Frequency Distribution of Prime Numbers between an Integer and its Square: A Case Study

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FREQUENCY DISTRIBUTION OF PRIME NUMBERS.pdf (910.68 KB)

Date

2022-09-26

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Publisher

arXiv

Abstract

The chronicle of prime numbers travel back thousands of years in human history. Not only the traits of prime numbers have surprised people, but also all those endeavors made for ages to find a pattern in the appearance of prime numbers has been captivating them. Until recently, it was firmly believed that prime numbers do not maintain any pattern of occurrence among themselves. This statement is conferred not to be completely true. This paper is also an attempt to discover a pattern in the occurrence of prime numbers. This work intends to introduce some mathematical well-known equations that point to the existence of a simplistic pattern in the number of primes within the range of a number and its square. We assume that the rigorous evaluation of the perceived pattern may benefit in many aspects such as applications of encryption, algorithms concerning prime numbers, and many more.

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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

Keywords

Prime Numbers, Prime Number Count

Citation

Muhammad, T., Shahariar, G. M., Aziz, T., & Alam, M. S. (2022). Frequency Distribution of Prime Numbers between an Integer and its Square: A Case Study. arXiv preprint arXiv:2209.12494.

URI

https://hdl.handle.net/10294/16562

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Tahsin Aziz