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

newcool

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

thanks

kreil

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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newcool	How many primes are there in a certain range of numbers? Tweet Hi, what would be the best estimate in the # of primes between [tex]10^{100}[/tex] and [tex]10^{101} [/tex] thanks

kreil Recognitions: 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.