Different Credit cards and their lengths Credit Card Name Length AMEX MASTERCARD VISA DISCOVER DINERS CLUB/ CARTE BLANCHE 15 16 13 and 16 16 14 Actually, credit card numbers have some structure to them. American Express numbers all start with 34 or 37; MasterCard numbers all start with 51, 52, 53, 54, or 55; Visa numbers all start with 4; Discover numbers all start with 6011; and Diners Club (Carte Blanche) numbers start with 300, 301, 302, 303, 304, 305, 36, or 38. But credit card numbers also have a "checksum" built into them, a mathematical relationship between at least one number and others. That checksum enables computers (or humans who like math) to: detect typos (e.g., transpositions), if not fraudulent numbers, without having to query a database, which can be slow. (Consider the awkward silence you may have experienced at some point while paying by credit card at a store whose computer uses a dialup modem to verify your card.) Of course, a dishonest mathematician could certainly craft a fake number that nonetheless respects the mathematical constraint, so a database lookup is still necessary for more rigorous checks. So what's the secret formula? Well, most cards use an algorithm invented by Hans Peter Luhn, a nice fellow from IBM. According to Luhn's algorithm, you can determine if a credit card number is (syntactically) valid as follows: 1. Multiply every other digit by 2, starting with the number's second- to-last digit, and then add those products' digits together. 2. Add the sum to the sum of the digits that weren't multiplied by 2.