A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms. (10th September 2020)

• Record Type: Journal Article
• Authors: Mayer, B. L.; Monteiro, L. H. A.
• Other Names: Campos Eric Academic Editor.
• Is Part Of: Complexity. Volume 2020(2020)
• Publication Date: 2020-09-10
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2020/1480890
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : 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.