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

1. ### newcool

42
Hi, what would be the best estimate in the # of primes between $$10^{100}$$ and $$10^{101}$$

thanks

2. ### kreil

619
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:

$$Li(x)=\int_0^x\frac{dt}{log(t)}$$

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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