prime n-manifold

A n-manifold (http://planetmath.org/TopologicalManifold) $M$ is called if for all the factorizations of $M$, as a connected sum (http://planetmath.org/ConnectedSum2) $M=M_1\mathrm{\#}{M}_2$, one finds that one of the factors $M_1$ or $M_2$ is the n-sphere $S^n$.

The importance for 3-manifold is the existence and uniqueness prime decomposition theorem which says: Each 3-manifold can be decomposed as a connected sum of prime manifolds.