Version 1
: Received: 28 July 2024 / Approved: 29 July 2024 / Online: 30 July 2024 (00:07:38 CEST)
How to cite:
Shiraishi, H.; Shiraishi, H.; Taniguchi, Y. Development of a Simple Prime Number Determination Method by excluding Composite Numbers on 6n±1. Preprints2024, 2024072314. https://doi.org/10.20944/preprints202407.2314.v1
Shiraishi, H.; Shiraishi, H.; Taniguchi, Y. Development of a Simple Prime Number Determination Method by excluding Composite Numbers on 6n±1. Preprints 2024, 2024072314. https://doi.org/10.20944/preprints202407.2314.v1
Shiraishi, H.; Shiraishi, H.; Taniguchi, Y. Development of a Simple Prime Number Determination Method by excluding Composite Numbers on 6n±1. Preprints2024, 2024072314. https://doi.org/10.20944/preprints202407.2314.v1
APA Style
Shiraishi, H., Shiraishi, H., & Taniguchi, Y. (2024). Development of a Simple Prime Number Determination Method by excluding Composite Numbers on 6n±1. Preprints. https://doi.org/10.20944/preprints202407.2314.v1
Chicago/Turabian Style
Shiraishi, H., Hajime Shiraishi and Yukiya Taniguchi. 2024 "Development of a Simple Prime Number Determination Method by excluding Composite Numbers on 6n±1" Preprints. https://doi.org/10.20944/preprints202407.2314.v1
Abstract
A prime number is a natural number with no divisors other than itself and the number 1. There are many unsolved problems related to prime numbers. One such problem is finding a general method for identifying prime numbers. Although it is known that all prime numbers fall under the categories of 2, 3, or 6n±1 (where n≥1), a formalized method for eliminating composite numbers (non-prime numbers) from these categories has yet to be developed. This paper aims to explore a possible method for such elimination, which involves checking whether there exists an n that satisfies n = 6km+k+m or n = 6km+k-m (where k and m are non-zero integers). This method is expected to be a major step forward in the derivation of prime numbers.
Keywords
Prime numbers; Composite numbers; 6n±1
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
