This is one of those models where the book that gives us the answers is very,
very vague. It says that the range from 54474 to 122678 was built from 1949 to 1974.
In this case, you can use the math to get an "idea" but you'd have to be lucky to be right, however without access to the records that Roy Jinks has, anyone out there would have no more information to counter your mathematical assertion.
So, there's two other options for getting a more accurate date of birth.
First is to contact S&W Historian Roy Jinks and request a factory letter. This will cost $50 and take 6-8 weeks, but it's
very cool. You'll find out the features it had as shipped, when it was shipped and WHERE they sent it. He'll also give a brief rundown of the model & the history of that model. Very cool letter.
The other option is cheaper, less accurate, not nearly as cool and more difficult to obtain...
That's to spend a lot of free time searching the web & stopping at every one you see at a gun show (needs to be a high quality gun show!) and look for similar guns with factory letters that are also displayed. Find a revolver of the same model with a serial number that is close... and ALSO has a Roy Jinks letter and you'll get an idea of when yours was built.
If we just use simple math (which may or may not reflect reality...) then math says it was built in/around 1955.