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Edited on Thu Mar-13-08 10:21 PM by RoyGBiv
ISP = Internet Service Provider
ISPs offer two kinds of service, one of which gives you a static IP, the other a dynamic IP. A static IP will not change, and they tend to cost a lot of money, and very few private individuals have one. A dynamic IP, which is what most people have, can change at any time. With dialup service you likely have a new IP every time you log in. (You can "accidentally" end up with the same IP as the one you had before, but this is uncommon now. My first ISP only had 10 lines, so it was fairly common to log off then log back in and get the same IP address.) With broadband, you can often have the same IP for weeks, months, or even years, but you can't count on that.
The way it works, in a typical nutshell, is this:
Your provider "leases" you an IP for a certain period of time, usually 24 hours, but I've seen other time variables. At the end of that lease, your modem or "bridge" releases the IP and, if still connected, renews the lease. Since those with broadband tend always to have their modems connected, the renewal usually results in renewing the same IP that was just released.
In practice, you can have the same IP for years. I had service with Cox in OKC for 7 years. I had three total IP addresses that entire time. I forced a new IP the first time it changed, then had it change again after I was offline for many days, and then had the last one for four years.
As was already mentioned, no two computers have (or should have, but that's a huge tangent) the same IP address at any given time. So, you can be identified through server logs if someone has your IP and a time to which to attach it. ISPs don't easily give up these logs, if for no other reason than its not the quickest process in the world, but law enforcement and more covert forms of information gathering can identify a person (or a household or office to be more precise) relatively easily through the IP address.
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