  We determine birational superrigidity for a quasi-smooth prime Fano 3-fold of
codimension 4 with no projection centers. In particular we prove birational
superrigidity for Fano 3-folds of codimension 4 with no projection centers
which are recently constructed by Coughlan and Ducat. We also pose some
questions and a conjecture regarding the classification of birationally
superrigid Fano 3-folds.
