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Nuclear shell structures—the distribution of the quantum states of individual protons and neutrons—provide one of our most important guides for understanding the stability of atomic nuclei. Nuclei with ‘magic numbers’ of protons and/or neutrons (corresponding to closed shells of strongly bound nucleons) are particularly stable. Whether the major shell closures and magic numbers change in very neutron-rich nuclei (potentially causing shape deformations) is a fundamental, and at present open, question. A unique opportunity to study these shell effects is offered by the 42Si nucleus, which has 28 neutrons—a magic number in stable nuclei—and 14 protons. This nucleus has a 12-neutron excess over the heaviest stable silicon nuclide, and has only one neutron fewer than the heaviest silicon nuclide observed so far. Here we report measurements of 42Si and two neighbouring nuclei using a technique involving one- and two-nucleon knockout from beams of exotic nuclei. We present strong evidence for a well-developed proton subshell closure at Z = 14 (14 protons), the near degeneracy of two different (s1/2 and d3/2) proton orbits in the vicinity of 42Si, and a nearly spherical shape for 42Si. [ABSTRACT FROM AUTHOR]