Upper bound on the scale of Majorana-neutrino mass generation

We derive a model-independent upper bound on the scale of Majorana-neutrino mass generation. The upper bound is $4\pi v^2/\sqrt 3 m_\nu$, where $v \simeq 246$ GeV is the weak scale and $m_\nu$ is the Majorana neutrino mass. For neutrino masses implied by neutrino oscillation experiments, all but one of these bounds are less than the Planck scale, and they are all within a few orders of magnitude of the grand-unification scale.