I was curious about how third party libraries check the validity of credit card numbers so quickly. These libraries work locally on your device and they do not need an internet connection to tell you if a number is wrong. I discovered that the secret is a clever piece of math called the Luhn Algorithm.

The Luhn Algorithm is a checksum formula. It is used to validate identity numbers like credit cards or even the IMEI number on your phone. It is not meant for security. Instead, it is meant to catch common human mistakes like typing a wrong digit or swapping two numbers by accident.

🧠 How the Algorithm Works

The math follows a few simple steps. To understand the logic, let us look at a sample 11 digit number: 49927398716.

We always process the number from right to left.

  1. Look at the digits. Start from the very last digit on the right. This is the check digit.

  2. Double every second digit. Moving left from the check digit, you leave the first one alone and double the next one. You repeat this pattern for the whole number.

  3. Handle large results. If doubling a number results in something larger than 9, you subtract 9 from it. For example, if you double 7 and get 14, you calculate 14 minus 9 to get 5.

  4. Sum everything up. Add all the modified digits and the original digits together.

  5. Check the total. If the final sum ends in a zero, the number is valid.

Position Original Digit Action Result
1st (Right) 6 Keep it 6
2nd 1 Double it (1×2) 2
3rd 7 Keep it 7
4th 8 Double it (8×2=16) 7 (1+6)
5th 9 Keep it 9
6th 3 Double it (3×2) 6
7th 7 Keep it 7
8th 2 Double it (2×2) 4
9th 9 Keep it 9
10th 9 Double it (9×2=18) 9 (1+8)
11th 4 Keep it 4

📊 Summary:

  • Total Sum: 6 + 2 + 7 + 7 + 9 + 6 + 7 + 4 + 9 + 9 + 4 = 70
  • Check Digit Status: ✅ Valid (70 % 10 == 0)

The Result: Since 70 is divisible by 10, this number is valid. If the sum was 71 or 69, we would know immediately that the number is wrong.

💻 Implementing Luhn in Swift

We can use Swift to handle this logic with just a few lines of code.

func isLuhnValid(_ input: String) -> Bool {
    // Turn the string into a list of numbers
    let digits = input.compactMap { char in char.wholeNumberValue }
    
    // A real card needs at least two digits
    if digits.count < 2 {
        return false
    }

    var totalSum = 0
    // We reverse the list to start from the right
    let reversedDigits = digits.reversed()
    
    for (index, digit) in reversedDigits.enumerated() {
        if index % 2 == 1 {
            // This is every second digit, so we double it
            let doubled = digit * 2
            // If the result is more than 9, we subtract 9 
            // This is the same as adding the two digits together
            totalSum += doubled > 9 ? doubled - 9 : doubled
        } else {
            // Keep the digit as it is
            totalSum += digit
        }
    }

    // If the total ends in zero, the number is valid
    return totalSum % 10 == 0
}

🤷‍♂️ Why Use This in Your Apps?

The biggest benefit of using this algorithm is the user experience. You can give your users instant feedback the moment they finish typing. This prevents your app from making unnecessary network requests to a payment provider when a number is clearly mistyped.

💳 Bonus: The Anatomy of a Card Number

There is a very strict pattern to credit card numbers. They aren’t just random digits; they follow a structural standard called ISO/IEC 7812.

A typical 16-digit card number is broken down into three main “zones”:

  1. Major Industry Identifier (MII): The very first digit.
    • 3 = Travel/Entertainment (Amex)
    • 4 = Visa
    • 5 = Mastercard
    • 6 = Discover/Merchandising

  2. Issuer Identification Number (IIN/BIN): The first 6 to 8 digits. This identifies the specific bank (e.g., Chase, Wells Fargo, or a bank in Indonesia like BCA).

  3. Account Identifier: The digits after the BIN, up until the very last digit. This is unique to you.

  4. The Check Digit (Luhn): The final 16th digit, which we discussed earlier.

💭 Final Thoughts

The Luhn Algorithm is a perfect example of how simple math can solve a big problem for developers. It makes our apps feel faster and more professional by catching errors before they reach our servers.

Because the Luhn algorithm only checks for “validity,” 1 out of every 10 random 16-digit numbers will technically pass the Luhn check.

For a card to be real, it must also:

  1. Belong to an active BIN.
  2. Be currently assigned to a human by that bank.
  3. Pass CVV and Expiry checks.

This tool is not meant for security. Its main job is to help your users find simple typing mistakes as they enter their data. It ensures that the number follows the basic rules of the card industry before you try to process a payment.