A139856 Primes of the form 5x^2 + 24y^2.

5, 29, 101, 149, 269, 389, 461, 509, 701, 821, 941, 1061, 1109, 1181, 1229, 1301, 1709, 1901, 1949, 2069, 2141, 2309, 2381, 2549, 2621, 2741, 2789, 2861, 2909, 3221, 3389, 3461, 3581, 3701, 3821, 3989, 4229, 4349, 4421, 5021, 5189, 5261

Offset

1,1

Comments

Discriminant=-480. See A139827 for more information.

Except for 5, also primes of the form 21x^2+6xy+29y^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)

Formula

Except for 5, the primes are congruent to {29, 101} (mod 120).

Mathematica

QuadPrimes2[5, 0, 24, 10000] (* see A106856 *)

Prog

(Magma) [5] cat [ p: p in PrimesUpTo(6000) | p mod 120 in {29, 101}]; // Vincenzo Librandi, Jul 29 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=1, sqrtint(lim\5), w=5*x^2; for(y=0, sqrtint((lim-w)\24), if(isprime(t=w+24*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 22 2017

Crossrefs

Cf. A140633.

Sequence in context: A330700 A264750 A205172 * A097345 A097344 A153076

Adjacent sequences: A139853 A139854 A139855 * A139857 A139858 A139859

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved