Take your card number and starting from the second-to-last digit, double every second digit moving left. If doubling a digit produces a number greater than nine, subtract nine from the result. Then add all the digits together, the doubled ones and the untouched ones. If the total is divisible by ten, the number is valid. If it isn’t, the number is mathematically impossible as a card number and the form rejects it on the spot. This is the Luhn algorithm written in 1954 by a computer scientist at IBM named Hans Peter Luhn. It still runs inside every payment form on the internet today. And it turns out that valid card numbers are not random. They follow this mathematical rule, and any number that breaks it is immediately disqualified without ever touching a bank’s systems. No server contacted. No database checked. No network request made. The validation happens entirely on your device, in milliseconds. The first six digits do additional work before the Luhn check even runs. They are called the Issuer Identification Number; the first digit identifies the card network (4 means Visa, 5 means Mastercard, 3 means Amex), and the following digits identify the specific bank that issued the card. This is why payment forms show you the Visa or Mastercard logo the moment you type the first digit. No server needed. The network is encoded in the number itself. The last digit of every card number is called the check digit it exists for no other purpose than to make the entire number pass the Luhn algorithm. When a bank generates a new card number, it calculates what the last digit must be to make the sequence valid, then stamps it on the card. It is a built-in mathematical fingerprint.