Pseudoprimes stronger than strong pseudoprimes

TL;DR

This paper introduces Midy pseudoprimes, explores their properties, and reveals their relationships with other pseudoprimes, including the connection to strong pseudoprimes, expanding the understanding of pseudoprime classifications.

Contribution

The paper characterizes Midy pseudoprimes, details their properties, and links them to known pseudoprimes, notably showing divisors are either primes or Midy pseudoprimes, with some being strong pseudoprimes.

Findings

Every divisor of a Midy pseudoprime is either prime or a Midy pseudoprime.

If a divisor is a Midy pseudoprime, it is a strong pseudoprime.

Midy pseudoprimes have unique properties connecting them to existing pseudoprime classes.

Abstract

We introduce a new class of pseudoprimes. In this work we characterize Midy pseudoprimes, give some of their properties and established interesting connections with other known pseudoprimes, in particular we show that every divisor of a Midy pseudoprime is either a prime or a Midy pseudoprime and in the last case it is a strong pseudoprime.