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The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple check digit formula used to validate a variety of identification numbers.
The last digit is the check digit "7", and if the other numbers are correct then the check digit calculation must produce 7. Add the odd number digits: 0+6+0+2+1+5 = 14. Multiply the result by 3: 14 × 3 = 42. Add the even number digits: 3+0+0+4+4 = 11. Add the two results together: 42 + 11 = 53. To calculate the check digit, take the remainder ...
The Luhn mod N algorithm generates a check digit (more precisely, a check character) within the same range of valid characters as the input string. For example, if the algorithm is applied to a string of lower-case letters (a to z), the check character will also be a lower-case letter.
For every digit, multiply it by its weight factor and take their modulus 10 (modulus is the Remainder of the integer division. The modulus X of a baseX number is its rightmost digit). Sum all of the calculated products, and take modulus 10 again. Subtract the sum to 10, take modulus 10, and you have the resulting control digit. So, as an example:
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
The 9th digit is an automatically generated check digit using the "Modulus 10 Double Add Double" technique based on the Luhn algorithm. [12] To calculate the check digit every second digit is multiplied by two. Letters are converted to numbers based on their ordinal position in the alphabet, starting with A equal to 10.
Consider b = 5 × 10 76 and e = 17, both of which are perfectly reasonable values. In this example, b is 77 digits in length and e is 2 digits in length, but the value b e is 1,304 decimal digits in length. Such calculations are possible on modern computers, but the sheer magnitude of such numbers causes the speed of calculations to slow ...
The algorithm to create the check digit the same algorithm, with an extra step at the end. Put 0 in as a temporary placeholder for the check digit, then calculate the sum (as explained in the article). Calculate the sum modulus 10. If the result is 0, then you're done - the check digit is zero. Otherwise, the check digit is 10 - (sum modulus 10).