Anomalous Primes and the Elliptic Korselt Criterion

TL;DR

This paper investigates the connection between elliptic Korselt numbers of Type I and anomalous primes, providing conditions under which such Korselt numbers are products of anomalous primes, and showing this is true for most cases of a certain form.

Contribution

It generalizes previous results by establishing sufficient conditions for elliptic Korselt numbers of Type I to be products of anomalous primes and proves this for most numbers of a specific form.

Findings

Almost all elliptic Korselt numbers of the form n=pq are products of anomalous primes.

Provides generalized sufficient conditions linking elliptic Korselt numbers and anomalous primes.

Enhances understanding of the structure of elliptic Korselt numbers in relation to anomalous primes.

Abstract

We explore the relationship between elliptic Korselt numbers of Type I, a class of pseudoprimes introduced by Silverman in [20], and anomalous primes. We generalize a result in [20] that gives sufficient conditions for an elliptic Korselt number of Type I to be a product of anomalous primes. Finally, we prove that almost all elliptic Korselt numbers of Type I of the form n=pq are a product of anomalous primes