Luhn Algorithm
The numbers of all credit and debit cards must comply to a complex formula called the Luhn algorithm. The process here that offers you the ability to check the validity of any kind of credit card is a simple implementation of this algorithm. For any request, or in any case of difficulty, please feel free to contact the webmaster.
Security
This checking process is completely safe. You enter only the credit card numbers but absolutely not any personal information such as Name, Expiring Date, and the most critical the CVV (Card Verification Value) which is usually at the back (except for Amex cards). This sequence of digits alone is useless and cannot serve any fraudulous goal.
Furthermore, no data is stored on the server and all the computations are done on the fly.
The secrets of the credit card numbers
Each number position has a special purpose among defining the type of issuer (IIN), the account number, a check-sum digit, etc... The following link specifies all group of digits and their purpose: Cracking the credit card digits
Usefull links
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Luhn Algorithm 
8 safety tips for you credit card 