Numerical Investigation of the Primety of Real numbers
Publikation: Forskning - peer review › Konferenceartikel i proceeding
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.
|Titel||Second International ICST Conference on Arts and Technology|
|Konference||Second International ICST Conference on Arts and Technology|
|Periode||07-12-11 → 09-12-11|
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