English

Cyclotomic primes

Number Theory 2024-12-05 v2

Abstract

Mersenne primes and Fermat primes may be thought of as primes of the form Φm(2)\Phi_m(2), where Φm(x)\Phi_m(x) is the mmth cyclotomic polynomial. This paper discusses the more general problem of primes and composites of this form.

Keywords

Cite

@article{arxiv.2411.04213,
  title  = {Cyclotomic primes},
  author = {Carl Pomerance},
  journal= {arXiv preprint arXiv:2411.04213},
  year   = {2024}
}

Comments

13 pages, latest version has calculations to 2^{17}

R2 v1 2026-06-28T19:50:37.404Z