In practice, it turns out to be more convenient if the definition excludes 1, rather than put a qualifier in every place which uses the term "prime". For examp

In practice, it turns out to be more convenient if the definition excludes 1, rather than put a qualifier in every place which uses the term "prime". For example, it's more convenient to write "every integer greater than 1 is a unique product of prime numbers" than to say "every integer greater than 1 is a unique product of {prime numbers excluding 1}" (That's the fundamental theorem of arithmetic https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithme... .)