The 1913-S Twenty dollar gold double eagle is part of a series of Saint Gaudens gold double eagle coins struck from 1908-1933. Struck in San Francisco and designated as a Business (MS) strike, this coin is made of 90% gold; 10% copper from a mintage of 34,000 struck.
About 10% of the scant 34,000-piece mintage survives according to Roger Burdette's research, a high percentage of a small mintage. Struck at the end of 1913, the 1913-S was either an afterthought or perhaps struck from a late-season gold deposit, but no commercial reason exists for such a minute mintage. Collectors were (and are) delighted.
While one of the lowest-mintage regular-issue Saints, the 1913-S $20 is not necessarily among the rarest on the marketplace. In fact, it is probably more fairly described only as a better date, rather than as a rarity -- at least when discussing all 1913-S Saint-Gaudens $20s as a group. Certainly, better-grade examples are scarce, and this is evidenced by the very few Gems known to exist -- all told, pieces grading MS65 or better number fewer than 50 pieces and are the darlings of registry set collectors.
PCGS reports only 24 numerically finer examples, plus 28 pieces in 64+.