--- In

primenumbers@yahoogroups.com, "Payam Samidoost" <sami@a...> wrote:

> Saeed (or REZA)

>

> > I want to know that ,is there q,p (that is q is positive integer

and p

> 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

arithmetic

> progression with length m+1".

>

> The longest (an AP23) is discovered recently by Markus Frind, Paul

Jobling

> and Paul Underwood:

> 56,211,383,760,397 +K*44,546,738,095,860 for K =0 to 22

> see: http://primes.plentyoffish.com/

> and

>

http://listserv.nodak.edu/scripts/wa.exe?A2=ind0407&L=nmbrthry&F=&S=&P=2520 >

> Regards,

> Payam

Here is a pre-print of the proof that there are arbritarily long PAP's:

http://arxiv.org/abs/math.NT/0404188
Paul