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Re: Prime factorization
Posted:
Nov 12, 2013 11:41 AM


On Tuesday, November 12, 2013 9:38:32 AM UTC5, Pubkeybreaker wrote: > On Tuesday, November 12, 2013 8:35:56 AM UTC5, scattered wrote: > > > > <snip> > > > > >> You seem to need some valium or something. To say that a method is efficient isn't to say that it is the most efficient method in existence. I wrote an inefficient Python implementation of Pollard's rho when I first read about it a few years ago (idle curiosity on my part, this isn't my area of expertise). I just tried it on 130642890110987 and the factorization appeared on my screen even before my pinky left the enter key (even though Python is a "slow" interpreted language). That is "almost instantly" in any reasonable interpretation of that phrase. > > > > You have a strange notion of the word "efficient". The topic of discussion > > is computer implementation of factoring methods. In that domain human > > perception of "almost instantly" is meaningless. What does have meaning is > > how well the method performs when called as a subroutine. By any reasonable > > interpretation of the word "efficient", an exponential time algorithm is > > NOT efficient. Indeed, even from a theoretical computer science point of view > > exponential time algorithms are NOT efficient. > > > > > > > > >There is no reason to adopt a scolding tone againt somebody who make the true albeit unnuanced claim that Pollard's rho can efficiently factor numbers of that size. > > > > This NG has become overwhelmed with cranks, spammers, and nonsense. When I > > see someone who is ignorant of a subject make an ignorant and erroneous claim, > > I respond. > > > > To claim that Pollard Rho is efficient is wrong. It is not.
The claim was that Pollard's rho was efficient *for numbers of that size*. If you want to be pedandic, Pollard's rho is O(1) when applied to numbers of bounded size. You seem to be reading more into a post than is warranted. Pollard's rho is stunningly efficient at factoring numbers which 100 years ago were outside of the reach of human factoring. It does date to 1975, and since then some even more stunningly efficient algorithms have been invented. *None* of them are polynomial time in the number of digits, so perhaps none of them are efficient in *some* sense of the word "efficient"  but not all uses of the word "efficient" are intended to be understood in a technical sense involving asymptotic worstcase running time. There is no evidence that the other poster intended such technical meanings in his use of the word efficient, so it can't be dismissed as simply "wrong" in any unqualified sense. In context, it seems that he meant something akin to "effective" (one of the standard synonyms of the word "efficient") in which case he is 100% correct in his assessment, especially given his qualifier ("of that size").



