A107178 Primes of the form 7x^2 + 10y^2.

7, 17, 47, 73, 97, 103, 167, 223, 257, 313, 353, 367, 383, 433, 503, 577, 593, 607, 647, 727, 857, 887, 937, 983, 1063, 1097, 1153, 1193, 1217, 1223, 1433, 1447, 1487, 1543, 1553, 1567, 1657, 1697, 1753, 1777, 1783, 1823, 1847, 1993, 2063, 2113

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 {7, 17, 33, 47, 73, 87, 97, 103, 143, 153, 167, 223, 257} (mod 280). - T. D. Noe, May 02 2008

Mathematica

QuadPrimes2[7, 0, 10, 10000] (* see A106856 *)

Prog

(Magma) [ p: p in PrimesUpTo(3000) | p mod 280 in {7, 17, 33, 47, 73, 87, 97, 103, 143, 153, 167, 223, 257} ]; // Vincenzo Librandi, Jul 26 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=1, sqrtint(lim\7), w=7*x^2; for(y=0, sqrtint((lim-w)\10), if(isprime(t=w+10*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Cf. A139827.

Sequence in context: A347124 A179030 A179031 * A061722 A195905 A104164

Adjacent sequences: A107175 A107176 A107177 * A107179 A107180 A107181

Keyword

nonn,easy

Author

T. D. Noe, May 13 2005

Status

approved