Least Consecutive Pair of Primitive Roots

N. A. Carella

Least Consecutive Pair of Primitive Roots

General Mathematics 2026-04-16 v1

Authors: N. A. Carella

Abstract

Let $p>1$ be a large prime number and let $x=O((\log p)^2(\log\log p)^5$ be a real number. It is proved that the least consecutive pair of primitive roots $u\ne\pm1, v^2$ and $u+1$ satisfies the upper bound $u\ll x$ in the prime field $\mathbb{F}_p$ .

Keywords

prime number theory prime numbers

Cite

@article{arxiv.2604.13090,
  title  = {Least Consecutive Pair of Primitive Roots},
  author = {N. A. Carella},
  journal= {arXiv preprint arXiv:2604.13090},
  year   = {2026}
}