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

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

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