  We give a complete classification of smooth, complex projective Fano 4-folds
of Picard number 3 having a prime divisor of Picard number 1. They form 28
distinct families, and we compute the main numerical invariants, study the base
locus of the anticanonical divisor, and give a comment on rationality.
Furthermore, we give an upper bound of both the dimension of the automorphism
group and the dimension of the base of the Kuranishi family of a general
member.
