--- In firstname.lastname@example.org
, "Payam Samidoost" <sami@a...> wrote:
> Saeed (or REZA)
> > I want to know that ,is there q,p (that is q is positive integer
> is a prime number )
> > that qK+p is prime for 1<k<m(k can be 1 or m )that is m is free
> positive integer .
> If you let k be zero then the sequence qk+p is called "primes in
> progression with length m+1".
> The longest (an AP23) is discovered recently by Markus Frind, Paul
> and Paul Underwood:http://listserv.nodak.edu/scripts/wa.exe?A2=ind0407&L=nmbrthry&F=&S=&P=2520
> 56,211,383,760,397 +K*44,546,738,095,860 for K =0 to 22
> see: http://primes.plentyoffish.com/
Here is a pre-print of the proof that there are arbritarily long PAP's: