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Re: [PrimeNumbers] Do these prime runs have a name?

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  • Jens Kruse Andersen
    ... 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 1 of 3 , Aug 7 6:29 AM
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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
    • Robert
      ... Chain) ... http://ourworld.compuserve.com/homepages/hlifchitz/Henri/us/CunnGenus.htm, ... I can feel another project coming on: The longest chains
      Message 2 of 3 , Aug 12 2:31 AM
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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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