So I know this is very silly and obviously hypothetical, but I've wondered about it for a while.

Let's say you aren't doing anything (else) illegal, you don't have anything illegal on you, and you don't have any warrants for your arrest or anything. And let's say we're talking about this occurring in the USA.

Now let's say there's a cop on the street and you're walking by him, and suddenly you yell "Oh shit! The police!" and then bolt down the street in the opposite direction, such that they clearly heard you say that and see you running.

Is that illegal? First, assuming that the cop doesn't chase you. Is it just illegal to "provoke" a cop like this?

Then let's assume the cop is intrigued and does chase you. Is it illegal to keep running? Would it make a difference whether he yelled for you to stop or not?