In this article, we investigate symmetric (v,k,λ) designs D with λ prime ad- mitting 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 D is either the point-hyperplane design of a projective space PGn−1(q), or it is of parameters (7, 4, 2), (11, 5, 2), (11, 6, 3) or (45, 12, 3).
