Computation of the least primitive root

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 $g(p)<p^{5\mathrm{/}8}$ for all primes $p>3$ and that $h(p)<p^{2\mathrm{/}3}$ for all primes $p$.