  In this article, we investigate symmetric $(v,k,\lambda)$ designs
$\mathcal{D}$ with $\lambda$ prime admitting flag-transitive and
point-primitive automorphism groups $G$. We prove that if $G$ is an almost
simple group with socle a finite simple group of Lie type, then $\mathcal{D}$
is either the point-hyperplane design of a projective space
$\mathrm{PG}_{n-1}(q)$, or it is of parameters $(7,4,2)$, $(11,5,2)$,
$(11,6,2)$ or $(45,12,3)$.
