Prime numbers and random walks in a square grid
Number Theory
2021-11-24 v1 History and Overview
Abstract
In recent years, computer simulations are playing a fundamental role in unveiling some of the most intriguing features of prime numbers. In this work, we define an algorithm for a deterministic walk through a two-dimensional grid that we refer to as Prime Walk. The walk is constructed from a sequence of steps dictated by and dependent on the sequence of last digits of the primes. Despite the apparent randomness of this generating sequence, the resulting structure -- both in 2d and 3d -- created by the algorithm presents remarkable properties and regularities in its pattern that we proceed to analyze in detail.
Cite
@article{arxiv.2105.12547,
title = {Prime numbers and random walks in a square grid},
author = {Alberto Fraile and Osame Kinouchi and Prashant Dwivedi and Roberto Martínez and Theophanes E. Raptis and Daniel Fernández},
journal= {arXiv preprint arXiv:2105.12547},
year = {2021}
}
Comments
7 pages, 7 figures