According to that Wikipedia link there are 1 million registered firearms in the USA and 400 million unregistered firearms. Could somebody explain these numbers, since they seem very odd?

I'm not sure how Wikipedia is distinguishing them but for the most part firearms do not have to be registered in the United States. Some states require firearms to be registered but most do not. Unregistered firearms can nonetheless be counted because they are inventoried and sold legally (firearms dealers must be licensed and regulated), even though the end purchaser is not registered anywhere.

Federally, only specific categories like fully-automatic machine guns and short-barreled rifles have to be registered.

Only a tiny minority of firearms need to be registered. My guess is that covers NFA weapons like machine-guns, which are uncommon. Virtually all typical firearms people own don't need to be registered.

No one really knows how many firearms there are in the US or who owns them. Just the fact that something like 15 million firearms are sold every year in the US gives a sense of the scale. The number of firearms in the US is staggering, no one knows the true number, and they have an indefinite lifespan if stored in halfway decent conditions.

Most weapons in the US don't require registration.

Certain kinds of firearms are required to be registered, like machine guns, short barrel rifles, and short barrel shotguns.

Tons of guns are not those limited categories, so they are not required to be registered.

Its entirely possible to sell a gun in the US without any kind of paperwork depending on the type of firearm sold, the buyer of the firearm, and the seller of the firearm. I'm in Texas, so I'll use that as an example. Lets say I want to sell a regular shotgun I currently own to a friend. IANAL, this is not legal advice, but my understanding from reading the applicable laws would be all I have to do is verify they are over the age of 18 and that I think they are probably legally able to own a gun (I have no prior knowledge of any legal restrictions against them owning the gun). We can meet up, check he's probably over 18 and can probably legally own a gun and is a Texas resident, he can hand me cash or whatever for trade, I can give him the gun, and we go our separate ways. I do not need to do a background check. I do not need to file any registration. Nobody would know this guy now owns this gun. I do not need to keep any record of this sale at all. This shotgun has been an unregistered gun for its entire exstence.

This wouldn't necessarily be true if I trade some certain amount of guns as then I would probably need a federal firearms license and thus have some additional restrictions on facilitiating a sale. This also isn't necessarily true in other states which have additional restrictions on gun sales. But if I haven't done any gun sales in a long while, such restrictions wouldn't apply (according to my current understanding of the law, IANAL, not legal advice).

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