Sieving for Pseudosquares and Pseudocubes in Parallel Using Doubly-Focused Enumeration and Wheel Datastructures

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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.

Supported by a grant from the Holcomb Awards Committe, and computing resources provided by the Frank Levinson Supercomputing Center at Butler University.