A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms

A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms

Let a d-prime be a positive integer number with d divisors. From this definition, the usual prime numbers correspond to the particular case d=2. Here, the seemingly random sequence of gaps between consecutive d-primes is numerically investigated. First, the variability of the gap sequences for d∈2,3...

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Main Authors: B. L. Mayer, L. H. A. Monteiro
Format: Article
Language:English
Published: Hindawi-Wiley 2020-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2020/1480890
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spelling doaj-8764effee01040b3a7d638bfe5d57a852020-11-25T04:10:29ZengHindawi-WileyComplexity1076-27871099-05262020-01-01202010.1155/2020/14808901480890A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility AlgorithmsB. L. Mayer0L. H. A. Monteiro1Universidade Presbiteriana Mackenzie, PPGEEC, São Paulo, SP, BrazilUniversidade Presbiteriana Mackenzie, PPGEEC, São Paulo, SP, BrazilLet a d-prime be a positive integer number with d divisors. From this definition, the usual prime numbers correspond to the particular case d=2. Here, the seemingly random sequence of gaps between consecutive d-primes is numerically investigated. First, the variability of the gap sequences for d∈2,3,…,11 is evaluated by calculating the informational entropy. Then, these sequences are mapped into graphs by employing two visibility algorithms. Computer simulations reveal that the degree distribution of most of these graphs follows a power law. Conjectures on how some topological features of these graphs depend on d are proposed.http://dx.doi.org/10.1155/2020/1480890
collection DOAJ
language English
format Article
sources DOAJ
author B. L. Mayer
L. H. A. Monteiro
spellingShingle B. L. Mayer
L. H. A. Monteiro
A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms
Complexity
author_facet B. L. Mayer
L. H. A. Monteiro
author_sort B. L. Mayer
title A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms
title_short A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms
title_full A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms
title_fullStr A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms
title_full_unstemmed A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms
title_sort numerical study on the regularity of d-primes via informational entropy and visibility algorithms
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2020-01-01
description Let a d-prime be a positive integer number with d divisors. From this definition, the usual prime numbers correspond to the particular case d=2. Here, the seemingly random sequence of gaps between consecutive d-primes is numerically investigated. First, the variability of the gap sequences for d∈2,3,…,11 is evaluated by calculating the informational entropy. Then, these sequences are mapped into graphs by employing two visibility algorithms. Computer simulations reveal that the degree distribution of most of these graphs follows a power law. Conjectures on how some topological features of these graphs depend on d are proposed.
url http://dx.doi.org/10.1155/2020/1480890
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