Factor Stencils by Derrick N. Lehmer

Derrick Norman Lehmer (1867–1938) was a distinguished American number theorist. Born in Somerset, Indiana, he obtained his BS from the University of Nebraska in 1893, taught there and at a Nebraska academy for a time, and then moved on to the University of Chicago where he studied with E. H. Moore. After obtaining his PhD in 1900, he was hired by the University of California at Berkeley, rising through the ranks until his retirement in 1937. Assisted by the Carnegie Institution of Washington, Lehmer developed this set of factor stencils to aid in factoring large numbers.

Each sheet is for a different quadratic residue, R. At the very top of each sheet is printed: R=. Different values of the quadratic residue R have been typed in next to the equals sign. Values range from R= -238 to R= -1 and from R= +3 to R= +238, with one stencil for each value of R. Values of R for which there are stencils correspond to those for which there are sets of punched cards in object 1988.0316.02. (The set of cards includes some higher values of R.) There are a total of 295 sheets. The sheets have fifty columns and 100 rows, allowing a position for each of the first 5000 prime numbers. If a prime number had a given quadratic residue, a hole is punched in the corresponding position on the sheet. Superimposing the sheets assisted in finding numbers with a group of quadratic residues, and greatly reduced the time required for factoring.

Working with his son, number theorist D. H. Lehmer, D. N. Lehmer went on to develop an electric version of the factor stencils, which was exhibited at the Chicago World’s Fair in in the 1930s.

Reference:

Derrick N. Lehmer, Factor Stencils, Washington, DC: Carnegie Institution of Washington, 1929.

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