Numerical Investigation of the Primety of Real numbers

Kristoffer Jensen

doi:10.1007/978-3-642-33329-3_19

Numerical Investigation of the Primety of Real numbers

Kristoffer Jensen

Department of Architecture, Design and Media Technology

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

Abstract

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.

Original language	English
Title of host publication	Arts and Technology : Second International Conference, ArtsIT 2011, Esbjerg, Denmark, December 10-11, 2011, Revised Selected Papers
Editors	Anthony L. Brooks
Number of pages	8
Volume	101
Place of Publication	Berlin
Publisher	Springer
Publication date	2012
Pages	160-167
ISBN (Print)	978-3-642-33328-6
ISBN (Electronic)	978-3-642-33329-3
DOIs	https://doi.org/10.1007/978-3-642-33329-3_19
Publication status	Published - 2012
Event	ArtsIT - Esbjerg, Denmark Duration: 7 Dec 2011 → 9 Dec 2011 Conference number: 2

Conference

Conference	ArtsIT
Number	2
Country/Territory	Denmark
City	Esbjerg
Period	07/12/2011 → 09/12/2011

Series	Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering (LNICST)
Volume	101
ISSN	1867-8211

Access to Document

10.1007/978-3-642-33329-3_19

AUB Link

Search for the material in Aalborg University Library's search engine

Cite this

Jensen, Kristoffer. / Numerical Investigation of the Primety of Real numbers. Arts and Technology: Second International Conference, ArtsIT 2011, Esbjerg, Denmark, December 10-11, 2011, Revised Selected Papers. editor / Anthony L. Brooks. Vol. 101 Berlin : Springer, 2012. pp. 160-167 (Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering (LNICST), Vol. 101).

@inproceedings{2fb600847d254a798b72ad1449230a65,

title = "Numerical Investigation of the Primety of Real numbers",

abstract = "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.",

author = "Kristoffer Jensen",

year = "2012",

doi = "10.1007/978-3-642-33329-3_19",

language = "English",

isbn = "978-3-642-33328-6",

volume = "101",

series = "Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering (LNICST)",

publisher = "Springer",

pages = "160--167",

editor = "Brooks, {Anthony L.}",

booktitle = "Arts and Technology",

address = "Germany",

note = "ArtsIT ; Conference date: 07-12-2011 Through 09-12-2011",

}

Jensen, K 2012, Numerical Investigation of the Primety of Real numbers. in AL Brooks (ed.), Arts and Technology: Second International Conference, ArtsIT 2011, Esbjerg, Denmark, December 10-11, 2011, Revised Selected Papers. vol. 101, Springer, Berlin, Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering (LNICST), vol. 101, pp. 160-167, ArtsIT, Esbjerg, Denmark, 07/12/2011. https://doi.org/10.1007/978-3-642-33329-3_19

Numerical Investigation of the Primety of Real numbers. / Jensen, Kristoffer.
Arts and Technology: Second International Conference, ArtsIT 2011, Esbjerg, Denmark, December 10-11, 2011, Revised Selected Papers. ed. / Anthony L. Brooks. Vol. 101 Berlin: Springer, 2012. p. 160-167 (Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering (LNICST), Vol. 101).

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

TY - GEN

T1 - Numerical Investigation of the Primety of Real numbers

AU - Jensen, Kristoffer

N1 - Conference code: 2

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84869598512&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-33329-3_19

DO - 10.1007/978-3-642-33329-3_19

M3 - Article in proceeding

SN - 978-3-642-33328-6

VL - 101

T3 - Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering (LNICST)

SP - 160

EP - 167

BT - Arts and Technology

A2 - Brooks, Anthony L.

PB - Springer

CY - Berlin

T2 - ArtsIT

Y2 - 7 December 2011 through 9 December 2011

ER -

Jensen K. Numerical Investigation of the Primety of Real numbers. In Brooks AL, editor, Arts and Technology: Second International Conference, ArtsIT 2011, Esbjerg, Denmark, December 10-11, 2011, Revised Selected Papers. Vol. 101. Berlin: Springer. 2012. p. 160-167. (Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering (LNICST), Vol. 101). doi: 10.1007/978-3-642-33329-3_19

Numerical Investigation of the Primety of Real numbers

Abstract

Conference

Access to Document

AUB Link

Other files and links

Cite this