Arts and Technology. Second International Conference, ArtsIT 2011, Esbjerg, Denmark, December 10-11, 2011, Revised Selected Papers

Research Article

Numerical Investigation of the Primety of Real Numbers

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  • @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
Kristoffer Jensen1,*
  • 1: Aalborg University Esbjerg
*Contact email: krist@create.aau.dk

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.