20070311, 13:21  #1 
Oct 2004
23^{2} Posts 
Applications of factoring
One of the reasons people would like to be able to factor large products of 2 primes is to break the encryption techniques currently popular for ecommerce etc.
The guy from mwave systems argued that "factoring" is not the killer app for quantum computing. His reasoning was that once current encryption was broken, people would just move to a new encryption algorithm which was not easily solvable using quantum techniques. Of course if messages now were archived, they could be decrypted retrospectively which might still reveal valuable information. He seemed to be dismissing factoring as an app for quantum hardware. That set me thinking: I know that being able to factor is actually useful to us here in searching for primes ie eliminating candidates in early stages. If a quantum computer could help us do that it would be irrelevant that contemporary encryption was obsolete. So, my question to the forum is: Can factoring of itself actually be useful for other things? 
20070311, 19:52  #2 
Aug 2004
New Zealand
11100011_{2} Posts 
Factoring is used in more than one way in primality proving. You seem to be aware that is used to eliminate candidates for primality testing, but it is also used in the construction of some forms of primality proof. For example, if you have have putative prime p, then factoring circa 30% of p1 and/or p+1 is enough to generate a proof of primality.
There is also a project discussed elsewhere in this forum where factoring is used to help establish bounds for the existence (if any) of an odd perfect number. 
20070313, 01:10  #3 
Mar 2003
New Zealand
485_{16} Posts 
Studying the structure of composite integers has been of interest for thousands of years, and will be of interest for thousands more. It is just a coincidence that for a few decades it was useful too.

20070313, 21:32  #4 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2C1F_{16} Posts 

20070313, 21:58  #5 
Banned
"Luigi"
Aug 2002
Team Italia
4844_{10} Posts 

20070314, 12:14  #6 
Nov 2003
2^{2}·5·373 Posts 

20070315, 19:32  #7  
∂^{2}ω=0
Sep 2002
Repรบblica de California
3^{2}·1,303 Posts 
Quote:
When I moved to Silicon Valley in 1999, given the local job market, nobody around here cared one whit about the area I'd done my University work in, namely Theoretical and Computational Fluid Mechanics. But when I had my first few interviews with (typically quite skeptical, given my background) recuiters for local tech companies, I found when I mentioned my primetesting coding work (which had begun as a sidelight, an interesting application of FFTs to help my engineering students understand applications of transforms), their eyes invariably lit up  bigtime technerd cool factor there. These days of course I have enough actual siliconrelated work to put on my CV that I no longer need to worry about my qualifications being of interest to Silicon Valley employers, but am proud to say that my primesrelated work, modest as it has been, was key to getting me that first "In." Last fiddled with by ewmayer on 20070315 at 19:33 

20070315, 19:54  #8 
Feb 2007
2^{4}×3^{3} Posts 
In some sense, factoring is more productive than primality testing... (the latter just produces a single bit of information)...
I apologize for a somewhat illplaced question : (which will again reveal my ignorance on the subject...) The file lowm.txt seems to give complete factorizations of Mersennes Mq for q=2^k from q=16384 up to q=67108864 plus smaller values of qn from 787 to 9973 (looks as if this were (all(?)) primes between 787 and 1e4) Is there some explanation available ? why "small" primes > 787 and < 9973 and "big" powers of 2 ? PS: a google search for "lowmtxt lowptxt files contain factors of Mersenne numbers" gives only 6 pages on which I did not find the info on my question 
20070316, 05:41  #9  
Tribal Bullet
Oct 2004
5·709 Posts 
Quote:
jasonp 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Wired digital cock has appeared on certain Windows applications  kladner  Information & Answers  20  20150122 19:24 
Microsoft, ignoring the irony, files 10 software patent applications per day  ewmayer  Lounge  0  20050731 19:42 
AMD64 Applications with Visual Studio 6 or .Net  Ethan (EO)  Software  0  20040809 04:07 