Luhn Algorithm Validator

Luhn Algorithm (Mod 10)

The Luhn algorithm is a simple checksum formula used to validate identification numbers. It was created in 1954 by Hans Peter Luhn, a German-American computer scientist at IBM.

The algorithm is used to validate:

• Credit and debit card numbers (Visa, Mastercard, American Express, Discover)
• IMEI (International Mobile Equipment Identity) numbers, which identify mobile phones
• National identification numbers in some countries
• Canadian Social Insurance Numbers

How it works (step by step):

Starting from the rightmost digit (the check digit) and moving left:

1. Leave every second digit unchanged (positions 1, 3, 5… from the right)
2. Double every other digit (positions 2, 4, 6… from the right)
3. If doubling produces a number > 9, subtract 9 from it
4. Sum all digits
5. If the total sum mod 10 = 0, the number is valid

Worked example, card number 4532015112830366:

Position (from right): 1→6, 2→6×2=12→3, 3→3, 4→0×2=0, 5→3, 6→8×2=16→7, 7→2, 8→1×2=2, 9→1, 10→5×2=10→1, 11→1, 12→0×2=0, 13→2, 14→3×2=6, 15→5, 16→4×2=8

Sum = 6+3+3+0+3+7+2+2+1+1+1+0+2+6+5+8 = 50. 50 mod 10 = 0 → Valid!

Card type detection by prefix:

Read those as numeric ranges, not text prefixes, because the difference bites. Mastercard’s second block is 2221 to 2720, so 2200 is not a Mastercard even though it starts with 22. Discover’s is 622126 to 622925, so 622100 is not a Discover even though it starts with 6221. Plenty of validators get this wrong by treating the range as a string match, and the result is a card that gets labelled as the wrong network.

Important: The Luhn algorithm detects accidental errors, not deliberate fraud. A number passing the Luhn check does not mean it is a real, active account number.