On Grosswald’s conjecture on primitive roots
Volume 172 / 2016
Acta Arithmetica 172 (2016), 263-270
MSC: Primary 11L40; Secondary 11A07.
DOI: 10.4064/aa8109-12-2015
Published online: 16 December 2015
Abstract
Grosswald’s conjecture is that $g(p)$, the least primitive root modulo $p$, satisfies $g(p) \leq \sqrt{p} - 2$ for all $p>409$. We make progress towards this conjecture by proving that $g(p) \leq \sqrt{p} -2$ for all $409 < p < 2.5\times 10^{15}$ and for all $p > 3.38\times 10^{71}$.
