English

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.

Keywords

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

R2 v1 2026-06-24T02:29:14.346Z