An Upper Estimate for the Overpseudoprime Counting Function

TL;DR

This paper establishes an upper bound on the count of overpseudoprimes to base 2 up to a given number x, showing it grows no faster than approximately x to the three-fourths power.

Contribution

It provides the first known upper estimate for the overpseudoprime counting function to base 2, advancing understanding of pseudoprime distribution.

Findings

Number of overpseudoprimes to base 2 up to x is at most x^(3/4)(1+o(1))

The growth rate of overpseudoprimes is significantly slower than x

New bounds improve previous estimates on pseudoprime counts

Abstract

We prove that the number of overpseudoprimes to base 2 not exceeding x does not exceed x^(3/4)(1+o(1)).