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In this article, we investigate symmetric $(v,k,\lambda)$ designs$\mathcal{D}$ with $\lambda$ prime admitting flag-transitive andpoint-primitive automorphism groups $G$. We prove that if $G$ is an almostsimple 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 $(45,12,3)$.

Almost simple groups of Lie type and symmetric designs with $\lambda$ prime