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Prime number counting formula up to any natural number

04 November 2025, Version 1
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

The main aim of this paper is to provide a new prime number counting formula, since it's one of the mathematical tools required to achieve a better understanding of prime numbers properties. By providing a way to determine the amount of prime numbers that exist up to any natural number in a different way this might offer some insight into other theorems related to prime numbers. Using a new method to determine primality in any integer number, new possibilities are open for number theory and some unsolved mathematical problems.

Keywords

Prime number
Primality
Prime number counting formula
Mathematical properties

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Version History

Nov 04, 2025 Version 1

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License

All Rights Reserved

DOI

10.33774/coe-2025-3n3dn
D O I: 10.33774/coe-2025-3n3dn [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) declare that they have sought and gained approval from the relevant ethics committee/IRB for this research and its publication.

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