I have a J.C. Higgins mod 20-12Ga. series 583-200, but where do they hide the serial number?
On a lot of those guns made before serial numbers were mandatory, and especially those for Sears, there was simply no serial number. I would suspect the gun has no serial number and the BATF makes allowances for that in their record keeping by allowing you to put No Serial Number in the space for the serial number.