Suppose there is some positive integer n that is four digits long and is relatively prime to 100! (meaning n and 100! have no common factors other than 1). n must be prime, but why?
100! is a composite number, but composite numbers can be relatively prime to other composite numbers, so that can't be the reason n is prime. n being four digits long and 100! having factors that are all less than four digits must have something to do with it, but I can't wrap my head around the exact reason.
So, why does n have to be prime in this situation?