English

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.

Keywords

Cite

@article{arxiv.1903.06825,
  title  = {There are Infinitely Many Perrin Pseudoprimes},
  author = {Jon Grantham},
  journal= {arXiv preprint arXiv:1903.06825},
  year   = {2019}
}
R2 v1 2026-06-23T08:09:58.591Z