Hi, Wayne .. I wasn't so much interested in the serial number ... rather, the model name/number. For example, my oldest non Damascus Elsy is that 00E that I referenced yesterday. The 00 was the model ... a field grade piece .. the "E" was for "ejectors" as opposed to "extractors". Those with extractors were simply a 00. Then there were various model names, representing various grades.
I had no idea that the Remington Nylon 66 was collectible. They used to be as common as house flies. I had, at one time, the Nylon 77, which was the lever action. I got it when I was nine ... Loved that gun ...
If that pump .22 is not a "hardware store" brand, it might be worth a nickel 'r two .. does it have an octagonal barrel? Is it chambered for .22 shorts, only?
Back to your Elsy ... the model number/name should be on the barrels, close to where they meet the receiver.