Let $p$ be an odd prime, $g(p)$ be the least primitive root modulo $p$ and $G(p)$ be the least prime primitive root mod $p$. We consider the distribution of $g(p)$ and $G(p)$, and obtain the following results, which show that, in most cases, $g(p)$ and $G(p)$ are very small. We assume the Generalized Riemann Hypothesis (G.R.H.). Let $\psi (x)$ be a monotone increasing positive function with the properties $\lim _{x\to \infty }\psi (x)=+\infty , \psi (x)\ll (\log x)^A\hbox { for some }A>0, \psi (x)\ll \psi (\frac x{\log x}).$ Then we have $|\{p\leq x ; G(p) > \psi (p)\}|\ll \frac {\pi (x)}{\log \psi (x)}.$ We assume G.R.H. For any $\varepsilon >0$, we have $\pi (x)^{-1}\sum _{p\leq x}g(p)\leq \pi (x)^{-1}\sum _{p\leq x}G(p)\ll (\log x)(\log \log x)^{1+\varepsilon }.$ If $\delta < \frac 12$, then we have $\pi (x)^{-1}\sum _{p\leq x}g(p)^\delta =E_\delta +o(1), \pi (x)^{-1}\sum _{p\leq x}G(p)=E'_\delta +o(1)$ where $E_\delta $ and $E'_\delta $ are constants depending only on $\delta $.