Proof

[Max Alekseyev]

On Wed, Apr 23, 2008 at 4:13 PM, N. J. A. Sloane <njas at research.att.com> wrote:

>  The classic work is:
>
>  D. Cox, Primes of the form x^2+ny^2, Wiley, 1989.
>
>  This gives a standard mechanism for proving or disproving
>  such assertions.

Essential excerpt from a similar book can be downloaded for free from:
http://www.math.uoc.gr/~marios/primzahl/en.htm

A question whether a prime p can be represented by a binary form x^2 +
6*y^2 is equivalent to whether -6 is a square modulo p and x^2 - 2*x -
1 is solvable modulo p (i.e., whether (-6/p)=1 and (2/p)=1).
The latter condition can be easily established for primes of the form 24k+7.

Regards,
Max