[amalcon]

factorization of course as it has never been demonstrated to be polynomially reducible to NPC.

Every NP problem is polynomial-time reducible to SAT. I do not recall the title of the paper off the top of my head, but it has been proven that the definition of an NP problem (a question that can be answered given some additional piece of information, a "certificate") is polynomial-time reducible to SAT.

The methodology was basically an algorithm taking as input a description of such a solution, and producing a boolean expression on the certificate and some other values needed to maintain integrity. The expression is satisfiable if and only if the answer is affirmative.

The reason that factorization is not known to be NP-complete is that the reverse is not known. That is, no NP-complete problem is known to be polynomial-time reducible to factorization.