I don’t know if prime factorization is the correct English word for it but the operation I am referring to takes a (non zero) natural number and returns a multiset of primes that give you the original number when multiplied together.
Example: pf(12)={2,2,3}
if we allowed 1 to be a prime then prime factorization cease to be a function as pf(12)={1,2,2,3} and pf(12)={1,1,1,1,2,2,3} become valid solutions.
1 being prime breaks a lot of the useful properties of primes, such as the uniqueness of prime factorization.
Isn’t that function listing all the numbers? Not only the primes?
I don’t know if prime factorization is the correct English word for it but the operation I am referring to takes a (non zero) natural number and returns a multiset of primes that give you the original number when multiplied together. Example:
pf(12)={2,2,3}if we allowed 1 to be a prime then prime factorization cease to be a function aspf(12)={1,2,2,3}andpf(12)={1,1,1,1,2,2,3}become valid solutions.