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I was reading about Lehmer's bicycle chain sieve today. The underlying principle is outlined in this paper [Lehmer1928] by Lehmer.

While there are faster factoring methods available, the physical nature of Lehmer's method is fascinating.

I am trying to understand why this method is not suitable for factoring large integers.

References:

[Lehmer1928]: D. H. Lehmer (1928) The Mechanical Combination of Linear Forms, The American Mathematical Monthly, 35:3, 114-121, DOI: 10.1080/00029890.1928.11986799

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    The wikipedia article says that the machine was capable of effectively testing 5000 cases per second. That's peanuts to what computers can do. – Jyrki Lahtonen Jan 01 '23 at 15:18
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    Mind you, the machine was a marvel of its time (IIRC factoring was based on using quadratic residues to find potential factors). I once had the pleasure of attending a talk where Brillhart described its operation. It was just fascinating. Like when they replaced bicycle chains with films because the chains would start making figure 8 loops if you speeded up the crank too much. – Jyrki Lahtonen Jan 01 '23 at 15:21
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    You can find more info on the history and evolution of (sieve based) factoring machines in the thesis I cite here. See also the citations in Discovery of a lost factoring machine – Bill Dubuque Jan 01 '23 at 15:35

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