Let $\Gamma$ be a group acting properly and cocompactly by isometries on a proper geodesic Gromov-hyperbolic metric space $X$. For all $t \geq 0$, let $P(t)$ denote the number of conjugacy classes of primitive elements $\gamma \in \Gamma$ whose minimal displacement on $X$ does not exceed $t$. I will present asymptotic estimates for $P(t)$ as $t \to \infty$ obtained in collaboration with Gerhard Knieper.