A107180 Primes of the form 2x^2 + 35y^2.

2, 37, 43, 53, 67, 107, 163, 197, 277, 317, 347, 373, 443, 547, 557, 613, 653, 683, 757, 827, 877, 883, 907, 947, 1093, 1117, 1163, 1187, 1213, 1283, 1373, 1453, 1493, 1523, 1597, 1667, 1723, 1733, 1747, 1787, 1877, 1933, 1997, 2003, 2027, 2053

Offset

1,1

Comments

Discriminant = -280. 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)

Formula

The primes are congruent to {2, 37, 43, 53, 67, 93, 107, 123, 163, 197, 253, 267, 277} (mod 280). - T. D. Noe, May 02 2008

Mathematica

QuadPrimes2[2, 0, 35, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(3000) | p mod 280 in {2, 37, 43, 53, 67, 93, 107, 123, 163, 197, 253, 267, 277} ]; // Vincenzo Librandi, Jul 26 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=1, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\35), if(isprime(t=w+35*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Cf. A139827.

Sequence in context: A290803 A042569 A066196 * A162577 A199980 A084548

Adjacent sequences: A107177 A107178 A107179 * A107181 A107182 A107183

Keyword

nonn,easy

Author

T. D. Noe, May 13 2005

Status

approved