## Do these prime runs have a name?

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• 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)
Message 1 of 3 , Aug 7, 2007
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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
Message 2 of 3 , Aug 7, 2007
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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
• ... Chain) ... http://ourworld.compuserve.com/homepages/hlifchitz/Henri/us/CunnGenus.htm, ... I can feel another project coming on: The longest chains
Message 3 of 3 , Aug 12, 2007
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--- 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
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