To my delight, I received an email from "Ulrich Meyer" stating "I built a functioning bicycle chain sieve with LEGO bricks." Here is a link to the URL he sent. Uli, as he calls himself, has a description and photos of his LEGO Lehmer Chain and the mathematics behind it in a PDF file. There is a link to an HTML page with more detailed description of where the pins are set, further down.
Uli, and his correspondence has stimulated my interest, so I decided I should update what I had about the Lehmer sieve. This is a first start. Here is a page about a factoring technique by Fermat based on recognizing numbers that are squares.
After the 2002 Vintage Computer Festival I realize more what people want to know about the Lehmer Chain and how it works. Here is a great write up with more details about computing where the "stopping screws" go. It was from this write up, I figured out how to write the program to simulate Lehmer's Chain machine.
Thanks to: Douglas DeVore & Wendy Van Wazer of Digital Turbulence I now have a photo of the Lehmer Chain Machine at the Computer History Museum. The machine is described in the 1928 "Volume XXXV" of "The American Mathematical Monthly" titled "The Mechanical Combination of Linear Forms" by D. H. Lehmer. Thanks to Ed Thelen the article is available on his web site. Here is a Good article about the use Lehmer's machines.
I have written a couple programs to simulate the "Chain Machine". The programs, which can be run at a DOS prompt, are available in demo.zip. I used them to show the technique at the 2002 Vintage Computer fair. For those who may wonder: Yes, they were all written in 8086 Assembly Language. My program SC for (Simulate Chains) in the .ZIP file is described here.
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