The Luhn algorithm, also known as the "modulus 10" algorithm, is a checksum formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, National Provider Identifier numbers in the United States, Canadian Social Insurance Numbers and Israel ID Numbers.

Algorithm:

Generating check digit:

• Lets assume you have a number as: 3 - 7 - 5 - 6 - 2 - 1 - 9 - 8 - 6 - 7 - X where X is the check digit.
• Now starting from the right most digit i.e. check digit, double the every second digit. New number will be: 3 - 14 - 5 - 12 - 2 - 2 - 9 - 16 - 6 - 14 - X
• Now if double of a digit is more then 9, add the digits. So the number will become: 3 - 5 - 5 - 3 - 2 - 2 - 9 - 7 - 6 - 5 - X
• Now add all digits. 47 + X
• Multiply the non-check part by 9. So it will be 47 * 9 = 423
• Unit digit in the multiplication result is the check digit. X = 3
• Valid number would be 37562198673.

Validating the generated number:

Python Script to validate credit card number:

"""
Python script to check validity of credit card numbers
Author : https://www.pythoncircle.Com
"""

import sys


def usage():
    msg = """
        
        usage:
        python3 credit_card_validator credit_card_number
        
        example:
        python3 credit_card_validator 34678253793
        
    """
    print(msg)


def get_cc_number():
    if len(sys.argv) < 2:
        usage()
        sys.exit(1)

    return sys.argv[1]


def sum_digits(digit):
    if digit < 10:
        return digit
    else:
        sum = (digit % 10) + (digit // 10)
        return sum


def validate(cc_num):
    # reverse the credit card number
    cc_num = cc_num[::-1]
    # convert to integer
    cc_num = [int(x) for x in cc_num]
    # double every second digit
    doubled_second_digit_list = list()
    digits = list(enumerate(cc_num, start=1))
    for index, digit in digits:
        if index % 2 == 0:
            doubled_second_digit_list.append(digit * 2)
        else:
            doubled_second_digit_list.append(digit)

    # add the digits if any number is more than 9
    doubled_second_digit_list = [sum_digits(x) for x in doubled_second_digit_list]
    # sum all digits
    sum_of_digits = sum(doubled_second_digit_list)
    # return True or False
    return sum_of_digits % 10 == 0
     


if __name__ == "__main__":
    print(validate(get_cc_number()))

Code is available on github.  

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