Given the Lucas sequence U_n(b, -1) and V_n(b, -1), define Δ = b^2 + 4. Then an extra strong Lucas pseudoprime to the base b is a composite number n = 2^r s + (Δ/n), where s is odd and (n, 2Δ) = 1 such that either U_s congruent 0 (mod n) and V_s congruent ± 2 (mod n), or V_(2^t s) congruent 0 (mod n) for some t with 0<=t

Lucas pseudoprime | strong Lucas pseudoprime