  We confirm by using the Skyrme Hartree-Fock-Bogoliubov calculation that $
{}^{164} \mathrm{Pb} $ is a possible heaviest $ N = Z $ doubly-magic nucleus
whose life time is long enough to be measured on accelerator experiment. We
estimate the proton-emission and alpha-decay half lives of $ {}^{164}
\mathrm{Pb} $. The estimated proton-emission half life ranges from $ 0.1 \,
\mathrm{ps} $ to $ 10 \, \mathrm{ns} $, while the alpha decay can be safely
neglected.
