Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

# Distribution of Composite Numbers and Determination of Prime Numbers

Version 1 : Received: 12 December 2021 / Approved: 15 December 2021 / Online: 15 December 2021 (08:35:38 CET)
Version 2 : Received: 15 December 2021 / Approved: 16 December 2021 / Online: 16 December 2021 (10:52:02 CET)
Version 3 : Received: 18 December 2021 / Approved: 20 December 2021 / Online: 20 December 2021 (11:53:57 CET)
Version 4 : Received: 22 December 2021 / Approved: 24 December 2021 / Online: 24 December 2021 (07:36:30 CET)

How to cite: Gocgen, A.F. Distribution of Composite Numbers and Determination of Prime Numbers. Preprints 2021, 2021120249. https://doi.org/10.20944/preprints202112.0249.v2 Gocgen, A.F. Distribution of Composite Numbers and Determination of Prime Numbers. Preprints 2021, 2021120249. https://doi.org/10.20944/preprints202112.0249.v2

## Abstract

Integer is either a composite number or a prime number. Therefore, detecting composite numbers is important for solving prime numbers. The study of prime numbers, apart from satisfying human curiosity, can be very important. In this article, the order of composite numbers has been detected. And explained with a simple method and a simple function. And, a method has been developed in which all composite numbers and therefore prime numbers can be determined by using the specified methods, functions and formulas.

## Keywords

composite number; composite numbers distribution; composite numbers generation; prime number

## Subject

Computer Science and Mathematics, Algebra and Number Theory

Comment 1
Commenter: Ahmet Gocgen
Commenter's Conflict of Interests: Author
Comment: Fixed typos that caused confusion of meaning in second article version.
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Comment 2
Commenter: Bill McEachen
The commenter has declared there is no conflict of interests.
Comment: Mr Gocgen:

I am unsure what new insight you provide.

Hugh Barker (2012) provides the equation that produces all odd composites:
2x + 4y(x+y) -1 (x,y integers each > 0)
ref: http://barkerhugh.blogspot.in/2012/05/composite-number-formula.html

This combined with knowing all primes (after 2,3) must appear at 6m+/-1 completely dictates the location of the primes.

Bill
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