Just so you know:
Virtually all ISPs frown on people who insist on changing their IP address. If you have to contact your ISP for assistance with this, be warned that an IT techie knows full well that hackers and high risk users look to change their IP often. And they know all the good stories.
Power cycling a cable router can repeatedly produce the same IP numerous times, because servers are programmed to always try to give you back the same IP you had before, if available.
If you're up to mischief on the web, some sites may blacklist the IP you're coming from. Limiting the number of IP's a server gives you, limits their exposure if you should turn out to be a bad apple.
You may need to break the DHCP lease for extended periods, until your old IP is picked up by someone else, and is literally unavailable when you try to renew the lease. Sometimes it can take 2 days, other times it can happen in 4 minutes.
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