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Re: pi(x) - pi(x/7) > sqrt(x)

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  • djbroadhurst
    ... A proof, for integer x 2, was given by Harold Shapiro in 1953 and may be found here: http://tinyurl.com/3yycvms The inequality is true by inspection for
    Message 1 of 4 , Jul 14, 2010
      --- In primenumbers@yahoogroups.com,
      "John W. Nicholson" <reddwarf2956@...> wrote:

      > pi(x) - pi(x/7) > sqrt(x) proved by N. Shapiro

      A proof, for integer x > 2, was given by Harold Shapiro
      in 1953 and may be found here:

      http://tinyurl.com/3yycvms

      The inequality is true by inspection for 2 < x < 10590
      and for larger x follows from a stronger result by
      Ramanujan, given in Eq. (3.2) of Shapiro's paper.

      David
    • John
      David thanks, Sorry I left off the Harold in Harold N. Shapiro. John W. Nicholson
      Message 2 of 4 , Jul 14, 2010
        David thanks,

        Sorry I left off the "Harold" in Harold N. Shapiro.

        John W. Nicholson


        --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
        >
        >
        >
        > --- In primenumbers@yahoogroups.com,
        > "John W. Nicholson" <reddwarf2956@> wrote:
        >
        > > pi(x) - pi(x/7) > sqrt(x) proved by N. Shapiro
        >
        > A proof, for integer x > 2, was given by Harold Shapiro
        > in 1953 and may be found here:
        >
        > http://tinyurl.com/3yycvms
        >
        > The inequality is true by inspection for 2 < x < 10590
        > and for larger x follows from a stronger result by
        > Ramanujan, given in Eq. (3.2) of Shapiro's paper.
        >
        > David
        >
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