Sieving for pseudosquares and pseudocubes in parallel using doubly-focused enumeration and wheel datastructures

TL;DR

This paper introduces a parallel algorithm using wheel data structures and doubly-focused enumeration to extend tables of pseudosquares and pseudocubes, impacting their distribution conjectures.

Contribution

It presents a novel parallel algorithm combining wheel data structures with doubly-focused enumeration for efficient computation of pseudosquares and pseudocubes.

Findings

Extended tables of pseudosquares and pseudocubes.

Implications for distribution conjectures.

Demonstrated efficiency of the parallel algorithm.

Abstract

We extend the known tables of pseudosquares and pseudocubes, discuss the implications of these new data on the conjectured distribution of pseudosquares and pseudocubes, and present the details of the algorithm used to do this work. Our algorithm is based on the space-saving wheel data structure combined with doubly-focused enumeration, run in parallel on a cluster supercomputer.