prime n-manifold
A n-manifold (http://planetmath.org/TopologicalManifold) is called if for all the factorizations of , as a connected sum (http://planetmath.org/ConnectedSum2) , one finds that one of the factors or is the n-sphere .
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.