PSET 1 Credit AMEX

Question

I've calculated the Luhn's algorithm for all the credit cards and it works fine. The only issue I have is that the American Express cards which are tested don't fulfill the Luhn's algorithm!

This is the Luhn's algorithm as described in the PSET:

1. Multiply every other digit by 2, starting with the number’s second-to-last digit

2. Then add those products’ digits together.

3. Add the sum to the sum of the digits that weren’t multiplied by 2.

4.If the total’s last digit is 0 (or, put more formally, if the total modulo 10 is congruent to 0), the number is valid!

Check it for yourself:

American Express 378282246310005

1. 6 + 16 + 16 + 4 + 12 + 2 + 0 + 10
2. 6 + 1 + 6 + 1 + 6 + 4 + 1 + 2 + 2 + 0 + 1 + 0 = 30
3. 7 + 2 + 2 + 4 + 3 + 0 + 0 = 18
4. results in checksum: 30 + 18 = 48 !!

American Express 371449635398431 ->

1. 6 + 2 + 8 + 12 + 10 + 18 + 8 + 2

2. 6 + 2 + 8 + 1 + 2 + 1 + 0 + 1 + 8 + 8 + 2 = 39

3. 7 + 4 + 9 + 3 + 3 + 8 + 3 = 37

4. results in checksum: 39 + 37 = 76 !!

Both don't fulfill the Luhn's Algorithm. Yet they are valid AMEX for testing (https://developer.paypal.com/docs/payflow/payflow-pro/payflow-pro-testing/#testing-guidelines)

Has anyone else encountered this issue?

Answer 1

Your calculation must start at the second-to-last digit. The arithmetic you have displayed, starts at the last digit.

From the first example: 378282246310005,

• the second-to-last digit is 0,

• step 1 6 + 16 + 16 + 4 + 12 + 2 + 0 + 10 should end with a + 0 (not + 10)