Loading ...
Sorry, an error occurred while loading the content.

PNT and an attempt to persuade

Expand Messages
  • gulland68
    I Have a mathematician friend and I am trying to convince him of the following: Take P(m) to be the set of primes less than the square root of an integer n.
    Message 1 of 2 , Mar 17, 2008
    • 0 Attachment
      I Have a mathematician friend and I am trying to convince him of the
      following:

      Take P(m) to be the set of primes less than the square root of an
      integer n.
      Take a(m) to be their product.
      Consider a matrix in which members of P(m) index rows and in which
      each column that is defined as 'unoccupied' is on that does not index
      a multiple of a member of P(m).
      Take the number of unoccupied columns in an interval of length a(m) to
      be u.
      By the proof of the Prime Number Theorem, as n increases
      pi(n)converges on u*n/a(m).

      How can I do this?

      Cheers.
      Tom
    • Bhupinder Singh Anand
      On Tuesday, March 18, 2008 8:09 AM, gulland68 wrote in primenumbers: TG Consider a matrix in which members of P(m) index rows and in which each column that
      Message 2 of 2 , Mar 19, 2008
      • 0 Attachment
        On Tuesday, March 18, 2008 8:09 AM, gulland68 wrote in primenumbers:

        TG>> Consider a matrix in which members of P(m) index rows and in which each
        column that is defined as 'unoccupied' is on that does not index a multiple
        of a member of P(m). . How can I do this? <<TG

        Tom
        ====
        See if this matrix for generating the primes helps:

        http://alixcomsi.com/A_Minimal_Prime.htm

        Bhup
      Your message has been successfully submitted and would be delivered to recipients shortly.