A107151 Primes of the form 5x^2 + 9y^2.

5, 29, 41, 89, 101, 149, 269, 281, 389, 401, 449, 461, 509, 521, 569, 641, 701, 761, 809, 821, 881, 929, 941, 1049, 1061, 1109, 1181, 1229, 1289, 1301, 1361, 1409, 1481, 1601, 1709, 1721, 1889, 1901, 1949, 2069, 2081, 2129, 2141, 2309, 2381

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -180. See A107132 for more information.

Except for 5, also primes of the form 9x^2 + 6xy + 26y^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)

Crossrefs

Cf. A139827.

Programs

Magma

[5] cat [ p: p in PrimesUpTo(3000) | p mod 60 in {29, 41 } ]; // Vincenzo Librandi, Jul 24 2012

Mathematica

QuadPrimes2[5, 0, 9, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List([5]),t); forprime(p=29,lim, t=p%60; if(t==29||t==41, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Formula

Except for 5, the primes are congruent to {29, 41} (mod 60). - T. D. Noe, May 02 2008