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You’re at the checkout screen after an online shopping spree, ready to enter your credit card number. You type it in and instantly see a red error message: “Please enter a valid credit card number.” Annoyed, you scan back through each digit and spot the culprit: you tapped the 6 key where a 5 belonged. Typo corrected; purchase complete. But how did the website detect your error so quickly? Does the online platform keep a master list of every valid credit card number to compare your entry against? Did it ping your bank in a split second? The explanation is much cleverer.

All mainstream credit card numbers obey a mathematical trick designed to catch the most common typos. It’s called the Luhn algorithm, named after IBM researcher Hans Peter Luhn, who patented it in 1960. Similar error-checking schemes lurk in many of the numbers you encounter daily: barcodes, package tracking numbers, bank account numbers, and even ISBNs on books.

Grab a credit card from your wallet, and you’ll find it contains more structure than first glance suggests. The anatomy of a credit card number includes four main parts. To demonstrate, I’ll use my personal Visa. [Stretch your math muscles with these puzzles]

The first digit is the major industry identifier. Visas always begin with a 4, and Discover always start with a 6. The next five to seven digits pinpoint the bank or institution that issued the card. What remains (sans the final digit) is your specific account number within that bank. The final digit, sometimes called the “check digit,” has nothing to do with financial institutions. Issuers tack it on so that the whole card number will satisfy a specific mathematical test—the Luhn algorithm. Here’s how the algorithm works:

1. Write out all but the last digit of the card number.
2. Double every other number starting at the right.
3. Sum the resulting digits (not numbers). E.g., if you doubled a 7 to become a 14 in Step 2, this will become 1 + 4 = 5 in this step.
4. Add the check digit to the sum. If the result is not a multiple of 10, then the credit card number is invalid.

I’ll show the Luhn algorithm in action on my Visa, but you should try it with your credit card, too.

The number crunching culminates in 75, which is not a multiple of 10. So this cannot be my real credit card number; I must have mistyped it.

Credit card issuers first assign the account numbers and then compute steps one through three of the Luhn algorithm to determine the appropriate check digit. In this case, the card number should have ended in a 3 because 67 + 3 = 70, a multiple of 10.

This particular dance of digits has come to dominate credit card verification because of its simplicity and powerful set of features. If you mess up any single digit when entering your card number, the Luhn algorithm will detect it. If you accidentally swap adjacent card digits while inputting, it will detect that, too (with the one exception of flipping 09 to 90, or vice versa).

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Isabel Pavia/Getty Images

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