How to get rid of 'FastCGI sent in stderr: Primary script unknown' in nginx logs

I've tried countless methods to get rid of annoying messages in my nginx log, like [error] 358#0: *44 open() and [error] 10643#0: *2262 FastCGI sent in stderr: "Primary script unknown" while reading response header from upstream.

These are errors, sent to STDERR by the FastCGI upstream, in this case, PHP-FPM, and they happen when either index.php is not present in the folder or when a nonexistent file gets redirected to index.php and in can't handle it.

Apparently, I was missing a single line:

location ~ ^(?<script_name>.+?\.php)(?<path_info>.*)$ {
    try_files $uri $script_name =404;
    ...
}

That try_files $uri $script_name =404; needs to go into the PHP handling block of nginx, and the error vanishes from the logs.

(Oh, by the way: this entry was written by Peter Molnar, and originally posted on petermolnar dot net.)