“No input file specified” or “Primary script unknown” in the error log is one of the most frequently encountered issues in nginx+PHP. People on serverfault and in the #nginx IRC channel asks for help with this so often that this post is mostly to allow me to be lazy and not have to type up the same answer every time.
This is actually an error from PHP and due to display_errors being 0ff people will often just get a blank page with no output. In a typical setup PHP will then send the error to stderr or stdout and nginx will pick up on it and log it in the nginx error log file. Thus people spend a ton of time trying to figure out why nginx isn’t working.
The root cause of the error is that PHP cannot find the file nginx is telling it to look for, and there are a few common cases that causes this.