>>11551072There really isn't a pretty and efficient way of doing it. Eisenstein criteria is the best you can hope in terms of easiness of use, I guess.
What you could do is computing the Galois group and seeing if it is transitive on {1,2,...,n} (n being the polynomial's degree).
There are algorithms to determine the Galois group of a polynomial, but they aren't nice to do by hand.
