A theoretical method for estimates of a width of "true" four-nucleon decays is developed. Several candidate isotopes to possess this property are considered. Our lifetime estimates compare one-neutron, true two-neutron, and true four-neutron emissions at similar conditions. Prospects of experimental search for two-neutron, fourproton, and four-neutron radioactivity are discussed. DOI: 10.1103/PhysRevC.84.021303 PACS number(s): 25.45.Hi, 24.50.+g, 24.70.+s, 27.20.+n Nuclear disintegration via fission or the emission of protons, α-particles, or nuclear clusters is a phenomenon that has been investigated since more than one century ago. This research has laid the foundation to the understanding of atomic nuclei, it exhibits many different facets of the strong force and has a large variety of applications. Nevertheless, neutron radioactivity, i.e., the spontaneous emission of one or more neutrons from the ground state of a nucleus, has not yet been observed experimentally. This will be a challenge for present and nextgeneration radioactive beam facilities. Even more surprising is the fact that there is no theoretical treatise of this phenomenon.In this paper, we approach this question via two-proton (2p) radioactivity, which is the most-recently discovered mode of radioactive decay. Predicted by Goldansky [1] in 1960, it was observed only 42 years later [2,3] in 45 Fe. Now this process is under intense investigations, which provide new decay cases [4][5][6], detailed correlations of fragments [7], and new candidates for prospective studies [8,9]. The reason for the phenomenon of 2p radioactivity (or a "true" 2p decay in the case of short-lived states) is founded in the specific energy conditions of daughter nuclei, which make one-proton emission energetically impossible; see Fig. 1(a). In this case, both protons have to be emitted simultaneously, which results in specific lifetime systematics (much longer lifetimes compared to ordinary binary decays) and complicated correlation patterns among the decay fragments. Such energy conditions evidently take place in systems with an even number of valence nucleons due to the pairing interaction.There are two straightforward generalizations of 2p radioactivity (true 2p decay) phenomenon, which we discuss in this article in order to explore theoretically and experimentally two new decay modes:(i) The direct analog of true 2p decay across the isobar is the true two-neutron (2n) decay. With the progress in reaching experimentally the neutron drip-line, the interest to nuclei beyond this limit is increasing. E.g., some aspects of such processes were discussed by Thoennessen [10]. There is possibility that neutron(s) emission may take the form of 2n radioactivity.(ii) It is possible that two more nucleons added on top of a true two-nucleon precursor compose a system that has only a true four-nucleon decay branch; see Fig. 1(b). True four-nucleon decays are defined by energy conditions S 4N < 0 and {S N , S 2N , S 3N } > 0, in analogy with a true two-nucleon decay. This is an...