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

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  • Phil Carmody
    ... You re being willed on from here in Estonia, too, Kevin! I always like to believe that the same kind of influence that sticks the e^-gamma term into prime
    Message 1 of 143 , Jan 3, 2011
      --- On Mon, 1/3/11, djbroadhurst <d.broadhurst@...> wrote:
      > --- 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!

      You're being willed on from here in Estonia, too, Kevin!
      I always like to believe that the same kind of influence that sticks the e^-gamma term into prime density expressions is kind enough to violate the Poisson independence criterion too.

      Phil
    • 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
        --- 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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