How can the number of peers from the same IP address be counted?

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There can be any number of computers on a LAN (Ya! It may depend on the physical medium used between them i.e. cables, repeaters etc.), normally there is a single Gateway (at least one is must) to connect to the Internet. These Gateways normally have multiple IPs (both private and public) for the communication.

Now as the LAN can inturn be set of LANs... figuring out the correct client is a herculean task if not impossible... Though u can still get to that by looking to the routing tables of Gateway or by accessing NAT. . .This Link may help

Most of the times public IP is used by ISPs and Large or Mid size Organizations... That is why using client IP is not considered a wise idea now a...

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Q: How do they get that many publicly-routable IPs?

Your school could possibly have a static IP address range assigned to them by their Internet Service Provider (ISP), by virtue of the fact that a school district is a fairly large customer (orders of magnitude larger in terms of money than a single family home, to be sure). Note that you can't simply change a setting in your router to enable additional IP addresses; you must specifically have them assigned to you, by your ISP.

Since IPv4 space is limited, and is becoming more limited by the day -- see IPv4 Exhaustion -- end users are the first "victims" of having more limited access to IPv4 addresses, since (ISPs think that) most end users don't have many use cases for exposing "listening" services to the public Internet. In fact, many residential ISPs write into their Terms of Service (ToS) that you are forbidden from hosting any Web or Email servers on your home internet connection.

This ToS policy is at...

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