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Math Help - Prime number computation

  1. #1
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    Prime number computation

    Approximately how many primes less than one trillion (10^12) are there? I.e, compute pi(1000000000000) (Show computation)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by purplerain View Post
    Approximately how many primes less than one trillion (10^{12}) are there? I.e, compute pi(1000000000000) (Show computation)
    See this thread (among others).

    The simplest approximation is:

    \pi(x)\approx \frac{x}{\ln(x)}

    so:

    \pi(10^{12})\approx \frac{10^{12}}{\ln(10^{12})}\approx 3.619 \times 10^{10}

    CB
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