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## Main Question or Discussion Point

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

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- Thread starter matqkks
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How do computers evaluate the number of primes below a given integer?

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jedishrfu

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Another way is:

https://primes.utm.edu/howmany.html

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fresh_42

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

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

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