Gn,3(C) is prime if n is odd

A finite CW complex X is said to be prime if for every Hurewicz fibration F → E → B with E homotopy equivalent to X, and B and F homotopically equivalent to finite CW complexes, either B or F is contractible. We show that the 3-plane complex Grassmannian Gn,3(C) is prime if n is odd.