K68483 and K68510 are both Pre-16s. There are no other serial numbers that I can document from that range, though other numbers may be known. My impression is that S&W tended to make up batches of a particular model in round number lots of 20, 25 or 30 at a time depending on the era. I would guess that K68470 (or probably K68471) through K68530 would be a run of Pre-16s. But I wouldn't be surprised if someone could show me that one or more of those were made up as K-38s. If a rush order for an out-of-stock item came in, S&W was completely capable of diverting a frame from the production stream and finishing it as something else. The company could also take a completed model out of the vault and modify it to be something for which there was an immediate demand, which would also create a serial number/model discontinuity.

It's easy to guess but hard to know without crawling the records, so take this answer with a grain of salt.

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David Wilson