I missed that you are a new member so welcome aboard,
The early pre Model 29 is a very fine revolver.
There are quite a few threads on the Model, basicly it was introduced in 1955 as a 6.5" length barrel built on the "N" frame , those earlier ones had an upper sideplate screw so are called "5 screw" frames.
The factory introduced a 4" length version near the end of 1956, by early 1957 they deleted the upper sideplate screw (like yours) those are referred to as "4 screw" frames, early versions like yours were made prior to the introduction of the Model marking system so some people would call your gun a "Pre Model 29 four screw"
S&W did not build or ship guns in numerical order, build dates were not recorded at the factory, after guns were built they were boxed with a screw driver, cleaning patch and rod and placed in the factory vault.
As orders were filled the serial numbers were recorded and where the shipments went.
Prior to model marking S&W's had names,
Yours was called the "44 Magnum" as it was the only one offered, this changed to the " Model 29" sometime in 1957-58 although non Model marked guns sometimes hid in the vault and got shipped later than Model marked guns.
There were a few small amounts of various other barrel lengths made but they are rare, the most common early ones are 6.5" blued like yours,
Nickel was the other option but they are the minority.
Your gun would have originally shipped in a blue case with a brass latch, if your father tucked that away make sure to keep it with the gun as many were lost or tossed through the years, those can fetch a pretty penny as do your original wood "Coke botte" style target stocks.
If you have any questions don't be afraid to ask, the members here are very friendly and knowledgeable.
Best regards
Brad in Florida.
... There is another pistol I have of his that I know he got in 58 because his Dad gave it to him when he graduated high school. He cherished it and hardly ever shot it. 
