The Luhn algorithm, also known as the Luhn Mod 10 algorithm or simply "Mod 10", is a straightforward public domain formula used to validate various identification numbers, including credit card numbers. While this algorithm can catch most errors in card data entry, it is not infallible.

Payment card issuers use the Luhn algorithm to generate valid numbers. Consequently, Authorize.net uses the same algorithm to validate the numbers when they are submitted to our systems. However, it's important to note that this algorithm only verifies the validity of the card numbers. It does not confirm whether the card numbers were issued by a legitimate card issuer, nor does it verify if the card numbers are currently linked to active accounts.

Therefore, it is possible for a card number to be accepted by Authorize.net but subsequently rejected by a payment processor when an attempt is made to process a transaction against that card.

Additionally, since the Luhn algorithm is publicly available, it is possible to generate numbers that resemble card numbers and pass the Luhn algorithm checks. This could potentially be exploited to find valid and active card numbers for fraudulent or malicious purposes. The Payment Card Industry has taken measures to mitigate this risk. However, it's crucial to understand that merchants should use the Luhn algorithm in conjunction with other methods to help reduce credit card fraud. These methods include, but are not limited to, using the Address Verification Service (AVS) and the Advanced Fraud Detection Suite (AFDS).

Developers interested in incorporating the Luhn algorithm into their website's scripting can find numerous online resources explaining its implementation. For a comprehensive description of the basic algorithm, you can visit Luhn Algorithm for more information.