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The check digit is calculated by (()), where s is the sum from step 3. This is the smallest number (possibly zero) that must be added to s {\displaystyle s} to make a multiple of 10. Other valid formulas giving the same value are 9 − ( ( s + 9 ) mod 1 0 ) {\displaystyle 9-((s+9){\bmod {1}}0)} , ( 10 − s ) mod 1 0 {\displaystyle (10-s){\bmod ...
A range check is a check to make sure a number is within a certain range; for example, to ensure that a value about to be assigned to a 16-bit integer is within the capacity of a 16-bit integer (i.e. checking against wrap-around).
For instance, the UPC-A barcode for a box of tissues is "036000241457". 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.
The smallest example is n = 561 = 3·11·17, for which a 560 is 1 (modulo 561) for all a coprime to 561. Nevertheless, the Fermat test is often used if a rapid screening of numbers is needed, for instance in the key generation phase of the RSA public key cryptographic algorithm.
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This template will not recognize formatted numbers, which is by design since formatted numbers will break expression parsers. To remove the formatting from a number, you can wrap the number first in {{formatnum: number |R}} .
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