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

Density of Prime Numbers

Expand Messages
  • Milton Brown
    The number of primes with exactly 100 digits is approximately 4*10^97.The number of primes with exactly 200 digits is approximately 2.4*10^196. Does this mean
    Message 1 of 2 , Jun 13, 2004
    • 0 Attachment
      The number of primes with exactly 100
      digits is approximately 4*10^97.The
      number of primes with exactly 200 digits
      is approximately 2.4*10^196.

      Does this mean that density of 200 digit
      primes is approximately

      1/17 = 2.4/40 less dense than 100 digit

      primes?

      Milton L. Brown
      miltbrown at earthlink.net
      miltbrown@...

      [Non-text portions of this message have been removed]
    • Jens Kruse Andersen
      ... No. Using the approximation pi(n) = n/ln n, the number of 200-digit primes is around 2*10^197. ... No. The approximate ratio is 0.5. The density of primes
      Message 2 of 2 , Jun 14, 2004
      • 0 Attachment
        Milton Brown wrote:
        > The number of primes with exactly 100
        > digits is approximately 4*10^97. The
        > number of primes with exactly 200 digits
        > is approximately 2.4*10^196.

        No. Using the approximation pi(n) = n/ln n, the number of 200-digit primes is
        around 2*10^197.

        > Does this mean that density of 200 digit
        > primes is approximately
        >
        > 1/17 = 2.4/40 less dense than 100 digit
        >
        > primes?

        No. The approximate ratio is 0.5.
        The density of primes is around reversely proportional to the number of digits,
        i.e. twice the digits, half the chance.
        A simple approximation to the density near n is 1/ln n.

        --
        Jens Kruse Andersen
      Your message has been successfully submitted and would be delivered to recipients shortly.