20150513, 16:40  #1 
2^{2}·3·61 Posts 
Utility of integer factorization.
Other than the obvious, RSA and P:NP, how would the ability to factor integers of any magnitude affect the sciences?
A natural extension includes factors such as complex (Gaussian) primes and quotients. Will such a tool provide deeper insight into the results of numerical calculations, fundamental physical or mathematical constants? PSLQ has provided insight into some structures and Plouffe (unsuccessfully as far as I am aware) attempted the same for some physical constants. (Regarding constants, Steven Finch's expositions are a good complementary reference.) The work of Mandelbrot and Thom has helped to conceptualize order from apparent disorder and I was wondering if `reversing the multiplicative process (a solid notion of primality is crucial)` would have a similar effect. Mandelbrot's, "The Fractalist", is a bargain in paperback and for those with some time, any of the books in the "Library of Living Philosophers" are worth [the] while. As usual, Google and Wikipedia will point and introduce the sources but will not replace them. Rational creativity, I guess, would be a way of encapsulating the above. Looking at "Wired's" review of Mandelbrot's memoir, this point is a carryover from prior thread, "... Mandelbrot was a brilliant idealist who struggled with the gap between thought and language..." which may be considered as an aspect of the SW hypothese. Last fiddled with by jwaltos on 20150513 at 16:56 Reason: corrections 
20150516, 22:18  #2 
Dec 2012
The Netherlands
5×353 Posts 
Hendrik Lenstra jokingly encourages his students to solve such problems so that number theory will lose its value to cryptography and commercial companies and return to being an area of research where you only meet people who are passionate about the mathematics for its own sake.

20150517, 05:17  #3 
Romulan Interpreter
"name field"
Jun 2011
Thailand
2×47×109 Posts 

20150517, 05:41  #4 
"Bob Silverman"
Nov 2003
North of Boston
2^{3}×937 Posts 

20150517, 07:13  #5 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
5×7×331 Posts 

20150517, 13:49  #6 
Einyen
Dec 2003
Denmark
D57_{16} Posts 
Last fiddled with by ATH on 20150517 at 13:49 
20150521, 16:25  #7  
"Bob Silverman"
Nov 2003
North of Boston
2^{3}·937 Posts 
Quote:
comments. He just made another one about factors of Fermat numbers. 

20150522, 02:14  #8 
Romulan Interpreter
"name field"
Jun 2011
Thailand
10100000000110_{2} Posts 

20150522, 12:20  #9 
5·7·73 Posts 
Aspects of factorization.
FFT improvement, quantum wave functions, commutative and noncommutative representations...etc.
Last fiddled with by jwaltos on 20150522 at 12:37 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Integer factorization?  bearnol2  Information & Answers  7  20101209 02:50 
Integer factorization with q < 2p  mgb  Math  36  20091107 15:59 
CADO workshop on integer factorization  akruppa  Factoring  14  20080918 23:52 
Integer Factorization  mgb  Math  16  20071217 10:43 
Integer Factorization 2  mgb  Math  5  20070723 12:55 