Numerical Investigation of the Primety of Real numbers
Publikation: Forskning - peer review › Konferenceartikel i proceeding
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 |
|---|---|
| Titel | Second International ICST Conference on Arts and Technology |
| Antal sider | 9 |
| Udgivelsessted | Esbjerg |
| Udgiver | ICST |
| Udgivelsesdato | dec 2011 |
| Status | Udgivet |
Konference
| Konference | Second International ICST Conference on Arts and Technology |
|---|---|
| Nummer | 2 |
| Land | Danmark |
| By | Esbjerg |
| Periode | 07-12-11 → 09-12-11 |
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