Interesting. Of the three algorithms textbooks I have lying around, one doesn’t mention bubblesort at all, one has the early termination condition, and one doesn’t.
If you figured out how to factor numbers quickly, you’d sell it to the security services for millions, and not enter it into an RSA competition to win a few thousand 
Especially given the existence of \prec.
Well, of course. 
But imagine one day if someone did figure out a relatively quick algorithm to solve such problems. Do you realize what kind of power he or she would wield? Can you imagine how much $$$ that would be worth not to security services, but to governments themselves? Hey, sounds like a movie plot.
a) There already is an algorithm. It’s down to the engineering problem of building the computer which can run it.
b) You really wouldn’t wield that much power. RSA, and public-key encryption schemes in general, are relatively slow and get used for securely sharing a private key to use a faster cipher like DES or IDEA. There are currently two companies, with two more on the way, selling quantum cryptography systems which are not only literally impossible to break (in theory if not implementation), but alert the users if anyone is trying to listen in. The only catch is that they only work at a range of tens to low hundreds of kilometers.