Number of primes

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Main Question or Discussion Point

How do computers evaluate the number of primes below a given integer?
 

Answers and Replies

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How do computers evaluate the number of primes below a given integer?
This depends on so many parameters, that it can't be answered, except perhaps by the sieve of Eratosthenes, or simply by ##|\pi(x)-\operatorname{Li}(x)|<\dfrac{\sqrt{x}\ln x}{8\pi}##.

The literature has many algorithms as well as estimations for ##\pi(x)##. Just search for them.
 

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