Prescribed Primitive Roots And The Least Primes

N. A. Carella

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arXiv · 2111.06188

Prescribed Primitive Roots And The Least Primes

N. A. Carella

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Abstract

Let $q\ne \pm1,v^2$ be a fixed integer, and let $x\geq 1$ be a large number. The least prime number $p \geq3 $ such that $q$ is a primitive root modulo $p$ is conjectured to be $p\ll (\log q)(\log \log q)^3),$ where $\gcd(p,q)=1$. This note proves the existence of small primes $p\ll(\log x)^c$, where $c>0$ is a constant, a close approximation to the conjectured upper bound.

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N. A. Carella. 2021-11-11. Prescribed Primitive Roots And The Least Primes. https://arxiv.org/abs/2111.06188

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