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. Even better Uli, as he calls himself, has a great description of the Lehmer Chain and the mathematics behind it in a PDF file.
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 an earlier page I had about a factoring technique by Fermat.See My Chain Machine description and photo.
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 Vintage Computer fair. For those who may wonder: Yes, they were all written in 8086 Assembly Language. My program SC for (Simulate Chains) which is in the .ZIP file is described here.
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