Luhn

The Luhn algorithm, also known as the Luhn check or LUHN formula, is a simple checksum used to validate identification numbers such as credit card numbers and IMEI identifiers. It was developed by IBM scientist Hans Peter Luhn in 1954 and has since become a widely adopted method for detecting basic input errors in numeric identifiers.

The validation process proceeds as follows: take the number as written, and starting from the rightmost digit, move left and double every second digit. If doubling yields a number greater than 9, subtract 9 from it (equivalently, sum the digits of the doubled value). Sum all the resulting digits, including the digits that were not doubled. If the total is a multiple of 10, the number passes the Luhn check; otherwise, it fails.

Applications and limitations: The Luhn check is widely used to validate credit card numbers and is also employed for other identifiers such as IMEI numbers and some national IDs. It is effective at catching many common input errors, such as single-digit mistakes and many adjacent transpositions. However, it is not a secure or cryptographic method and does not protect against fraud or tampering. Numbers can be constructed to pass the check, so the algorithm should be viewed as a practical error-detection tool rather than a security feature.