Credit card numbers valid or invalid?

Credit card numbers valid or invalid?

Have you ever wondered if those numbers on the fake plastic or cardboard credit cards that come with the “preapproved” offers are real or imaginary? If they are not valid, how do you know it?…Just apply the Luhn check and all the those fake credit cards will invariably fail.Here is an example of a VISA credit card (look at the expiry date - 01/09 ..it’s still valid ! )

Note that the credit card number starts with “4″…so it is indeed a VISA issued credit card (VISA cards start with “4″ and MasterCard/Maestro cards start with “5″). Now, let us apply the Luhn algorithm to this card. To make it easier on you guys, I have created a schematic of the steps towards the Luhn check (below) for this card number 4552 7204 1234 5678:

In this case, when we sum up the total, it comes to 61 which is not perfectly divisible by 10, and hence this credit card number is invalid.
If such a credit card number is ever generated, the value of the check digit would be adjusted in such a way as to satisfy the Luhn condition. In this case, the only value of the check digit, that will create a valid credit card number, is 7. Choosing 7 as the check digit will bring the total to 60 (which is perfectly divisible by 10) and the Luhn condition will be satisfied. So the valid credit card number will be 4552 7204 1234 5677

The total comes to 65 which is not perfectly divisible by 10. Hence this credit card number is invalid.
In this case, a valid credit card number will result only if the check digit is 8. This will bring the total to 70 which is perfectly divisible by 10. So the valid credit card number will be 5490 1234 5678 9128.
Closing remarks
If I still have your attention, here are some additional thoughts. In the context of this post, by the term “valid”, I mean “mathematically valid”. A mathematically valid credit card does not mean a “working” credit card. The Luhn formula validates only the credit card number; it does not validate the expiry date and/or card security code (CVV, CVC). Plus, as discussed before, the 9 digit account number will yield 1 billion combinations; so the chances of getting a working credit card number are very remote. It should also be noted that, this validation is usually employed at the transaction end; which means that numbers that do not satisfy the Luhn check are not forwarded to the card issuer and the transaction is terminated. If you have a fake credit card which satisfies the Luhn check, it will go through at the transaction end, but the card issuer will most likely catch the mischief. So don’t go about trying to use these numbers to buy stuff.