Speeding Fermat's factoring method

A factoring method is presented which, heuristically, splits composite in steps. There are two ideas: an integer approximation to provides an algorithm in which is represented as the difference of two rational squares; observing that if a prime divides a square, then divides that square, a heuristic speed-up to steps is achieved. The method is well-suited for use with small computers: the storage required is negligible, and one never needs to work with numbers larger than itself.