First, I think you mean register. In MOST of the US, there is no requirement to register ordinary firearms. Now, about the serial number- it is unlawful to REMOVE a serial number, or to possess a gun that has had the SN removed. However, there are guns that do not HAVE a serial number, and they are legal. Rifles and shotguns made prior to 1968 were not required to have serial number. Those guns are listed as NSN- No Serial Number- on paperwork that asks for a serial number.
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