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

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.