A Luhn check test recalculates the final digit of a number sequence and compares the result with the digit already written there. If the two match, the number passes. It is a math checksum rather than a database lookup, so a passing result means the digits are formatted correctly and nothing more. It does not confirm that a card exists, is active, has funds, or belongs to any particular person.

How the Luhn algorithm works

The Luhn algorithm is also called the modulus 10 or mod 10 algorithm. IBM researcher Hans Peter Luhn developed it in the 1950s, and it was later adopted as a standard check digit method for identification numbers. The procedure is short enough to run by hand.

1. Write the digits in order and find the rightmost digit. That is the check digit.
2. Moving right to left, double every second digit, starting with the digit immediately left of the check digit.
3. If a doubled value is 10 or higher, subtract 9 from it. This is the same as adding the two digits of the product together.
4. Add the check digit and all the transformed digits together.
5. If the total is a multiple of 10, the number passes. If not, it fails.

A worked example

Consider the sequence 79927398713. From the right, the check digit is 3 and does not get doubled. The digits doubled are the second 9, the 2, the 3, the 8, and the 1.

• Doubled values: the second 9 becomes 18, the 2 becomes 4, the 3 becomes 6, the 8 becomes 16, and the 1 becomes 2.
• Reduce anything above 9 by subtracting 9: 18 becomes 9 and 16 becomes 7.
• Transformed sequence, left to right: 7, 9, 9, 4, 7, 6, 9, 7, 7, 2, 3.
• Sum: 70. Because 70 divides evenly by 10, the sequence passes the Luhn check test.

Change any single digit in that sequence and the total will no longer be a multiple of 10. That sensitivity is the point of the method.

What a Luhn check test proves and what it does not

It can tell you

• Whether a string of digits is internally consistent.
• Whether a single mistyped digit or a swapped pair was likely entered.
• Whether the length and format match a numbering scheme that uses check digits.

It cannot tell you

• Whether the number is assigned to a real account.
• Whether an account is open, closed, frozen, or funded.
• Whether the number is authorized for any transaction.

Where check digit validation shows up

The method is used in many numbering systems, not just payments. Common examples include payment card numbers, IMEI numbers on mobile devices, Canadian Social Insurance Numbers, National Provider Identifiers in US healthcare, some gift and loyalty card numbers, and internal account numbering schemes at banks and utilities. In each case the check digit guards against clerical errors during data entry, not against fraud.

Running a test on numbers you control

You can validate any number you own with a spreadsheet formula, a short script, or an online validator. The five steps above translate directly into a loop: walk the digits from right to left, double every second one, subtract 9 when needed, and check the total. When you build a test set, use synthetic values rather than real account numbers so that nothing sensitive ends up in logs, screenshots, or shared files.

Legal boundaries around card numbers

Only run a Luhn check test on numbers you own or on clearly synthetic test data. Handling payment card numbers that belong to other people is regulated. PCI DSS requires organizations to protect stored account data, including primary account numbers, and in the United States, producing, selling, or using payment card numbers without authorization is a federal crime. A passing checksum has no bearing on whether a number may lawfully be used, and a format check is never a substitute for authorization.