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Re: Prime chains x-->Ax+B [puzzle 2]

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  • djbroadhurst
    ... The bad news, of course, is that Poisson gives you no credit whatsoever for the 18 previous failures. Your chance of success with the next 6 is about 1 -
    Message 1 of 143 , Jan 3, 2011
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      --- In primenumbers@yahoogroups.com,
      Kevin Acres <research@...> wrote:

      > I expect this to give an extra 6 or so 15/16 chains on
      > top of the 18 I have now.

      The bad news, of course, is that Poisson gives you
      no credit whatsoever for the 18 previous failures.
      Your chance of success with the next 6 is about
      1 - exp(-6*mu) =~ 50%
      if we are are right about the mean probability
      mu =~ 1/9.

      Good luck!

      David
    • djbroadhurst
      ... Suppose that we want to start with a square and get a square. Then we must solve the Diophantine equation y^2 = a*x^2 + b For any pair (a,b), Dario will
      Message 143 of 143 , Jan 7, 2011
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        --- In primenumbers@yahoogroups.com,
        Kevin Acres <research@...> wrote:

        > x=a*x+b either is a square or has a square as a major factor.

        Suppose that we want to start with a square and get a square.
        Then we must solve the Diophantine equation
        y^2 = a*x^2 + b

        For any pair (a,b), Dario will tell us all the solutions:
        http://www.alpertron.com.ar/QUAD.HTM

        David
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