It has not actually been proven that RSA is backed by the difficulty of factoring. That is to say, it may be possible to break RSA without an efficient way to f

It has not actually been proven that RSA is backed by the difficulty of factoring. That is to say, it may be possible to break RSA without an efficient way to factor numbers. However, an efficient way to factor numbers does break RSA. Having said that, there is no obvious way that this result helps with factoring. Indeed, the Twin Prime Conjecture states that the gap is actually 2. Obviously, this has not been proven, but if there was a way to use a proof of this fact to efficiently factor numbers, then we would have used that method without the proof. If it ends up not working, then we would have disproven the Twin Prime Conjecture.