A140013 Primes of the form 41x^2+38xy+41y^2.

41, 281, 569, 761, 809, 1289, 1361, 1481, 1601, 1889, 2081, 2129, 2441, 2609, 2801, 2969, 3209, 3329, 3449, 3761, 3929, 4001, 4241, 4289, 4649, 4721, 5081, 5441, 5849, 6089, 6569, 6761, 8081, 8609, 8681, 9041, 9209, 9281, 9521, 9929, 10529

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-5280. See A139827 for more information.

Also primes of the forms 41x^2+6xy+129y^2 and 41x^2+10xy+65y^2. See A140633. - T. D. Noe, May 19 2008

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(11000) | p mod 1320 in {41, 161, 281, 329, 569, 689, 761, 809, 1121, 1289} ]; // _Vincenzo Librandi-, Aug 05 2012

Mathematica

Union[QuadPrimes2[41, 38, 41, 10000], QuadPrimes2[41, -38, 41, 10000]] (* see A106856 *)

Formula

The primes are congruent to {41, 161, 281, 329, 569, 689, 761, 809, 1121, 1289} (mod 1320).