A Cubic Composite Test

TL;DR

This paper introduces a new cubic composite primality test for odd positive integers based on the discriminant being a perfect square, comparing it with existing tests and noting its robustness due to no known counterexamples.

Contribution

The paper presents a novel cubic composite test relying on discriminant properties, expanding the toolkit for primality testing with no known counterexamples.

Findings

Test has no known counterexamples despite extensive checks

Comparison with Baillie-PSW tests shows differences in approach

Related quadratic test also lacks known counterexamples

Abstract

A single parameter cubic composite test for odd positive integers is given which relies on the discriminant always being a square integer. This test has no known counterexample despite extensive verifications. As well as a comparison with the Baillie-PSW tests, a related quadratic composite test is briefly examined which also has no known counterexample.