We show that eleven-dimensional supergravity backgrounds with thirty one
supersymmetries, N=31, admit an additional Killing spinor and so they are
locally isometric to maximally supersymmetric ones. This rules out the
existence of simply connected eleven-dimensional supergravity preons. We also
show that N=15 solutions of type I supergravities are locally isometric to
Minkowski spacetime.Comment: 17 page