The Luhn Algorithm (also known as the modulus 10 or mod 10 algorithm) is a simple checksum formula used to validate various identification numbers, such as:
- Credit card numbers
- Debit card numbers
- IMEI (International Mobile Equipment Identity) numbers
- National Provider Identifier numbers (in healthcare)
The Luhn algorithm is used to verify the accuracy of identification numbers and detect simple errors like mistyped or incorrect digits.
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Reverse the Number
Start from the rightmost digit of the number and reverse the order of the digits. -
Double Every Second Digit
Starting with the second digit from the right, double every second digit. If doubling a digit results in a number greater than 9, subtract 9 from the result. -
Sum the Digits
Add all the digits together (both the doubled and the undoubled ones). -
Check the Sum
If the total sum is a multiple of 10 (i.e., the remainder when divided by 10 is zero), the number is valid.
Let’s validate the number 4539 1488 0343 6467.
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Reverse the Number
7 6 4 6 3 4 3 0 8 8 4 1 9 5 3 4 -
Double Every Second Digit
Starting with the second digit from the right:7, 12, 4, 12, 3, 8, 3, 0, 16, 8, 8, 1, 18, 5, 6, 4
For numbers greater than 9 (e.g., 12, 16, 18), subtract 9:
7, 3, 4, 3, 3, 8, 3, 0, 7, 8, 8, 1, 9, 5, 6, 4
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Sum the Digits
Add all the digits together:7 + 3 + 4 + 3 + 3 + 8 + 3 + 0 + 7 + 8 + 8 + 1 + 9 + 5 + 6 + 4 = 79
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Check the Sum
Since 79 is not a multiple of 10, the number is invalid.
- Validating credit/debit card numbers during online transactions.
- Checking the validity of identification numbers without requiring a database lookup.
- Detecting accidental errors in typed numbers.
- The Luhn algorithm is not cryptographically secure and is only suitable for detecting errors, not for preventing fraud.
- It cannot detect all types of errors, such as transposition of two adjacent digits.
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