Comments on: Biweekly links for 01/11/2010 http://michaelnielsen.org/blog/biweekly-links-for-01112010/ Fri, 10 Feb 2012 10:56:26 +0000 hourly 1 http://wordpress.org/?v=3.3 By: Michael Nielsen http://michaelnielsen.org/blog/biweekly-links-for-01112010/comment-page-1/#comment-27937 Michael Nielsen Tue, 21 Dec 2010 17:55:11 +0000 http://michaelnielsen.org/blog/biweekly-links-for-01112010/#comment-27937 Woett - Note that I'm quoting someone (Martin Rees). When I first read his comments I winced slightly, for exactly the reason you mention: AKS proposed the first provably deterministic time primality test, not a method for factoring. But Rees' larger point about the connection of AKS to the wider world is very interesting. 100 years ago, AKS would likely have remained unknown. Woett – Note that I’m quoting someone (Martin Rees). When I first read his comments I winced slightly, for exactly the reason you mention: AKS proposed the first provably deterministic time primality test, not a method for factoring. But Rees’ larger point about the connection of AKS to the wider world is very interesting. 100 years ago, AKS would likely have remained unknown.

]]> By: Woett http://michaelnielsen.org/blog/biweekly-links-for-01112010/comment-page-1/#comment-27936 Woett Tue, 21 Dec 2010 17:43:33 +0000 http://michaelnielsen.org/blog/biweekly-links-for-01112010/#comment-27936 "In 2002, three Indian mathematicians (Manindra Agrewal, and his two students Neeraj Kayal and Nitin Saxena) invented a faster algorithm for factoring large numbers" Please correct me if I'm wrong, but afaik the AKS-algorithm has nothing to do with factoring integers, but focuses solely on deciding primality. Furthermore, I don't believe that the AKS-algorithm is 'faster'. Sure, it's the first general primality test that is deterministic and can be proven to be polynomial, but there are other tests that are faster, assuming widely believed conjectures. So while it was a theoretical breakthrough, I'm not sure if it's used that much in practice “In 2002, three Indian mathematicians (Manindra Agrewal, and his two students Neeraj Kayal and Nitin Saxena) invented a faster algorithm for factoring large numbers”

Please correct me if I’m wrong, but afaik the AKS-algorithm has nothing to do with factoring integers, but focuses solely on deciding primality. Furthermore, I don’t believe that the AKS-algorithm is ‘faster’. Sure, it’s the first general primality test that is deterministic and can be proven to be polynomial, but there are other tests that are faster, assuming widely believed conjectures. So while it was a theoretical breakthrough, I’m not sure if it’s used that much in practice

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