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I was wondering about the IPv4 problem and thought about one of the solutions where endpoints do not have their own public ip address, but rather an address only used within the VPN and a mapping by the router.

These local addresses fall in the range of 192.168.x.x, and in my experience mostly 192.168.0.x. But what happens to the public ip addresses in this range? Who owns them, and what are they used for? Can they even be practically used, and if they can, how does the endpoint know whether to connect to a local address or to the public one?

I tried to ping random addresses from the range, but none of them returned a response (except of course endpoints on my local network). So I would suspect the range is not used publicly. But isn't that a wast of the addresses?

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    Please read RFC1918 – Ricky Beam Oct 9 '15 at 19:54
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The three private address ranges, and many other address ranges, are not allowed to be routed on the Internet. IANA owns the private address ranges and has allowed anyone to use them as they wish, as long as they are not routed on the Internet. They are simply network addresses used the same way as public addresses, except that any Internet provider will drop any packets with a private address.

Your pings to private addresses on the Internet never made it to the Internet since your provider dropped them at the PE.

These private addresses actually save addresses since everyone can reuse the same addresses internally rather than needing unique public addresses. IPv4 would have been exhausted many years ago if we didn't have private addresses.

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