Justin - Beautiful gun and welcome to the forum. And nice photos, too. I think the only way to truly find out when it was shipped is to get a letter from S&W. Don't try to guess the date from others like it with close serial numbers as they jumped all over back in that time frame. For instance, an earlier poster has serial S161XXX from 1956, and I have a 4" 5 screw with serial S 153037 which shipped in February 1957. So the numbering didn't always match the shipping times. Also, I have seen some postings regarding the 4" 5 screw models that say there were 200 made in 1956 and about another 500 made in 1957. So they are kind of 'rare'. If you get a letter, please let us know what you find out. Good luck and enjoy your new revolver.

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John
SWCA #3401 SWHF #737