(If the serial starts with "C", but is C402923 or less, the gun actually isn't a model 10, but earlier.) If it starts with a "C" and has only numbers following the C, then it is pre 1968.
Since we are assuming it is a model 10, that is where I'll start the serial ranges. Before 1957, it wouldn't say "10, or Model 10" or anything like that anywhere on it. If it is really marked as a model 10, and isn't a. (SW added dashes after the main model number to designate model variations) Example "10-3 or 10-5" This is the model number. Also, if you open the cylinder, it will reveal a piece of metal on the left (probably where you got the 4 digit number) Under, or above that, there might be a number along with your 10. (never two, and if it has zero letters, then it actually pre-dates the model 10) A model 10 WILL ALWAYS have either one or three letters in it. The serial of a model 10 will have AT LEAST one letter in it, and will almost certainly be 7 characters total. If it is a newer gun, the serial might be elsewhere on the gun as well. If it has grips that cover that section of the frame, you may have to remove them.
The actual serial number will be on the butt - the very bottom of the gun's grip. The assembly numbers helped the people at the factory keep track of what parts went to what gun. The 4 digit number you've posted is an assembly number.