Version 1
: Received: 9 September 2024 / Approved: 11 September 2024 / Online: 12 September 2024 (14:09:37 CEST)
How to cite:
Gocgen, A. F.; Buyukyayla, E. M. Dynamics and Forms of Products of Twin, Cousin and Sexy Primes. Preprints2024, 2024091002. https://doi.org/10.20944/preprints202409.1002.v1
Gocgen, A. F.; Buyukyayla, E. M. Dynamics and Forms of Products of Twin, Cousin and Sexy Primes. Preprints 2024, 2024091002. https://doi.org/10.20944/preprints202409.1002.v1
Gocgen, A. F.; Buyukyayla, E. M. Dynamics and Forms of Products of Twin, Cousin and Sexy Primes. Preprints2024, 2024091002. https://doi.org/10.20944/preprints202409.1002.v1
APA Style
Gocgen, A. F., & Buyukyayla, E. M. (2024). Dynamics and Forms of Products of Twin, Cousin and Sexy Primes. Preprints. https://doi.org/10.20944/preprints202409.1002.v1
Chicago/Turabian Style
Gocgen, A. F. and Emin M. Buyukyayla. 2024 "Dynamics and Forms of Products of Twin, Cousin and Sexy Primes" Preprints. https://doi.org/10.20944/preprints202409.1002.v1
Abstract
Prime numbers are the building blocks of number theory, and their properties have intrigued mathematicians for centuries. In this paper, we explore a specific categorization of primes, which we refer to as "twin primes", “cousin primes” and "sexy primes". We begin by examining the form of prime numbers greater than 7 and analyze their potential to be expressed in terms of $6n + 5$ or $6n + 7$. This investigation leads to the identification of conditions under which prime numbers can form twin, cousin and sexy pairs. We further develop a general framework to characterize the product of all twin (except 15), cousin (except 21) and sexy primes, providing insights into their algebraic structure.
Keywords
number theory; cousin primes; product of cousin primes; prime products
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.