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RE reciprocal consecutive primes (typo)

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  • Jose Ramón Brox
    ... From: Jose Ramón Brox q/p 7. ... I mean it s a SUFFICIENT condition.
    Message 1 of 3 , Nov 2, 2005
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      ----- Original Message -----
      From: "Jose Ramón Brox" <ambroxius@...>

      q/p < 3/2 is a simpler necessary condition that seems to hold if p>7.

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

      I mean it's a SUFFICIENT condition. If q/p < 3/2, then by the inequalities developed in
      the former email, we got that 1/p < 1/q + 1/r.

      Regards. Jose Brox.
    • 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 2 of 3 , Nov 3, 2005
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        ----- 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 3 of 3 , Nov 3, 2005
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          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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