Plato and the Discovery of the Primes

Up to and including Plato’s generation, the concept of prime number isn’t found. Plato, who never mentions the primes, generates 2 and 3 in Parmenides, and with them the even and odd, and what is taken to be all other kinds of number. That project suggests the challenge of generating all numbers by Plato’s methods – a challenge which cannot be met because of the primes. I argue that this brought about the formation of the concept of prime number, probably in the Academy, and that the attempt to develop the Parmenides’ ideas led to the discovery that there are infinitely many primes.