Numerical Investigation of the Primety of Real numbers

Publikation: Forskning - peer reviewKonferenceartikel i proceeding

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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.
Originalsprog Dansk Second International ICST Conference on Arts and Technology 9 Esbjerg ICST dec 2011 Udgivet

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Konference Second International ICST Conference on Arts and Technology 2 Danmark Esbjerg 07-12-11 → 09-12-11
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