In 1863 the Mint used two different style 3 digits on the date to strike the circulation strike 1873 Indian Cents. These are referred to as an Open 3 and a Close 3 variety. The difference between the Open and Close 3 variety is obvious enough that it can be seen with the naked eye. For the 1873 Proof Cent the Mint only struck them with the Close 3 variety.
The 1873 Proof Cent is somewhere in the middle as far as scarcity since it is not one of the lowest mintages and also not one of the highest. With a mintage of 1,100 coins struck it is a semi scarce coin in the series. In MS66 grade it is very scarce with less than a dozen known examples and none being finer.