Improved error bounds for the Fermat primality test on random inputs

TL;DR

This paper improves the probability bounds for random odd composite numbers passing the Fermat primality test, significantly refining previous estimates especially for numbers up to 2^{200}.

Contribution

The authors provide tighter error bounds for the Fermat primality test on random inputs, enhancing the accuracy of primality testing in practical ranges.

Findings

Error bounds improved by nearly 3 orders of magnitude for numbers up to 2^{200}.

More accurate probability estimates for Fermat test passing rates.

Enhanced understanding of Fermat test reliability on random composite numbers.

Abstract

We investigate the probability that a random odd composite number passes a random Fermat primality test, improving on earlier estimates in moderate ranges. For example, with random numbers to $2^{200}$, our results improve on prior estimates by close to 3 orders of magnitude.