Decay properties and stability of heaviest nuclei with Z≤132 are studied within the macro-microscopical approach for nuclear ground state masses and phenomenological relations for the half-lives with respect to α-decay, β-decay and spontaneous fission. We found that at existing experimental facilities the synthesis and detection of nuclei with Z>120 produced in fusion reactions may be difficult due to their short half-lives (shorter than 1 μs). The nearest (more neutron-rich) isotopes of superheavy elements with 111≤Z≤115 to those synthesized recently in Dubna in 48Ca-induced fusion reactions are found to be β+-decaying. This fact may significantly complicate their experimental identification. However it gives a chance to synthesize in fusion reactions the most stable superheavy nuclei located at the center of the island of stability. Our calculations yield that the β-stable isotopes 291Cn and 293Cn with a half-life of about 100 years are the longest-living superheavy nuclei located at the island of stability.