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Re: Do these prime runs have a name?

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  • Robert
    ... Chain) ... http://ourworld.compuserve.com/homepages/hlifchitz/Henri/us/CunnGenus.htm, ... I can feel another project coming on: The longest chains
    Message 1 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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