Well, you can letter it, although it's no secret what the letter will say. Charles Pate devotes about two pages to these in his book.

They shipped to the Washington Navy Yard in ten shipments of 300 from March 14 to May 10, 1941. The letter will tell you which shipment. Your serial is in the correct range, so it is no doubt authentic.

Since the USNCPC never got off the ground, the guns ended up in various places that are probably buried in naval archives somewhere; some even got sent to Britain.

That's about it.