so I have to find all generators for modulo p. And I thought: isn't there are rule for it? As far as I remember, every number from {1,...,p-1} is a generator because p is a prime. Is that true? Or am I mistaken? What is the rule called?

Or how else do you find generator elements quickly? Do you really have to take each and every element and modulo it with p and figuring out if it returns all numbers n for 0 > n < p-1?