A139649 Primes of the form x^2 + 177*y^2.

181, 193, 241, 277, 373, 433, 577, 661, 709, 733, 757, 829, 853, 877, 997, 1069, 1201, 1237, 1549, 1597, 1609, 1621, 1657, 1669, 1693, 1777, 1789, 1933, 1993, 2113, 2269, 2293, 2377, 2389, 2557, 2617, 2677, 2749, 2833, 2857, 2917, 2953

Offset: 1

Author

T. D. Noe, Apr 29 2008

Keywords

• nonn
• easy

Comments

Discriminant = -708.

The primes are congruent to {1, 25, 49, 85, 121, 133, 145, 169, 181, 193, 205, 241, 253, 265, 277, 289, 361, 373, 433, 481, 493, 517, 529, 553, 577, 625, 661, 685, 697} (mod 708).

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(4000) | p mod 708 in {1, 25, 49, 85, 121, 133, 145, 169, 181, 193, 205, 241, 253, 265, 277, 289, 361, 373, 433, 481, 493, 517, 529, 553, 577, 625, 661, 685, 697}]; // Vincenzo Librandi, Jul 28 2012

Magma

k:=177; [p: p in PrimesUpTo(3000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

Mathematica

QuadPrimes2[1, 0, 177, 10000] (* see A106856 *)