Number of Primes: How Computers Evaluate

[matqkks]

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

 

[jedishrfu]

One way is to have a list of primes and search for the highest one less than your number.

Another way is:

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

 

[fresh_42]

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.