The numbering convention changed with the newer models. My two IIIR are:

- OK54/757
- OK55/955

The first character may be a zero instead of an "O". I can discern a pattern there: one of them could be the 757th camera from 1954, and the other the 955th from 1955. If the first character is actually a zero, it may become a number one if more than one thousand cameras were made that year. But, just two serials are not enough data. Time to ask other owners ;-)