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The Luhn algorithm ("modulus 10" or "mod 10" algorithm, Luhn formula) is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers (PAN) or IMEI numbers. The algorithm is specified in ISO/IEC 7812-1 and it was designed to protect against accidental errors. The Luhn algorithm will detect any single-digit error, as well as almost all transpositions of adjacent digits. It will not, however, detect transposition of the two-digit sequence 09 to 90 (or vice versa).

• From the rightmost digit, which is the check digit, moving left, double the value of every second digit;
• If the product of this doubling operation is greater than 9, then sum the digits of the products or alternatively subtract 9 from the product.
• Take the sum of all the digits.
• Multiply by 9.
• The last digit is the check digit.
Initial PAN
 PAN 3 7 1 4 4 9 6 3 5 3 9 8 4 3 X
Step 1 - double the values
 Double values 3 14 1 8 4 18 6 6 5 6 9 16 4 6 X
Step2 - sum the digits
 Sum digits 3 5 1 8 4 9 6 6 5 6 9 7 4 6 X
Step3 - sum all digits
3 + 5 + 1 + 8 + 4 + 9 + 6 + 6 + 5 + 6 + 9 + 7 + 4 + 6 = 79
79 x 9 = 711
Result
The check digit is 1.