Luhn algorithm: Difference between revisions

Revision as of 16:17, 26 September 2023

Revision as of 16:18, 26 September 2023

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# With the payload, start from the rightmost digit. Moving left, double the value of every second digit (including the rightmost digit).

# Sum the values of the resulting digits.

# The check digit is calculated by <math>(10 - (s \operatorname{mod} 10)) \operatorname{mod} 10</math>, where s is the sum from step 3. This is the leastsmallest number (possibly zero) that must be added to <math>s</math> to make a multiple of 10. Other valid formulas giving the same value are <math>9 - ((s + 9)\operatorname{mod} 10)</math>, <math>(10 - s)\operatorname{mod} 10</math>, and <math>10\lceil s/10\rceil - s</math>. Note that the formula <math>(10 - s)\operatorname{mod} 10</math> will not work in all environments due to differences in how negative numbers are handled by the [[modulo]] operation.

=== Example for computing check digit ===