Is it possible to use a proxy service, so that for each HTTP request from the server to outside, I’ll get different IP address
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This should be possible but there are a few moving pieces to think about.
You’ll want to set up a Dynamic DNS service. There are free public options or you could set up something yourself. The way this works is that the computer with a dynamic IP address runs an agent that reports into the Dynamic DNS service when it’s IP changes and a DNS record is automatically updated. These records are set up with a very low TTL (time to live) so that the changes happen as seamlessly as possible.
Once you have this in place, you can set up nginx using the proxy_pass directive so that it will pass requests to that new dynamic DNS name rather than an IP address. This way your static IP will host your proxy but the content served will come from your computer with the dynamic IP.
