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Old 2015-05-13, 16:40   #1
jwaltos's Avatar
Apr 2012

5728 Posts
Default 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 carry-over 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 S-W hypothese.

Last fiddled with by jwaltos on 2015-05-13 at 16:56 Reason: corrections
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