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Prime counting function




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The 60 first values of π(n)

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 [math]\pi(x)[/math],[1] but it is not related to the number π. Some key values of the function include [math]\pi(1)=0[/math], [math]\pi(2)=1[/math] and [math]\pi(3)=2[/math].

In general, if [math]p_n[/math]stands for the n-th prime number, then [math]\pi(p_n)=n[/math].[2]

Related pages

References

  1. "Comprehensive List of Algebra Symbols" (in en-US). 2020-03-25. https://mathvault.ca/hub/higher-math/math-symbols/algebra-symbols/. 
  2. Weisstein, Eric W.. "Prime Counting Function" (in en). https://mathworld.wolfram.com/PrimeCountingFunction.html.