A107145 Primes of the form x^2 + 40y^2.

41, 89, 241, 281, 401, 409, 449, 521, 569, 601, 641, 761, 769, 809, 881, 929, 1009, 1049, 1129, 1201, 1249, 1289, 1321, 1361, 1409, 1481, 1489, 1601, 1609, 1721, 1801, 1889, 2081, 2089, 2129, 2161, 2281, 2441, 2521, 2609, 2689, 2729, 2801

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -160. 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(3000) | p mod 40 in {1, 9} ]; // Vincenzo Librandi, Jul 24 2012

Mathematica

QuadPrimes2[1, 0, 40, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List(),t); forprime(p=41,lim, t=p%40; if(t==1||t==9, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Formula

The primes are congruent to {1, 9} (mod 40). - T. D. Noe, Apr 29 2008