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Lehmer Factoring Machines

Photo-electric,Chain, Gear

Manufacturer D.H. Lehmer
Identification,ID X85.82
Date of first manufacture 1932
Number produced 1
Estimated price or cost -
location in museum -
  • Photoelectric machine - D.H. Lehmer
  • Chain machine - " ... chain machine - replicated at the (Boston) Computer Museum by Roberto Canepa, Andrew Kristoffy and Richard Rubinstein."

The above two machines were combined on this page

as the principles of operation are identical,
even though the mechanical details differ.

Contents of this page:


Photoelectric Factoring Machine

Bicycle Chain Factoring Machine - reproduction


The Factoring Machines did NOT use the technique of Eratosthenes

The Lehmers were after much bigger fish - please see

Special features

Historical Notes
From: Robert D. Silverman 
Jim Roth 
Date: Thu, 23 May 1991 01:49:49 GMT
Subject: D. H. Lehmer

It is with a very great deal of sadness that I must report that D. H. Lehmer
passed away last night.

I am deeply saddened by this loss as Professor Lehmer's work has been a
source of personal inspiration for me. I consider him to be the father
of computational number theory; my major field of interest.

Bob Silverman
Mitre Corporation

Professor Lehmer worked on (among other things) the solution of sets of linear
Diophantine equations via Chinese Remainder Theorem. This involved building
a special-purpose computer which had many "delay lines" (recirculating loops)
of prime-integer length. When the numbers in all of the loops lined up (as in
a Las Vegas slot machine hitting a jackpot) a bell would ring and the data
would be dumped and printed out, then re-loaded into the loops. The first of
these machines was purely mechanical; later on (1965?) he bought surplus
radar delay lines and worked out a purely electronic number-theory machine
along the above lines, which he talked about at UCLA. He claimed that his
technique got answers hundreds of times faster than an IBM 704 would have.
Does anyone know whether he ever got a special VLSI chip built for
such purposes?

David L. Elliott
Washington University

There is a photograph and explanation of Dr. Lehmer's factoring machine
in the Dover book "Recreations in the Theory of Numbers" by Albert Beiler.
This machine had many gear driven wheels which would be halted when sets of
holes in them lined up, triggered by a photocell. It was called a
photoelectric number sieve.

Apparently it was an amazing, though tempermental, device, and was
inadvertantly "jammed" by a local Ham radio operator whose transmissions
triggered the photocell at times.

The book also mentions Lehmer's first factoring machine - a bicycle
sprocket and chain contraption!

Will future generations look back similarly at our current massively
parallel computers doing quantum chromodynamics calculations?

Jim Roth
Digital Equipment Corporation

This Artifact

Interesting Web Sites

Other information
"Recreations in the Theory of Numbers" - See page 239 for Lehmer gear machine

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Updated May 15, 2017