A short tutorial here on credit card numbers:

I liked the checksum explanation:

*Checksum*

*The final digit of your credit card number is a check digit, akin to a checksum. The LUHN Formula, known also as a Mod 10 calculation, can be used to validate account numbers. The following steps are required to validate the primary account number.*

*Step 1: Double the value of alternate digits of the credit card number beginning with the second digit from the right (the first right-hand digit is the check digit).*

*Step 2: Add the individual digits comprising the products obtained in Step 1 to each of the unaffected digits in the original number.*

*Step 3: The total obtained in Step 2 must be a number ending in zero (30, 40, 50, etc.) for the account number to be validated.*

*The LUHN formula was designed to protect against accidental errors, not malicious attacks. Most credit cards and many government identification numbers use the algorithm as a simple method of distinguishing valid numbers from random digits. The LUHN algorithm will detect almost any single-digit error.*