There are Infinitely Many Perrin Pseudoprimes
Number Theory
2019-03-19 v1
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.
Cite
@article{arxiv.1903.06825,
title = {There are Infinitely Many Perrin Pseudoprimes},
author = {Jon Grantham},
journal= {arXiv preprint arXiv:1903.06825},
year = {2019}
}