I have a site with some URLs that look like this: /prefix/ID, where /prefix is static and ID is unique. Using Nginx as a reverse proxy, I'd like to cache these pages at the /ID portion only, omitting the prefix.

Can I configure Nginx so that a request for the original URL is cached at the shortened URL?

I tried this (I'm omitting some irrelevant parts) but obviously it's not the correct solution:

http {
    map $request_uri $page_id {
        default $request_uri;
        ~^/prefix/(?<id>.+)$ $id;
    }

    location / {
        proxy_cache_key $page_id
    }
}