For a non-unit a of an atomic monoid H we call $L_H\left(a\right)=k\in \mathbb{N}|a=u₁...u_{k}withirreducible{u}_i\in H$ the set of lengths of a. Let H be a Krull monoid with infinite divisor class group such that each divisor class is the sum of a bounded number of prime divisor classes of H. We investigate factorization properties of H and show that H has sets of lengths containing large gaps. Finally we apply this result to finitely generated algebras over perfect fields with infinite divisor class group.