[ForOldHack]

Here is a prime factorization: 2 = 2 x 1. Every number has a product of 1. Every prime has itself as the only factor, and 1. Kind of silly to write about number theory and just pass over that simple fact.

[SyzygyRhythm]

That's why 1 is not generally considered prime. If it was, 2 could be factored as 2, 2x1, 2x1x1, etc., which breaks the uniqueness property.