A139854 Primes of the form 3x^2 + 40y^2.

3, 43, 67, 163, 283, 307, 523, 547, 643, 787, 883, 907, 1123, 1483, 1627, 1723, 1747, 1867, 1987, 2083, 2203, 2347, 2467, 2683, 2707, 2803, 3067, 3163, 3187, 3307, 3547, 3643, 3907, 4003, 4027, 4243, 4363, 4483, 4507, 4603, 4723, 4987, 5107

Offset: 1

Author

T. D. Noe, May 02 2008

Keywords

• nonn
• easy

Comments

Discriminant=-480. See A139827 for more information.

Except for 3, also primes of the form 27x^2+12xy+28y^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. A140633.

Programs

Magma

[3] cat [ p: p in PrimesUpTo(6000) | p mod 120 in {43, 67}]; // Vincenzo Librandi, Jul 29 2012

Mathematica

QuadPrimes2[3, 0, 40, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\3), w=3*x^2; for(y=0, sqrtint((lim-w)\40), if(isprime(t=w+40*y^2), listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Feb 22 2017

Formula

Except for 3, the primes are congruent to {43, 67} (mod 120).