The Luhn algorithm, also known as the "modulus 10" or "mod 10" algorithm, is a simple checksum formula used to validate a variety of identification numbers, most notably credit card numbers. Developed by IBM scientist Hans Peter Luhn in the late 1950s, this algorithm is not intended to be a cryptographically secure hash function; rather, it's designed to protect against accidental errors, such as a mistyped digit. Its widespread adoption in credit card number validation is due to its efficiency in distinguishing valid numbers from mistyped or otherwise incorrect strings of digits.

The Luhn algorithm works as follows: First, the credit card number is reversed, and then every second digit, starting from the first, is doubled. If doubling a number results in a two-digit number, then the digits of this product are summed to get a single digit (alternatively, 9 can be subtracted from the product). Next, all the untouched digits and the doubled digits (after adjustment) are added together. The total sum obtained is then checked to see if it is a multiple of 10. If it is, the credit card number is considered valid according to the Luhn formula. This method effectively catches any single-digit error, as well as most of the common transposition errors, where two adjacent digits are switched.