"I think whoever invented the numbers started by just inventing the numbers in the times tables. But that was too easy, so he invented the others to fill in the gaps." — 8 yo on the origin of the primes
Actually it seems that among the very first numbers to be studied systematically were the various figurate numbers, all of which are made by summing the terms of arithmetic sequences with initial term 1. These are mostly composite; but this was a theorem, rather than an axiom.