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Do these prime runs have a name?

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  • Robert
    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)
    • 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 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
      • Robert
        ... 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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