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"Everyday Engineering"

"Everyday Engineering" was a technical column posted regularly on the VACETS forum. The Chair of this column is Dr. Hoang Viet-Dung. For more publications produced by other VACETS  members, please visit the VACETS Member Publications page or Technical Columns page.

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The Factoring Machine - (Cranking Out Primes)

I read with great interest the battle of the prime generators several months ago. However, having not a bit curious to code-read, I called it a draw. But permit me though to contribute a footnote to this wonderful discussion.

Some 75 years ago, an ingenious mechanical device was constructed to automatically sift through arrays of numbers to identify patterns, from which mathematicians can determine whether a given number is a prime or the product of primes. In short, this little known machine is the first machine to successfully factoring whole numbers.

Built around 1920 by Euge`ne Oliver Carissan, an officer in the French infantry, it was forgotten for over 70 years. There was no hint of its existence in any museum or library, except in an article of an obscure 1920 French journal. If it was not for the efforts of Jeffrey Shallit of the University of Waterloo in Ontario, and Williams and Francois Morain of the E'cole Polytechnique in Palaiseau, France, this amazing apparatus probably will still be collecting dust in the Floirac astronomical observatory.

Slightly larger than today's laptop computers, the Carissan factoring device consists of a set of 14 rings that can rotate concentrically atop rollers mounted on a wooden base. Each ring has a different diameter, with gear teeth on its underside and a number of equally spaced steel studs screwed into its top. Assembled together, these rings look like a prickly phonograph record.

To use this device, the operator caps certain studs on each ring, following a mathematical recipe that involves a form of trial division. The idea is to divide by numbers smaller than the given number to look for a set of remainders. The rings are mounted on rollers in such a way that studs on different rings will line up in a specified way beneath an armature that resembles the arm of a phonograph.

As the operator turns the handle, the rings rotate at different rates. Capped studs brush against the armature. If capped studs from all 14 rings simultaneously brush against the armature, an electric circuit will be completed (closed), and the operator will hear a click. The number from the counter at that instance is part of the prime factoring solution.

Rotating the crank at two revolutions per minute, an operator can process 35 to 40 numbers per second. Up to 13-digit number can be factored. In fact, Carissan machine took but a cool 10 minutes to prove that 708,158,977 is a prime number.

Source: Science News, a weekly news magazine of science (P.O. Box 1925, Marion, Ohio 43305).

Viet-Dung Hoang, Ph.D.

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