Ooh! Ooh!

Sorry to go all Arnold Horshack on you, but something just occurred to me as I was archiving a piece of Gmail with a PDF attached. Google searches PDFs! Does it do it in Gmail? It should! (Though that would raise its own set of privacy concerns.) Checking the Help pages, I see you can search for PDFs, but I don't see anything about being able to search within them:

How do I use advanced search? [...]

filename: - Search for keywords that match the name of the attachment. This operator is also useful if you are searching for a specific attachment type, like PDF (.pdf). By searching for filename:pdf, you will find all messages with attachments that are PDF files.