Even if we ignore units (i.e. 1, -1 in the ring Z), the prime number is a factorization of itself (one factor). Otherwise the famous theorem that any integer >

Even if we ignore units (i.e. 1, -1 in the ring Z), the prime number is a factorization of itself (one factor). Otherwise the famous theorem that any integer >= 1 can be factored uniquely (up to order of the factors) into prime numbers would not hold (it even holds for 1, since 1 is defined as the product of zero factors).