Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# A Fundamental Study of Composite Numbers as a Different Perspective on Problems Related to Prime Numbers

Version 1 : Received: 2 March 2023 / Approved: 3 March 2023 / Online: 3 March 2023 (09:13:27 CET)

A peer-reviewed article of this Preprint also exists.

Aysun, E.; Gocgen, A.F. A Fundamental Study of Composite Numbers as a Different Perspective on Problems Related to Prime Numbers. International Journal of Pure and Applied Mathematics Research 2023, 3, 70–76, doi:10.51483/ijpamr.3.1.2023.70-76. Aysun, E.; Gocgen, A.F. A Fundamental Study of Composite Numbers as a Different Perspective on Problems Related to Prime Numbers. International Journal of Pure and Applied Mathematics Research 2023, 3, 70–76, doi:10.51483/ijpamr.3.1.2023.70-76.

## Abstract

Prime number-related issues can be viewed from drastically different perspectives by examining the close connections between prime numbers and composite numbers. We think that multiple perspectives are the pillars on the path to solutions so we have created this study. As a result of the study, we proposed two new formulas by presenting three theorems and one proof for each theorem, a total of three proofs. We proved that the formula p · n + p returns a composite number in the first of the theorems, which is the preliminary theorem. Our first theorem except the preliminary theorem is that the formula p · n + p returns all composite numbers, and we proved that too. Finally, we created Theorem II using Theorem I to use in our other work and proved that the formula 2 · n · p + p returns all odd composite numbers, which is Theorem II. Afterward, we presented the similarities of the 2 · n · p + p formula we put forth with another known formula.

## Keywords

prime numbers; composite numbers; prime-composite relationship; formula of composite; formula of all composite; formula of all odd composite

## Subject

Computer Science and Mathematics, Algebra and Number Theory

Comment 1
Commenter: James Grooven
The commenter has declared there is no conflict of interests.
Comment: That seems interesting. An equation that connects odd composites to prime would certainely solve lot of misteries in njmber theory
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Response 1 to Comment 1
Commenter:
The commenter has declared there is no conflict of interests.
Comment: Thanks for your evaluation. We will keep working because as you said there are a lot of mysteries in number theory waiting to be solved! :)
Comment 2
Commenter: Marouane RHAFLI
The commenter has declared there is no conflict of interests.
Comment: Hi,

I am Marouane RHAFLI, the developer of the formula (p^2+2pc=N), I read your article, and I would like to say congratulations to you as your new formula seems a great optimization to mine, I invite you to check my article about how I used the formula to give a solution to some unsolved conjectures. I do believe by using yours, you can solve other conjecture such as the beals conjecture.

All the best
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Response 1 to Comment 2
Commenter:
The commenter has declared there is no conflict of interests.
Comment: Good day.
Hi,

I am Ejder Aysun, co-author of this article. Thank you for your congratulations and evaluation. We will reread your article and work on conjectures such as the Beals Conjecture. Also, thank you for your suggestions.

All the best