The prime number theorem

Document Type : Review Paper

Author

Zanjan, University Boulevard, University of Zanjan, Faculty of Science, Department of Mathematics

Abstract

The Prime Number Theorem is one of the most important and prominent theorems in number theory. This theorem, which concerns the distribution of prime numbers and establishes an asymptotic relationship for the number of prime numbers, was first conjectured by Gauss and finally proven to be correct after about a hundred years. The Prime Number Theorem still holds great importance because a more precise approximation of this theorem, namely the Prime Number Theorem with Error Term, depends on the correctness of the Riemann Hypothesis, which to this day remains one of the greatest unsolved problems in mathematics. In this article, we provide a brief historical overview of this issue and the process of its proof, along with a relatively concise proof presented by Don Zagier at the centenary celebration.

Keywords

References

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Mathematics and Society
Volume 4, Issue 3 - Serial Number 3
September 2019
Pages 23-43

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