English

Kleene Star of the Primes is not Regular in Any Base

Formal Languages and Automata Theory 2022-04-12 v2

Abstract

Let PbP_b denote the primes expressed in base-bb. In this note, we prove that PbP_b^* is not regular. This strengthens a classical result that PbP_b is not regular, due to Minsky and Papert in 1966.

Keywords

Cite

@article{arxiv.2203.16088,
  title  = {Kleene Star of the Primes is not Regular in Any Base},
  author = {Jason Yuen},
  journal= {arXiv preprint arXiv:2203.16088},
  year   = {2022}
}

Comments

3 pages; typo corrected