eli5-Why is the number 1 not considered a prime number even though there isn’t any number that divides it?

Question

eli5-Why is the number 1 not considered a prime number even though there isn’t any number that divides it?

In: 2

Answer 1

There are a number of reasons. Fundamentally you could define primes to include it if you wanted, but it turns out to be mathematically convenient not to because a lot of theorems would have to say something like “…primes except 1”, which is a bad way to define a group of things.

For example, the fundamental theorem of arithmetic says that every number (positive integer) can be factored into a *unique* product of primes. But if you include 1, that’s no longer true, since (say) 6 can be factored as 2*3 or 1*2*3.