It is shown that the time to compute a monotone boolean function depending upon n variables on a CREW-PRAM satisfies the lower bound T=Θ(logl+(log n)/l), where l is the size of the largest prime implicant. It is also shown that the bound is existentially tight by constructing a family of monotone functions that can be computed in T=O(log l+(log n)/l), even by an EREW-PRAM. The same results hold if l is replaced by L, the size of the largest prime clause.