How many prime numbers in a given interval?

Use the prime-counting function and get $\pi(a_n)-\pi(a_1-1)$


The prime number theorem gives an approximation to $\pi(n),$ the number of primes less than $n$. You can subtract the values at the start and end of an interval. Mathematica and other software can compute exact values for small values of $n$ and approximate values for larger values of $n$. The first approximation is $\pi(n) \sim \frac n{\log n}$ but a much better one is $$\pi(n)\sim \int_2^n \frac {dt}{\log t}$$

Tags:

Interval Arithmetic

Prime Numbers

Prime Gaps

Natural Numbers

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