I think the title says it all; I've seen many implementations for checking credit card numbers and in my opinion there is really only one that you need and actually works.

Sadly, still in use today by many code examples that I've run across is the good old

if ( first_digit = 4 ) then "visa"
elseif ( first_digit = 5 ) then "mastercard"
elseif ( first_digit = 3 ) then "amex"
elseif ( first_digit = 6 ) then "discover"
else
"invalid card"
end if

/facepalm

This isn't entirely bad ( yes it is, I'm just trying to be nice ), most likely those first digits will always be associated with the cards mentioned above, the problem is the numbers that follow.

"But I found one that checks and second and third numbers!"

Awesome, one tiny step closer to almost not really getting anywhere!

Obviously I'm leading up to the one and only Luhn algorithm which is basically a simple checksum formula used to validate a few different sequences of numbers, for example credit card account numbers.

Straight from Wikipedia here is what is going on with the algorithm

The formula verifies a number against its included check digit, which is usually appended to a partial account number to generate the full account number. This account number must pass the following test:

1. Counting from the check digit, which is the rightmost, and moving left, double the value of every second digit.
2. Sum the digits of the products together with the undoubled digits from the original number.
3. If the total ends in 0 (put another way, if the total modulo 10 is congruent to 0), then the number is valid according to the Luhn formula; else it is not valid.

As an illustration, if the account number is 49927398716, it will be validated as follows:

1. Double every second digit, from the rightmost: (1×2) = 2, (8×2) = 16, (3×2) = 6, (2×2) = 4, (9×2) = 18
2. Sum all the individual digits (digits in parentheses are the products from Step 1): 6 + (2) + 7 + (1+6) + 9 + (6) + 7 + (4) + 9 + (1+8) + 4 = 70
3. Take the sum modulo 10: 70 mod 10 = 0; the account number is valid.

Below is an ASP version I've ported, enjoy.

ACCOUNT = "4500000000000001"
alt = false
sum = 0

    for i = len( ACCOUNT ) to 1 step - 1
    
        digit = mid( ACCOUNT, i, 1 )
        
            if ( alt = true ) then
                digit = digit * 2

                    if ( digit > 9 ) then digit = digit - 9 end if
            end if

        sum = ( sum + digit ) mod 10                                
        
        if ( alt = true ) then alt = false else alt = true
    next


if ( sum = 0 ) then
  'legit
else
  'did not pass the test
end if