A procedure is developed for determining the primality of a number, N, but does not examine the number, rather a function of that number.
The function has several properties, by means of which many of the non-primes may be identified and discarded without further investigation.
Using the concept of cage numbers (defined in the text) a matrix of all of the counting numbers is produced, where, with the exception of the prime numbers 2 and 3, all of the prime numbers are embedded in one column of the matrix. Strings of consecutive numbers are extracted from the matrix, and it is seen that the only places within the whole of the range of the counting numbers where prime numbers can exist is at the positions of the second and penultimate numbers within a string
By means of the function of N, all of the odd numbers may be generated and examined for primality.
Inhaltsverzeichnis (Table of Contents)
- Introduction
- Analysis
- Cage numbers and the Magic Matrix
- Strings and things
- The key to locating the prime numbers
- Examining odd numbers for integer square roots and primality
- Discussion
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This paper develops a new method for determining the primality of a number by examining a function of that number. The method relies on the concept of "cage numbers" and the properties of a matrix formed using these numbers. The goal of this work is to provide a new perspective on the determination of prime numbers, potentially offering a more efficient way to identify primes.
- Identification of prime numbers
- The use of a function to determine primality
- The concept of cage numbers and the Magic Matrix
- String extraction and its significance in locating prime numbers
- The relationship between odd numbers, integer square roots, and primality
Zusammenfassung der Kapitel (Chapter Summaries)
- Introduction: This chapter introduces the topic of prime numbers and their importance in mathematics, highlighting the enduring fascination surrounding their study. The author references the quote of Veisdal [1], which emphasizes the significance of finding a formula for predicting prime numbers.
- Analysis: This chapter presents the core of the paper's methodology. It introduces a matrix of odd numbers and demonstrates the pattern of prime numbers within this matrix. The chapter explores the properties of this matrix, including the concept of cage numbers, string extraction, and the relationship between prime numbers and the position of numbers within strings.
Schlüsselwörter (Keywords)
The key terms and concepts explored in this work include: prime numbers, primality determination, cage numbers, Magic Matrix, string extraction, integer square roots, odd numbers, and efficient prime number identification. This research focuses on developing a new methodology for determining the primality of numbers, potentially offering a more efficient approach to identifying prime numbers.
- Citation du texte
- William Fidler (Auteur), 2023, A new perspective on the determination of the prime numbers, Munich, GRIN Verlag, https://www.grin.com/document/1360641
