--- In

primenumbers@yahoogroups.com, "Jens Kruse Andersen"

<jens.k.a@...> wrote:

>

> Robert wrote:

> > 10347747270980*3^n+1, n from 1 to 10 all prime

> >

> > Do these prime runs have a name?(base 2 this would be a Cunningham

Chain)

>

> http://primes.utm.edu/glossary/page.php?sort=CunninghamChain says:

> "Note that some authors extend the definition of Cunningham Chain to

> all sequences of primes p_i the form p_(i+1) = a*p_i+b where a and b

> are fixed, relatively prime integers with a > 1."

>

> It has been called a generalized Cunningham chain, for example at

>

http://ourworld.compuserve.com/homepages/hlifchitz/Henri/us/CunnGenus.htm,
> but that term has also been used about other variations of

> Cunningham chains.

> Your chain corresponds to (a, b) = (3, -2): p_(i+1) = 3*p_i-2.

>

> --

> Jens Kruse Andersen

>

I can feel another project coming on:

The longest chains k*b^n+/-1 n from n(1) to n(x) all prime, and b= the

primes 2,3,5,7,11,...

It is relatively easy to find chains longer 8 for smaller primes, for

example:

550326588*5^n+1, n from 1 to 10, all prime

943151976*11^n+1, n from 1 to 9, all prime

678979904460*7^n+1, n from 1 to 9 all prime

Regards

Robert Smith