Oh, and Barbarian- Yes, American manufacturers MUST keep track of every single firearm they make, even if the frame is later discarded for quality-control purposes before it’s ever sold, or even finished.
Losing track of even ONE, even if it’s a bare frame, is bad juju. That’s reason enough for the ATF, if they’re feeling especially nasty that day, to pull the manufacturer’s license.
A gun maker MUST keep detailed, auditable records of every single firearm made, who it’s sold to, when it was sold, when it was shipped, who got what serial numbers, how it was shipped, whether or not it arrived, etc.
And, of course, the person selling it MUST keep track of who he or she sold it to, when it was sold, did the buyer buy more than one gun that day, and so on.
The buyer must fill out a form with one’s name, age, mailing address, SSN, and other data, as well as fill out a form stating, under penalty of law, that, among other things, the buyer is not a drug user, hasn’t been dishonorably discharged from the military, is not a foreign national, and so on.
AND, the buyer must then undergo an “instant check” via a telephone call to the FBI.
The ATF has detailed records of all the firearms imported to and sold in the US since at least 1968.
So they have a pretty good idea how many firearms… legal ones anyway… are in the US.