Editing Luhn algorithm (section)

==Strengths and weaknesses==
The Luhn algorithm will detect all single-digit errors, 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). It will detect most of the possible twin errors (it will not detect ''22'' ↔ ''55'', ''33'' ↔ ''66'' or ''44'' ↔ ''77'').

Other, more complex check-digit algorithms (such as the [[Verhoeff algorithm]] and the [[Damm algorithm]]) can detect more transcription errors. The [[Luhn mod N algorithm]] is an extension that supports non-numerical strings.

Because the algorithm operates on the digits in a right-to-left manner and zero digits affect the result only if they cause shift in position, zero-padding the beginning of a string of numbers does not affect the calculation.  Therefore, systems that pad to a specific number of digits (by converting 1234 to 0001234 for instance) can perform Luhn validation before or after the padding and achieve the same result.

The algorithm appeared in a United States Patent<ref name="US2950048A" /> for a simple, hand-held, mechanical device for computing the checksum. The device took the mod 10 sum by mechanical means. The ''substitution digits'', that is, the results of the double and reduce procedure, were not produced mechanically. Rather, the digits were marked in their permuted order on the body of the machine.