Of course it qualifies. No matter how a key gets broken, its broken. The point is that if a function exists which will tell you if a given number is larger than the RSA private key, that function can be used as a factoring algorithm.
I have to disagree. What I am asking is a binary question, not one of magnitude. I never care what the magnitude is. Don't want to know it. Will give it away unopened if I do get it. If all you know is 1/0 then you can't use it to factor the number. The other aspect of your method is, yes it can give you some of the factors, but it has no guarantee that you will find all of them. If your algorithm can'g guarantee it finds all of them every time then it can't be positively used to factor number.
No, what it means is that you would have to break most of number theory, and common sense, before having to worry about such a function. The risk of exploding in the vacuum caused by all of the molecules in the air of this room suddenly moving to the far corner is far higher than the chance of such a function existing.
To each their own (opinion). I am not breaking anything, I *am* asking for a reference. There seems to be a particular sub-set of prima donnas on c-punks who feel it is their duty to stipulate what kinds of questionsss can be asked and how much one has to know to ask them. I have only one other question for these folks, do you work for the government or the church?