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 P: 517 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.