![]() 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. But credit card numbers also have a “checksum” built into them, a mathematical relationship between at least one number and others. All American Express numbers start with 34 or 37 most MasterCard numbers start with 51, 52, 53, 54, or 55 (they also have some other potential starting numbers which we won’t concern ourselves with for this problem) and all Visa numbers start with 4. And those are decimal numbers (0 through 9), not binary, which means, for instance, that American Express could print as many as 10^15 = 1,000,000,000,000,000 unique cards! (That’s, um, a quadrillion.)Īctually, that’s a bit of an exaggeration, because credit card numbers actually have some structure to them. ![]() There are a lot of people with credit cards in this world, so those numbers are pretty long: American Express uses 15-digit numbers, MasterCard uses 16-digit numbers, and Visa uses 13- and 16-digit numbers. ![]() Printed on that card is a number that’s also stored in a database somewhere, so that when your card is used to buy something, the creditor knows whom to bill. A credit (or debit) card, of course, is a plastic card with which you can pay for goods and services.
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