Luhn algorithm

The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, National Provider Identifier numbers in the US, Canadian Social Insurance Numbers, and Greek Social Security Numbers (ΑΜΚΑ). It was created by IBM scientist Hans Peter Luhn and described in U.S. Patent No. 2,950,048, filed on January 6, 1954, and granted on August 23, 1960.

The algorithm is in the public domain and is in wide use today. It is specified in ISO/IEC 7812-1. It is not intended to be a cryptographically secure hash function; it was designed to protect against accidental errors, not malicious attacks. 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.

The formula verifies a number against its included check digit, which is usually appended to a partial account number to generate the full account number. This number must pass the following test:

Assume an example of an account number "7992739871" that will have a check digit added, making it of the form 7992739871x:

The sum of all the digits in the third row is 67+x.

The check digit (x) is obtained by computing the sum of the non-check digits then computing 9 times that value modulo 10 (in equation form, (67 × 9 mod 10)). In algorithm form:

(Alternative method) The check digit (x) is obtained by computing the sum of the other digits (third row) then subtracting the units digit from 10 (67 => Units digit 7; 10 − 7 = check digit 3). In algorithm form:

...
Wikipedia