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In this article, we study 2-designs with prime replication number admitting a flag-transitive automorphism group. The automorphism groups of these designs are point-primitive of almost simple or affine type. We determine 2-designs with prime replication number admitting an almost simple automorphism group and prove that such a design belongs to one of two infinite families of projective spaces or Witt-Bose-Shrikhande spaces or it is isomorphic to a design with parameters (6, 3, 2), (8, 4, 3), (11, 5, 2) or (12, 6, 5).

Flag-transitive block designs with prime replication number and almost simple groups