20150513, 16:40  #1 
Apr 2012
2^{3}×3^{2}×5 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
3053_{8} 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
Jun 2011
Thailand
3^{4}·113 Posts 

20150517, 05:41  #4 
Nov 2003
2^{2}×5×373 Posts 

20150517, 07:13  #5 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
10506_{10} Posts 

20150517, 13:49  #6 
Einyen
Dec 2003
Denmark
3×17×59 Posts 
Last fiddled with by ATH on 20150517 at 13:49 
20150521, 16:25  #7  
Nov 2003
2^{2}×5×373 Posts 
Quote:
comments. He just made another one about factors of Fermat numbers. 

20150522, 02:14  #8 
Romulan Interpreter
Jun 2011
Thailand
23C1_{16} Posts 

20150522, 12:20  #9 
Apr 2012
101101000_{2} Posts 
Aspects of factorization.
FFT improvement, quantum wave functions, commutative and noncommutative representations...etc.
Last fiddled with by jwaltos on 20150522 at 12:37 
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