Research Article
Numerical Investigation of the Primety of Real Numbers
@INPROCEEDINGS{10.1007/978-3-642-33329-3_19, author={Kristoffer Jensen}, title={Numerical Investigation of the Primety of Real Numbers}, proceedings={Arts and Technology. Second International Conference, ArtsIT 2011, Esbjerg, Denmark, December 10-11, 2011, Revised Selected Papers}, proceedings_a={ARTSIT}, year={2012}, month={10}, keywords={Farey sequences Totient function Primety Selfsimilarity Fractals}, doi={10.1007/978-3-642-33329-3_19} }- Kristoffer Jensen
Year: 2012
Numerical Investigation of the Primety of Real Numbers
ARTSIT
Springer
DOI: 10.1007/978-3-642-33329-3_19
Abstract
The Farey sequences can be used [1] to create the Eulers totient function (), by identifying the fractions for number that did not occur in all Farey sequences up to . 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. () has maximum for all prime numbers and minimum that decreases non-uniformly with n. Thus is the Primety function, which permits to designate a value of Primety of a number . If , then n is a prime. If <, n is not a prime, and the further is from n, the less n is a prime. () and 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.
