# Luhn Algorithm

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## Definition of 'Luhn Algorithm'

The Luhn algorithm, also known as the "mod 10" or "checksum" algorithm, is a simple check digit formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, and National Insurance Numbers. The algorithm is named after its inventor, Hans Peter Luhn, a German-American mathematician who worked for IBM.

The Luhn algorithm works by adding the digits of a number, starting with the rightmost digit, and then doubling the value of every second digit from the right. If the resulting number is divisible by 10, then the number is valid. If not, then the number is invalid.

For example, let's take the credit card number 4111111111111111. We start by adding the digits of the rightmost number, which is 1. We then double the value of the next digit, which is 1. This gives us 1 + 2 = 3. We then add the digits of the next number, which is 1. This gives us 3 + 1 = 4. We then double the value of the next digit, which is 1. This gives us 4 + 2 = 6. We then add the digits of the next number, which is 1. This gives us 6 + 1 = 7. We then double the value of the next digit, which is 1. This gives us 7 + 2 = 9. We then add the digits of the next number, which is 1. This gives us 9 + 1 = 10. We then divide the resulting number by 10, which gives us 10 / 10 = 1. Since 1 is divisible by 10, the credit card number is valid.

The Luhn algorithm is a simple but effective way to validate identification numbers. It is not foolproof, however, and there are ways to create invalid numbers that will still pass the Luhn algorithm. For this reason, the Luhn algorithm is often used in conjunction with other security measures, such as cardholder verification values (CVVs) and personal identification numbers (PINs).

The Luhn algorithm works by adding the digits of a number, starting with the rightmost digit, and then doubling the value of every second digit from the right. If the resulting number is divisible by 10, then the number is valid. If not, then the number is invalid.

For example, let's take the credit card number 4111111111111111. We start by adding the digits of the rightmost number, which is 1. We then double the value of the next digit, which is 1. This gives us 1 + 2 = 3. We then add the digits of the next number, which is 1. This gives us 3 + 1 = 4. We then double the value of the next digit, which is 1. This gives us 4 + 2 = 6. We then add the digits of the next number, which is 1. This gives us 6 + 1 = 7. We then double the value of the next digit, which is 1. This gives us 7 + 2 = 9. We then add the digits of the next number, which is 1. This gives us 9 + 1 = 10. We then divide the resulting number by 10, which gives us 10 / 10 = 1. Since 1 is divisible by 10, the credit card number is valid.

The Luhn algorithm is a simple but effective way to validate identification numbers. It is not foolproof, however, and there are ways to create invalid numbers that will still pass the Luhn algorithm. For this reason, the Luhn algorithm is often used in conjunction with other security measures, such as cardholder verification values (CVVs) and personal identification numbers (PINs).

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