Danielwere the k22 numbered in the same series
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After the war (1946), S&W began to use the K prefix serial numbers to designate all K frame models for which adjustable sights were standard. Initially, this included the K-22, the K-32 and the K-38. A bit later, it also included the Combat Masterpiece and the Combat Magnum lines. This practice lasted until about 1983, when the three-alpha, four digit numbers took over.
JSR III
.....S&W typically did runs of frames in groups. 50, 100, 200, 300 at a time depending on demand. SO, while it is possible to have a K 22 with serial number K 123456 and a K 38 with serial number K 123457, you won't find another K 22 with serial number K 123458.
In other words, they would run a batch of K 22's K 123456 through K 123500, and then possibly a batch of K 38's from K 123501 through K 123600. You won't find them randomly interspersed within the same serial number block.....