  We show that the presence of Majorana zero modes (2D), and chiral-dispersing
Majorana modes (3D), in the vortex cores of superconductors are neither
sufficient nor necessary conditions for one to conclude the superconductivity
is topologically non-trivial. We discuss the relevance of this result to the
proximity-induced superconductivity, in the presence of magnetic field, on the
surface of topological insulators.
