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arXiv · 2206.14193

Computation of the least primitive root

Kevin J. McGown·Jonathan P. Sorenson
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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 $g(p) 3$ and that $h(p)<p^{2/3}$ for all primes $p$.

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Kevin J. McGown, Jonathan P. Sorenson. 2023-07-24. Computation of the least primitive root. https://doi.org/10.1090/mcom%2F4003

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