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Math Help - Prime Number Theorem

  1. #1
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    Prime Number Theorem

    Can anyone show me how to work this?

    Consider the set of all prime numbers less that 80000. Estimate, using the Prime Number Theorem, the proportion which are less than 40000 and the proportion which are less than 8000.
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  2. #2
    MHF Contributor chisigma's Avatar
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    There are two simple approximations of the \pi (n) function, which gives the number of primes less or equal to n

    a) \pi(n) \approx \frac{n}{\ln n} proposed by Gauss

    b) \pi(n) \approx \frac{n}{\ln n - 1,08366} proposed by Legendre

    If we use a) is…

    \pi(80000) \approx 7086 , \pi(40000) \approx 3774 , \pi(8000) \approx 890

    If we use b) is…

    \pi(80000) \approx 7838 , \pi(40000) \approx 4204 , \pi(8000) \approx 1012

    Kind regards

    \chi \sigma
    Last edited by chisigma; April 1st 2009 at 11:14 AM.
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