Beyond element 164, the fissility line defining the limit of stability with respect to spontaneous fission may converge with the neutron drip line, posing a limit to the existence of heavier elements. Nevertheless, further magic numbers have been predicted at Z = 210, 274, and 354 and N = 308, 406, 524, 644, and 772, with two beta-stable doubly magic nuclei found at 210 and 274; the same calculation method reproduced the predictions for Fl and 164. (The doubly magic nuclei predicted for Z = 354 are beta-unstable, with 354 being neutron-deficient and 354 being neutron-rich.) Although additional stability toward alpha decay and fission are predicted for 210 and 274, with half-lives up to hundreds of microseconds for 210, there will not exist islands of stability as significant as those predicted at Z = 114 and 164. As the existence of superheavy elements is very strongly dependent on stabilizing effects from closed shells, nuclear instability and fission will likely determine the end of the periodic table beyond these islands of stability.