During the early '30s, production contracted because of the Great Depression. The factory did not ship guns in numerical order; when they had to ship one, they just took it off the shelf without much regard to original date of manufacture. So there is poor correlation between serial number and shipment date.
Serial numbers in the .32 HE series (which included the .32 Regulation Police and the .22/32 Target and Kit Gun models) hit the 500000 mark sometime in 1929, and I am guessing that is the actual date of manufacture for your gun. But it might have sat on the shelf for a few years before going out the door. A letter would give you the shipment date, not the date of manufacture.
David Wilson