^{1} Sektion Esbjerg, The Technical Faculty of IT and Design, Aalborg University, VBN^{2} Department of Architecture, Design and Media Technology, The Technical Faculty of IT and Design, Aalborg University, VBN^{3} The Faculty of Engineering and Science (TECH), Aalborg University, VBN^{4} Esbjerg Institute of Technology, Aalborg University, The Faculty of Engineering and Science (ENG), Aalborg University, VBN

DOI:

10.1007/978-3-642-33329-3_19

Abstract:

The Farey sequences can be used [1] to create the Eulers totient function φ(n), by identifying the fractions for number n that did not occur in all Farey sequences up to n-1. This function creates, when divided by n-1, what is here called the Primety measure, which is a measure of how close to being a prime number n is. P(n)=φ(n)/(n-1) has maximum 1 for all prime numbers and minimum that decreases non-uniformly with n. Thus P(n) is the Primety function, which permits to designate a value of Primety of a number n. If P(n)==1, then n is a prime. If P(n)<1, n is not a prime, and the further P(n) is from n, the less n is a prime. φ(n) and P(n) is generalized to real numbers through the use of real numbered Farey sequences. The corresponding numerical sequences are shown to have interesting mathematical and artistic properties.

ISBN:

9783642333293, 9783642333286

Type:

Conference paper

Language:

English

Published in:

Lecture Notes of the Institute for Computer Sciences, Social-informatics and Telecommunications Engineering: Second International Conference, Artsit 2011, Esbjerg, Denmark, December 10-11, 2011, Revised Selected Papers, 2012, p. 160-167

Main Research Area:

Science/technology

Publication Status:

Published

Series:

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering (lnicst)