If we let “1” in the club, then the prime number theorem gets messy. It’s the uniqueness part.
On the first day of basic training, the drill sergeant put his traumatized recruits into something of a platoon formation and directed the soldiers to count off. From somewhere in the third or fourth rank, he heard a soldier with a very effeminate voice drag out a long "oooooone" before the rest of the soldiers down the rank loudly and quickly barked out, "2, 3, 4, etc." Incensed at the apparent lack of motivation, the drill sergeant stormed over to the first file, eyed the apparent offender up and down and snarled, "Are you 'One'"?
The recruit lisped back with girlish grin, "Why yeth, thergeant. Are you one, too?"
I’d let in 1 before 2. Two isn’t even odd.