Now, this doesn't help much in many circumstances, because how likely is it that the box will still be around for as long as the gun exists.
A gun made of steel and wood can stand the test of time. Most people will have disposed of the box a long time ago, and so it's unfortunate that the serial numbers were not stamped on the barrel during those 3 years.
Remington Firearms Serial Numbers Decoding the serial number.
They use these documents as a reference and the documents should be limited to that use.
Click the image below to download the PDF document containing the serial number date-range information on many Winchester firearms.
Thankfully, after 2001, Remington went back to having the serial numbers stamped on the barrel again.
One thing that you might notice when you examine the chart above, the letters for the year code repeat themselves.
During World War Two Singer had back orders for over three millions machines!