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We could examine each of the candidate polynomials in turn and divide it by each of looking for gf 2 3 potentially irreducible polynomials of order less than n, of which there are fir two. While this is already quite manageable, we can reduce it even further my nothing that multiplication in any field is commutative and therefore if we order the elements of our set in any way we choose then we can limit ourselves to only evaluating those expressions in which the second factor is greater than or equal to the first factor. Connect and share knowledge within a single location that is structured and looking for gf 2 3 to search.