Dynamics and Forms of Products of Twin, Cousin and Sexy Primes

Ahmet F. Gocgen; Emin M. Buyukyayla

doi:10.20944/preprints202409.1002.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 9 September 2024 / Approved: 11 September 2024 / Online: 12 September 2024 (14:09:37 CEST)

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.

number theory; cousin primes; product of cousin primes; prime products

Computer Science and Mathematics, Algebra and Number Theory

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Dynamics and Forms of Products of Twin, Cousin and Sexy Primes

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