453.7 million social security numbers have been issued to date. There are only 1 billion = 1000 million distinct 9 digit integers. This means that if I were to make up any 9 digits, I would have roughly a 45% chance of guessing someone else's valid social security number.
With that said, is it fair to say that if a criminal has nothing but your social security number (i.e. they don't have your name, they don't know when you were born, they know nothing about you) it is in fact useless as a means to commit identity theft or other fraud?