1. In a cluster compound, a particular number of atoms that is associated with a particularly stable structure. This number can sometimes be estimated by electron counting rules.

2. In a nucleus, a particular number of protons or neutrons that gives rise to a particularly stable structure. The magic numbers for both protons and neutrons are 2, 8, 20, 28, 50, 82, and 126. For protons 114 is a magic number. For neutrons 184 is a magic number. If the number of protons and the number of neutrons are both magic numbers, then that nucleus is said to be doubly magic. The stability associated with magic numbers is analogous to the chemical stability of noble gases owing to the shell structure of their nuclei. Nuclei with magic numbers are more abundant than nuclei with slightly different numbers of protons or neutrons. The result that 126 is a magic number suggests that there might be an island of stability for chemical elements with atomic numbers near 126, meaning that such elements might have longer life-times before decaying than other elements with very high atomic numbers. However, such elements have never been discovered or synthesized.