Prime counting function

Function representing the number of primes less than or equal to a given number

In mathematics, the prime counting function is the function counting the number of prime numbers less than or equal to some real number x. It is written as ${\displaystyle \pi (x)}$,[1] but it is not related to the number π. Some key values of the function include ${\displaystyle \pi (1)=0}$, ${\displaystyle \pi (2)=1}$ and ${\displaystyle \pi (3)=2}$.

The 60 first values of π(n)

In general, if ${\displaystyle p_{n}}$stands for the n-th prime number, then ${\displaystyle \pi (p_{n})=n}$.[2]

References

1. "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-10-07.
2. Weisstein, Eric W. "Prime Counting Function". mathworld.wolfram.com. Retrieved 2020-10-07.