In 1929, Derrick N. Lehmer published a set of paper stencils used to factor large numbers by hand before the advent of computers. We explain the math behind the stencils, which includes modular arithmetic, quadratic residues, and continued fractions, including my favourite mathematical visualization for continued fractions.
Accompanying PDF writeup about these stencils: https://math.colorado.edu/~kstange/stencils/stencil-users-guide.pdf
Accompanying Python & SVG files to make your own: coming soon
Original stencils:
Derrick N. Lehmer, Factor Stencils, Washington, DC: Carnegie Institution of Washington, 1929.
- Worldcat link:
https://www.worldcat.org/title/factor-stencils-by-derrick-norman-lehmer/oclc/504616344&referer=brief_results
- Smithsonian Link: https://americanhistory.si.edu/collections/search/object/nmah_1214102
Updated on Hollerith cards:
D. N. Lehmer, Factor Stencils, rev. John D. Elder, Washington, D.C.: Carnegie Institution of Washington, 1939.
- Worldcat Link: https://www.worldcat.org/title/factor-stencils/oclc/9739317&referer=brief_results
- Smithsonian Link: https://americanhistory.si.edu/collections/search/object/nmah_1214103
Lehmer's essay on his factoring machine that I quote from in the video:
D. N. Lehmer, Hunting Big Game in the Theory of Numbers, Scripta Mathematica, September, 1932.
http://ed-thelen.org/comp-hist/Lehmer-NS03.html
A great video about homemade factor stencils by Chris Staecker:
https://www.youtube.com/watch?v=Fwn_6uqmeqw
Videos on modular arithmetic, done visually:
https://www.youtube.com/playlist?list=PLrm9Y---qlNyWBQEKBSrr_Uh16gEWhJzw
Thanks to:
Glen Whitney, of MOMATH, for help with paper cutter
3blue1brown and LeiosOS, for motivation (Summer of Math Exposition, SoME1 https://www.3blue1brown.com/blog/some1)
Jonathan Wise, as always
Image credits:
Lehmer on piano – Konrad Jacobs – CC-BY-SA 2.0 DE
https://commons.wikimedia.org/wiki/File:Derrick_Norman_Lehmer.jpg
Lehmer’s machines – Marcin Whichery – CC-BY 3.0 https://commons.wikimedia.org/wiki/File:Computer_History_Museum_(2664736595).jpg
RSA keyfob – Alexander Klink – CC-BY 3.0
https://commons.wikimedia.org/wiki/File:RSA_SecurID_SID800.jpg
Farey subdivision – collaboration with Edmund Harriss
and Steve Trettel
If you like, subscribe and comment, it does encourage me :)
Personal notes: This was my first real YouTube video project. I learned a lot of lessons, including that my voice is different on different days even with the same microphone setup! It was a fun adventure. I'm not going to be the next big YouTube star, but your comments and feedback make it feel worth the time and energy!
Licensed under CC BY-SA 4.0
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