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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:

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.

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:

You can use tools available online to validate that the number generated is valid as per Luhn's algorithm or not. You can validate the number by visiting this site.

#### 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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