Associated with every closed oriented smooth manifold $M$, let $R_M$ denote the space of all pair $(L,g)$, where $g$ is a Riemannian metric on $M$ and $L$ is a real number which is not the length of any closed $g$-geodesics. A locally constant geodesic count function $\pi_M:R_M\rightarrow \mathbb{Z}$ is defined which virtually counts the number of closed $g$-geodesics of length less than $L$ at $(L,g)\in R_M$. In particular, when $g$ is negatively curved, $\pi_M(L,g)$ is precisely the number of prime closed $g$-geodesics which have length smaller than $L$. The asymptotic growth of the number of closed $g$-geodesics may subsequently be studied.