Factoring as Optimization

The factoring of biprimes is proposed as a framework for exploring unconstrained optimization algorithms. A mapping from a given factoring problem to a positive degree four polynomial F is described. F has the properties that the global minima, which specify the factors, are at F = 0, and that all coefficients can be chosen to be of order unity. The factoring of biprimes is an attractive test bed because a large number of different F functions can be generated easily, in such a way that the complexity of the resulting minimization problem can be easily controlled. Representing the problem in this form also gives interesting perspectives on why factoring is hard.