Quadratic forms vs congruences

[Max Alekseyev]

On Thu, Apr 24, 2008 at 2:31 PM, T. D. Noe <noe at sspectra.com> wrote:

> Perhaps someone has already noticed that
>
>  A107003 appears to be primes of the form 5+24k
>  A107007 appears to be primes of the form 11+24k and 3
>  A107181 appears to be primes of the form 17+24k
>  A107154 appears to be primes of the form 19+24k and 3
>
>  I'm not proving these, but it should be possible.

That's rather simple, using Theorem 2.1.1 from
http://www.math.uoc.gr/~marios/primzahl/en.htm

>  Has anyone answered this question: what is the latest that sequences of
>  this type (quadratic forms and congruences) can disagree?  It seems that
>  the answer will depend on the discriminant.

For the form x^2+n*y^2, exceptional primes are factors of n and
Discriminant(f_n(t)) (see Theorem 2.1.1 for details).

Regards,
Max