Prime numbers and random walks in a square grid

TL;DR

This paper introduces a deterministic algorithm called Prime Walk that explores prime number patterns through a random walk in a grid, revealing unexpected regularities and structures.

Contribution

It presents a novel Prime Walk algorithm based on prime last digits, analyzing its surprising regularities in 2D and 3D grid structures.

Findings

The Prime Walk exhibits notable regularities in its pattern.

The structure shows unexpected geometric properties.

Prime last digits influence the walk's pattern significantly.

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.