I’d let in 1 before 2. Two isn’t even odd.
In number theory, the fundamental theorem of arithmetic (or the unique-prime-factorization theorem) states that any integer greater than 1 can be written as a unique product (up to ordering of the factors) of prime numbers.
We need two to take care to those pesky even numbers. If you let one in, then the factorization is not unique, since you can add as many factors of one as you please.
Frinstance: 6936 = 2^3 x 3^1 x 17^2 = 1 x 2^3 x 3^1 x 17^2 = 1^2 x 2^3 x 3^1 x 17^2 = 1^3 x 2^3 x 3^1 x 17^2