Prime numbers and random walks in a square grid.

Fraile, Alberto; Kinouchi, Osame; Dwivedi, Prashant; Martínez, Roberto; Raptis, Theophanes E; Fernández, Daniel · Phys Rev E · 2021

basic_science · Level V

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Abstract

In recent years, computer simulations have played a fundamental role in unveiling some of the most intriguing features of prime numbers. In this paper, we define an algorithm for a deterministic walk through a two-dimensional grid, which we refer to as a prime walk. The walk is constructed from a sequence of steps dictated by and dependent on the sequence of the last digits of the primes. Despite the apparent randomness of this generating sequence, the resulting structure-in both two and three dimensions-created by the algorithm presents remarkable properties and regularities in its pattern, which we proceed to analyze in detail.