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Other, more complex check-digit algorithms (such as the Verhoeff algorithm and the Damm algorithm) can detect more transcription errors.

It will detect most of the possible twin errors (it will not detect 22 ↔ 55, 33 ↔ 66 or 44 ↔ 77). It will not, however, detect transposition of the two-digit sequence 09 to 90 (or vice versa). The Luhn algorithm will detect all single-digit errors, as well as almost all transpositions of adjacent digits.

The check digit is calculated by 10 − ( s mod ⁡ 10 ) ).

Sum the values of the resulting digits.

Moving left, double the value of every second digit (including the rightmost digit).

With the payload, start from the rightmost digit.

The check digit is most often the last digit. If the number already contains the check digit, drop that digit to form the 'payload'.Most credit cards and many government identification numbers use the algorithm as a simple method of distinguishing valid numbers from mistyped or otherwise incorrect numbers. It is not intended to be a cryptographically secure hash function it was designed to protect against accidental errors, not malicious attacks. The algorithm is in the public domain and is in wide use today. The Luhn algorithm or Luhn formula, also known as the ' modulus 10' or 'mod 10' algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple check digit formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, National Provider Identifier numbers in the United States, Canadian social insurance numbers, Israeli ID numbers, South African ID numbers, Swedish national identification numbers, Swedish Corporate Identity Numbers (OrgNr), Greek Social Security Numbers (ΑΜΚΑ), SIM card numbers, European patent application number and survey codes appearing on McDonald's, Taco Bell, and Tractor Supply Co.

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