When something is notoriously a certain way, a lot of people already know it for that — and the thing they know is usually bad, or at least annoying. A test can be notoriously hard. A train can be notoriously late. A person can be notoriously rude. It is an adverb, so it usually sits before an adjective: notoriously difficult, notoriously unreliable. You will hear it in the news and in careful talk, but also in ordinary speech when someone wants to say “we all know this is a problem.” Though actually, people sometimes use it with a small smile, not only for truly terrible things: a friend can be notoriously bad at answering messages. The feeling is still “everyone knows, and it is not a compliment.” Famous for something good is just famous, not notoriously famous.