The Farey sequences can be used  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.
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
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Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering (lnicst)