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From the September 13, 2007 edition of The Economist. Algorithms
Business by numbers

People often make mistakes when they key in their credit-card numbers online. With millions of transactions being processed at a time, a rapid way to weed out invalid numbers helps to keep processing times down. Enter the Luhn algorithm (see [above] ), named after its inventor, Hans Luhn, an IBM researcher. The numbers on a credit card identify the card type, the issuer and the user's account number. The last number of all is set to ensure that the Luhn algorithm produces a figure divisible by ten. If it is, the card number has been properly entered and the processing can go ahead.