I just saw an article over at Mint that explains what each digit in a credit card is used for. It's a short read, but very well presented. Go read it now, then come back here.
So I got to thinking. The first 6 digits of my card are based on the type of card I have, and the entire lookup is available online. The last 4 digits are generally printed on credit card receipts. Now for most credit cards that have an 8 or 9 digit account number, this leaves 5 or 6 unknown digits. In the worst case that's a million possibilities. This isn't the worst case though, because we know the checksum, which is the last digit, and shows up on credit card receipts. Using the Luhn algorithm, we can reduce the search space by 90%. This leaves 100,000 possibilities for the unknown 6 digit number. If you have an 8 digit account number, then the space reduces to 10,000 possibilities.
It takes a computer very little time to generate that many numbers.
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