Pollard Monte Carlo factorization method

A prime factorization algorithm also known as Pollard Monte Carlo factorization method. There are two aspects to the Pollard ρ factorization method. The first is the idea of iterating a formula until it falls into a cycle. Let n = p q, where n is the number to be factored and p and q are its unknown prime factors. Iterating the formula x_(n + 1) = x_n^2 + a (mod n), or almost any polynomial formula (an exception being x_n^2 - 2) for any initial value x_0 will produce a sequence of number that eventually fall into a cycle. The expected time until the x_ns become cyclic and the expected length of the cycle are both proportional to sqrt(n).

Brent's factorization method | prime factorization algorithms