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Prime Counting Function

Tool for counting prime numbers via the prime-counting function denoted pi(n) which counts the prime numbers less than or equal to a real number n.

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Prime Counting Function -

Tag(s) : Arithmetics, Mathematics

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Prime Counting Function

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Prime Count π(n)


Tool for counting prime numbers via the prime-counting function denoted pi(n) which counts the prime numbers less than or equal to a real number n.

Answers to Questions

How to calculate pi(n)?

For small numbers, the easiest method is to use the Eratosthenes sieve to quickly list and count all the first ones less than \( n \).

Example: \( \pi(100) = 25 \) so there are 25 prime numbers less than 100.

How to calculate an approximation of pi(n)?

The value of pi(n) approaches \( n / \ln(n) \) when \( n \) is very big:

$$ \lim_{ n \to + \infty } \pi(n) = \frac{ n }{ \ln(n) } $$

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