A search for heavy Majorana neutrinos produced in the $B^- to pi^+mu^-mu^-$ decay mode is performed using 3 fb$^{-1}$ of integrated luminosity collected with the LHCb detector in $pp$ collisions at center-of-mass energies of 7 TeV and 8 TeV at the LHC. Neutrinos with masses in the range 250-5000 MeV and lifetimes from zero to 1000 ps are probed. In the absence of a signal, upper limits are set on the branching fraction ${cal{B}}(B^- to pi^+mu^-mu^-)$ as functions of neutrino mass and lifetime. These limits are on the order of $10^{-9}$ for short neutrino lifetimes of 1 ps or less. Limits are also set on the coupling between the muon and a possible fourth-generation neutrino.
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