Computation of the least primitive root
Abstract
Let $g(p)$ denote the least primitive root modulo $p$, and $h(p)$ the least primitive root modulo $p^2$. We computed $g(p)$ and $h(p)$ for all primes $p\le 10^{16}$. Here we present the results of that computation and prove three theorems as a consequence. In particular, we show that $g(p)<p^{5/8}$ for all primes $p>3$ and that $h(p)<p^{2/3}$ for all primes $p$.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2206.14193
- arXiv:
- arXiv:2206.14193
- Bibcode:
- 2022arXiv220614193M
- Keywords:
-
- Mathematics - Number Theory;
- 11A07;
- 11Y16