes of the form 9x^2 + 6xy + 17y^2. See A140633. - T. D. Noe, May 19 2008

All terms are of the form x^2 + y^2, see A002144. - Zak Seidov, Jan 26 2014

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

Subsequence of A002144 (Pythagorean primes).

Cf. A139827.

Programs

Magma

[ p: p in PrimesUpTo(5000) | p mod 24 eq 17 ]; // Vincenzo Librandi, Apr 19 2011

Mathematica

QuadPrimes2[8, 0, 9, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List()); forprime(p=17,lim, if(p%24==17, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 2017

Formula

The primes are congruent to 17 (mod 24). - T. D. Noe, May 02 2008