http://en.wikipedia.org/wiki/Lehmer_sieve
Apparently a Lehmer Sieve was a mechanical device that used chains and pulleys to factor numbers and solve diophantine equations. It once was able to factor $2^{93} + 1 = 3 \times 3 \times 529510939 \times 715827883 \times 2903110321$ in just 3 seconds according the book, Lehmer's Machine(1960). Just looking at its workings, and with a quick Google search I see several examples, but no explanations. Can anyone give me an explanation for how the setup for the device can be used to calculations so quickly?
Edit: Say I want to build one (because who doesn't?), how hard would this be with pulleys and loops of paper/fabric? How would I construct/set up it to do math? Mathematical explanations are good, but does anyone have any engineering diagrams or the like? I would love to make one. Links to sites that I may have missed would also be widely appreciated.