English

Sparse sets that satisfy the prime number theorem

Number Theory 2024-03-18 v4

Abstract

We investigate various sparse sets that satisfy the prime number theorem. The sparsest of these sets, {x/nt:nx}\{\lfloor x/n^t \rfloor:n \le x\}, has density approaching 1/x1/x as tt approaches infinity.

Keywords

Cite

@article{arxiv.2304.08736,
  title  = {Sparse sets that satisfy the prime number theorem},
  author = {Olivier Bordellès and Randell Heyman and Dion Nikolic},
  journal= {arXiv preprint arXiv:2304.08736},
  year   = {2024}
}
R2 v1 2026-06-28T10:09:15.957Z