All mainstream credit card numbers obey a mathematical trick designed to catch the most common typos. It’s called the Luhn ...

Credit card issuers first assign the account numbers and then compute steps one through three of the Luhn algorithm to determine the appropriate check digit.

Check digits aren’t infallible – some algorithms can’t tell the difference between sequences like 1 and 00001, for example; others will catch incorrect digits, but miss swapped pairs.

The Luhn algorithm uses modulo-10 mathematics. To calculate the check digit, multiply every even-position digit (when counted from the right) in the number by two.