Bush Dog,
First, let me welcome you to the S&W Forum . . . there are great folks here willing to share their passion and vast knowledge of Smith & Wessons.
With regard to your model 60, I'm not aware of any model 60 with just a 5-digit serial number. Is it possible the 343XX number you provided is located the yoke/crane of the gun? If so, it is an assembly number and not associated with the serial number which is found on the butt.
S&W began making the model 60 in 1965 and numbered in the Chief Special serial number range. The first ones were 401754 to 401792. In 1969 they added a letter R prefix and started with R001.
Russ
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