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RE reciprocal consecutive primes (typo)

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  • Jose Ramón Brox
    ... From: Jose Ramón Brox Consider b = a-1, then we have m*n = (p+a)(p-b) = (p+a)(p-a+1) = p^2 +p-a(a+1) ... The final equality should
    Message 1 of 3 , Nov 3, 2005
      ----- Original Message -----
      From: "Jose Ramón Brox" <ambroxius@...>

      Consider b = a-1, then we have

      m*n = (p+a)(p-b) = (p+a)(p-a+1) = p^2 +p-a(a+1)

      -----------------------------------

      The final equality should read p^2 + p -a(a-1)

      Jose Brox
    • Jeremy Wood
      Gauss-Legendre conjectured that the prime counting function of x is similar to x/ln(x). (Or more specifically that as x approaches infinity: pi(x)/(x/ln(x)) -
      Message 2 of 3 , Nov 3, 2005
        Gauss-Legendre conjectured that the prime counting
        function of x is similar to x/ln(x).
        (Or more specifically that as x approaches infinity:
        pi(x)/(x/ln(x)) -> 1)

        Are there other functions in number theory that are
        similar to the function:
        y = x/ln(x)?

        Specifically I'm studying a phenomenon that appears to
        resemble:
        y = x/ln(x+c)

        - Jeremy
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