[SOLVED] Can someone explain to me this part of Dixon's factorization algorithm?

Can someone explain to me this part of Dixon's factorization algorithm?

I've been trying to implement Dixon's factorization method in python, and I'm a bit confused. I know that you need to give some bound B and some number N and search for numbers between sqrtN and N whose squares are B-smooth, meaning all their factors are in the set of primes less than or equal to B. My question is, given N of a certain size, what determines B so that the algorithm will produce non-trivial factors of N? Here is a wikipedia article about the algorithm, and if it helps, here is my code for my implementation:

def factor(N, B):
    def isBsmooth(n, b):
        factors = []
        for i in b:
            while n % i == 0:
                n = int(n / i)
                if not i in factors:
                    factors.append(i)
        if n == 1 and factors == b:
            return True
        return False

    factor1 = 1
    while factor1 == 1 or factor1 == N:
        Bsmooth = []
        BsmoothMod = []
        for i in range(int(N ** 0.5), N):
            if len(Bsmooth) < 2 and isBsmooth(i ** 2 % N, B):
                Bsmooth.append(i)
                BsmoothMod.append(i ** 2 % N)
        gcd1 = (Bsmooth[0] * Bsmooth[1]) % N
        gcd2 = int((BsmoothMod[0] * BsmoothMod[1]) ** 0.5)
        factor1 = gcd(gcd1 - gcd2, N)
        factor2 = int(N / factor1)
    return (factor1, factor2)

Maybe someone could help clean my code up a bit, too? It seems very inefficient.

Solution