This data set includes names, designations, and discovery circumstances for the numbered asteroids, sorted in order of number. This data set supercedes past versions of both the ASTNAMES and DISCOVER asteroid data sets. It represents an extension of a file originally prepared by Pilcher (1979) [PILCHER1979] for the Tucson Revised Index of Asteroid Data (TRIAD) and updated in Pilcher (1989) [PILCHER1989] for the Asteroids II database. The data for asteroids numbered 4045 and greater were either provided by the Minor Planet Center or extracted from the Minor Planet Circulars, which are published by the Minor Planet Center on behalf of Commission 20 of the International Astronomical Union. In some cases, an institution or survey is credited with the discovery rather than an individual. No attempt has been made to correct the inconsistencies in the presentation of names (that is, some names are given with initials and some are not), or in the way locations are specified (for example, Pilcher distinguishes between the Lowell Observatory and Anderson Mesa locations in Flagstaff).