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How many primes are there in a certain range of numbers?

  1. Jan 19, 2005 #1
    Hi, what would be the best estimate in the # of primes between [tex]10^{100}[/tex] and [tex]10^{101} [/tex]

    thanks
     
  2. jcsd
  3. Jan 19, 2005 #2

    kreil

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    Gold Member

    I'm not sure if there is a newer equation, there probably is one from riemman, but Gauss had a formula for approximating the number of primes up to any number x:

    [tex]Li(x)=\int_0^x\frac{dt}{log(t)}[/tex]

    You could compute this for 10100 and then for 10101 and subtract the first result from the second and it will give a good estimate.
     
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