Applications of factoring besides crypto?

[SALMONMILK]

Hi all,


I am wondering if there are any uses for number factorization besides cryptography. I have been trying to research the answer for a long time and cannot seem to find anything besides cryptography. I am familiar with RSA and the other crypto schemes that are related on Wikipedia, but that is about it when it comes to factoring.


I have come across a version of the fast-fourier transform (https://en.wikipedia.org/wiki/Prime-..._FFT_algorithm) that says prime factor in its name, but I do not have the knowledge to be able to understand what it does or means. Does it utilize number factorization?



So really the main question: Are there any known applications for number factorization besides cryptography?


Any information is greatly appreciated. I am just deeply curious and have been unable to find any information.



Thanks so much

[xilman]

Originally Posted by SALMONMILK

I have come across a version of the fast-fourier transform (https://en.wikipedia.org/wiki/Prime-..._FFT_algorithm) that says prime factor in its name, but I do not have the knowledge to be able to understand what it does or means. Does it utilize number factorization?

The classical FFT, which applies to data with a length of 2ⁿ exploits the (almost trivial) factorization to earn the subriquet "Fast" by dividing a range of data into two sub-ranges each half the size of the original. Similar approaches, though not as efficient, can exploit small prime factors, p, to divide the range into p portions, each 1/p the size of the original.

[chris2be8]

AFAIK it's main other use is mathematical research.

Read the "Links to factoring projects" https://mersenneforum.org/showthread.php?t=9611 thread in this forum and follow the links to see what is being worked on now.

Chris

Technically it is still crypto but a different sort, proof of work for crypto collectibles.

[kriesel]

There are applications in engineering design sometimes for factoring of what mathematicians would consider small to trivial numbers or ratios. Clock drives for equatorial mounts for telescopes or tracking solar arrays when electronic or computer speed controls are impractical, obtaining gear reduction ratios near a given desired ratio with smooth numbers. The selection of prime factors in commercially available power gears or even instrument size gears or toothed-belt sprockets is pretty limited. The method of continued fractions is a way to derive a series of successive approximations of ratio, each of which can be evaluated for practicality.
https://en.wikipedia.org/wiki/Continued_fraction

[alpertron]

Solving Diophantine equations of second degree on two variables requires integer factorization.

For example: find the integer solutions (x, y) of a circle represented by x² + y² = N where N is a big integer number. You cannot solve this problem without factoring N.