Let f(x) be a monic polynomial of degree d with discriminant Δ. Then an odd integer n with (n, f(0) Δ) = 1 is called a Frobenius pseudoprime with respect to f(x) if it passes a certain algorithm given by Grantham. A Frobenius pseudoprime with respect to a polynomial f(x) element Z[x] is then a composite Frobenius probably prime with respect to the polynomial x - a.