| | Anatomy of Credit Card Numbers |
 | | The algorithm used to arrive at the proper check digit is called the Luhn algorithm, after IBM scientist Hans Peter Luhn (1896-1964), who was awarded US Patent 2950048 ("Computer for Verifying Numbers") for the technique in 1960. |
 | | The most succint description of the Luhn algorithm I have found comes from the hacker publication phrack 47-8: "For a card with an even number of digits, double every odd numbered digit and subtract 9 if the product is greater than 9. |
 | | By changing the check digit from 0 to 3, we arrive at the number 4408 0412 3456 7893, which does pass the Luhn check, since the sum of the digits in the bottom row would be 70, which is divisible by 10. |
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