Arthur Cohn's irreducibility criterion is a sufficient condition for a polynomial to be irreducible in —that is, for it to be unfactorable into the product of lower-degree polynomials with integer coefficients. The criterion is often stated as follows: If a prime number is expressed in base 10 as (where ) then the polynomialis irreducible in . The theorem can be generalized to other bases as follows: Assume that is a natural number and is a polynomial such that . If is a prime number then is irreducible in .