Number-theoretic generators of Costas arrays and generalizations in the literature and some presented here produce 526,908 of the known 663,703 known Costas arrays for orders up to 200. For orders higher than seven, there are more Costas arrays than the generators produce. A spin generalization is observed to find new Costas arrays for orders up to about 50, but none of higher order. This, and early work on the occurrence of Costas arrays, indicates that most, or all, Costas arrays are known, or are generated by known generators and their generalizations.