Proton-rich material in a state of nuclear statistical equilibrium is of the least studied regimes of nucleosysnthesis. One reason for this is that after hydrogen burning,stellar evolution proceeds at conditions of equal numbers of neutrons and protons or at a slight degree of neutron richness. Proton-rich nucleosynthesis in stars tends to occur only when hydrogen-rich material that accretes onto a white dwarf or neutron star explodes, or when neutrino interactions in the winds from a proto–neutron star or a collapsar disk, can make the matter proton-rich prior to or during the nucleosynthesis. This new project has two phases. The first phase seeks a comprehensive, quantitative understanding of the abundance levels of proton-rich material in nuclear statistical equilibrium. What are the mass fraction distributions, how do the distributions change when the thermodynamic conditions are varied, and are there exact analytical expressions that describe the main properties of the distributions? The figure shows an example of the mass fractions as a function the electron per baryon ratio (number of protons)/(number of nucleons) ratio for a specific temperature and density.