Welcome to the obsession erm... I mean forum! and congrats on your vintage machine. Minnesotas are reliable and good sew-ers.
Your Minnesota A was a mainstay of the Sears Catalog in the first 1/3 of the 20th century. Early models were made by Davis, but White and I think Domestic also made later ones. I don't know about the serial number. We have some real experts here who will see this thread shortly, I suspect.
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K