# Cohn's irreducibility criterion

Suppose  is a polynomial with integer coefficients, i.e., . Suppose that all the coefficients of  are nonnegative. Further, suppose  is a natural number strictly greater than all coefficients. Then, if  is a prime number,  must be an irreducible polynomial.
An alternate formulation is as follows: for any , if a number with digits  written in base  is prime (so in particular  for ) then the polynomial  is irreducible.