Primes of both forms 24n+7 and 7m+24

[Max Alekseyev]

On Thu, Apr 24, 2008 at 12:32 AM, zak seidov <zakseidov at yahoo.com> wrote:

> A1 Primes of the both forms 24n+7 and 7m+24

Zak,

Applying CRT to the system of congruences

p = 7 (mod 24)
p = 24 (mod 7)

we have p = 31 (mod 168).

>  Difference between m and n is always multiple of 17

It is clear, since n = (p-7)/24 and m = (p-24)/7, we have

m - n = (p-24)/7 - (p-7)/24 = 17 * (p - 31)/168

where (p - 31)/168 is integer (see above).

>  A4 Corresponding values of (m-n)/17

This is simply (p-31)/168.

>  Also all primes in A1 are of form 8k-1,

Of course, since 24n+7 = 8*(3n+1) - 1.

>  Are there any other (interesting) properties of primes in A1?

They are not interesting at all. Mostly trivial and useless.

Regards,
Max