# There are Infinitely Many Perrin Pseudoprimes

## TL;DR

This paper proves that there are infinitely many Perrin pseudoprimes, extending the understanding of pseudoprime distributions using advanced number theory techniques.

## Contribution

It establishes the infinitude of Perrin pseudoprimes for a broad class of recurrence-based pseudoprimes, confirming a longstanding conjecture.

## Key findings

- Proves the existence of infinitely many Perrin pseudoprimes.
- Uses zero-density estimates for Hecke L-functions in the proof.
- Extends methods from the proof of Carmichael numbers to Perrin pseudoprimes.

## Abstract

This paper proves the existence of infinitely many Perrin pseudoprimes, as conjectured by Adams and Shanks in 1982. The theorem proven covers a general class of pseudoprimes based on recurrence sequences. The result uses ingredients of the proof of the infinitude of Carmichael numbers, along with zero-density estimates for Hecke L-functions.