On Primes

It's a subject of much interest to armchair scholars, but the simple fact is that 1 is not prime.

1 is not prime because we have defined it that way.

A prime number has two divisors: 1 and itself. 1 divides 1, but that's all that divides it. 1 is not prime because 1 and itself are the same divisor.

We have defined it not to be prime because if 1 is prime, the rest of algebra gets messier, and mathematicians hate messy. They like elegant.

And having 1 not be prime is elegant. It may infuriate you to think so, but it's true.

Because we have defined it that way.

"But if every integer can be represented as a product of primes, and 1 is an integer, what are the prime factors of 1?" you may ask.

The answer is "There are none." Because we have defined it that way.

Wrap your head around that and you will know the essence of wisdom.