On Grosswald's conjecture on primitive roots

Abstract

Grosswald's conjecture is that $g(p)$, the least primitive root modulo $p$, satisfies $g(p)\le \sqrt{p}-2$ for all $p>409$. We make progress towards this conjecture by proving that $g(p)\le \sqrt{p}-2$ for all $409<p<2.5\times 10^{15}$ and for all $p>3.67\times 10^{71}$.

7 pages