With the new Gmail inbox, I've gotten into the habit of ignoring everything that's not in the Primary inbox. I don't care about anything that's in any of the other inboxes (inboxen?). When I search for something, I only want to see things from my primary inbox. However, searching for something brings up results from all the inboxes. How can I only search the Primary inbox?
The category filter now knows how to filter the "Primary" inbox, so you can use
Or, to show just unread messages in the "Primary inbox":
in:inbox category:primary is:unread
Doesn't look like the "category" filter knows how to filter to the "Primary" inbox, but you can do it by excluding the other categories like so:
in:inbox -category:(updates OR promotions OR social OR forums)
Or, to show just unread messages in the "Primary" inbox:
in:inbox -category:(updates OR promotions OR social OR forums) is:unread
I landed on this and what I ended up finding most useful was the source of information we are all looking for:
The GMail Advanced Search topic in Google's Help/Support documenation
This is the most important thing to remember as in the future it will change yet again. Remember to look up Advanced Search in Google's help forum for the current solution.
As of April 2014 what works and is supported is:
is:important is:unread to clean out your primary inbox.
"Meaning: Messages [...] that were marked as important by Priority Inbox"
I intend to, but of course cannot promise, I will update my answer as the solution changes. I am quite dependent on advanced search.