It is known that a free neutron decays into a proton, an electron, and an anti-neutrino. Interesting, recent attempts to measure the neutron's lifetime has led to two slightly different estimates: namely, the number of decaying neutrons is somewhat larger than the number of newly created protons. This difference is known as the neutron lifetime puzzle. A natural explanation for this difference is that in some cases, a neutron decays not into a proton, but into some other particle. If this explanation is true, this implies that nuclei with a sufficiently large number of neutrons will be unstable. Based on the observed difference between the two estimates of the neutron lifetime, we can estimate the largest number of neutrons in a stable nucleus to be between 80 and 128. The fact that the number of neutrons (125) in the actual largest stable nucleus (lead) lies within this interval can serve as an additional argument is favor of the current explanation of the neutron lifetime puzzle.