A139881 Primes of the form 2x^2+2xy+89y^2.

2, 89, 101, 113, 149, 173, 233, 269, 353, 401, 509, 569, 701, 773, 797, 809, 821, 857, 881, 929, 941, 977, 1013, 1061, 1109, 1193, 1217, 1277, 1289, 1409, 1481, 1493, 1601, 1637, 1721, 1901, 1949, 1997, 2213, 2237, 2273, 2297, 2309, 2333, 2357

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-708. 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(6000) | p mod 708 in {2, 65, 77, 89, 101, 113, 149, 161, 173, 185, 209, 221, 233, 269, 305, 329, 353, 365, 377, 401, 437, 485, 509, 533, 545, 569, 581, 629, 689, 701}]; // Vincenzo Librandi, Jul 30 2012

Mathematica

QuadPrimes2[2, -2, 89, 10000] (* see A106856 *)

Formula

The primes are congruent to {2, 65, 77, 89, 101, 113, 149, 161, 173, 185, 209, 221, 233, 269, 305, 329, 353, 365, 377, 401, 437, 485, 509, 533, 545, 569, 581, 629, 689, 701} (mod 708).