Punch Cards Used as Factor Stencils

Sorting punch cards had mathematical uses. In the late 1920s, number theorist Derek N. Lehmer of the University of California at Berkeley developed a set of punched stencils to assist in factoring large numbers (see 1988.0316.01). In 1939, John D. Elder, then an instructor at the University of Michigan, published a version of Lehmer’s factor stencils on punched cards.

The cards are divided into groups of seven, with each card in a group stamped with the same number (a quadratic residue R). Cards within a group are arranged according to the color of the top edge; the order of the colors is rose, brown, violet, yellow, blue, green and tan (uncolored). The numbers on the groups of cards range from -249 up to -1 and from 2 to 249. The rose card is not stamped for the groups "R=82" and "R=26". There are only 3 cards stamped "R=3" and only 6 stamped "R=2". There is not a group of cards for every number, although there are cards for numbers of the same absolute set of cards for R = 1. The cards are stored in an oak box which was made at the museum. In addition to the punched cards, there is a smaller card indicating the cells included on cards of differing color.

Reference:

D. N. Lehmer, Factor Stencils, rev. John D. Elder, Washington, D.C.: Carnegie Institution of Washington, 1939. A copy of this is 1988.0316.04.

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