Prime numbers are not especially interesting. E.g. all groups of prime size are cyclic. But each composite number has its own "character".
The "interesting" number among primes is 2. Almost every theorem about prime numbers has to consider 2 as a special case.
Except that it's interesting that prime numbers have led inordinate numbers of individuals to devote uncountable but significants chunks of their lives investigating them.
It's not their fault that they're leftovers when an artificial grid is created by crossing-out every multiple of 2, 3, 5, or other prime numbers. Yet for some reason this seems to give them a fascinating aura for many. Maybe naming them 'prime' instead of 'leftover' is to blame.
