There is a generalized version of Pocklington's theorem is more widely applicable because it does not require finding a large prime factor of N-1; also, it allows a different value of to be used for each known prime factor of N-1.
Factor N &minus; 1 as N &minus; 1 = AB, where A and B are relatively prime, A > \sqrt{N}, the prime factorization of A is known, but the factorization of B is not necessarily known.