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"""

Functions for testing the validity of credit card numbers.

https://en.wikipedia.org/wiki/Luhn_algorithm

"""

def validate_initial_digits(credit_card_number: str) -> bool:

"""

Function to validate initial digits of a given credit card number.

>>> valid = "4111111111111111 41111111111111 34 35 37 412345 523456 634567"

>>> all(validate_initial_digits(cc) for cc in valid.split())

True

>>> invalid = "14 25 76 32323 36111111111111"

>>> all(validate_initial_digits(cc) is False for cc in invalid.split())

True

"""

return credit_card_number.startswith(("34", "35", "37", "4", "5", "6"))

def luhn_validation(credit_card_number: str) -> bool:

"""

Function to luhn algorithm validation for a given credit card number.

>>> luhn_validation('4111111111111111')

True

>>> luhn_validation('36111111111111')

True

>>> luhn_validation('41111111111111')

False

"""

cc_number = credit_card_number

total = 0

half_len = len(cc_number) - 2

for i in range(half_len, -1, -2):

# double the value of every second digit

digit = int(cc_number[i])

digit *= 2

# If doubling of a number results in a two digit number

# i.e greater than 9(e.g., 6 × 2 = 12),

# then add the digits of the product (e.g., 12: 1 + 2 = 3, 15: 1 + 5 = 6),

# to get a single digit number.

if digit > 9:

digit %= 10

digit += 1

cc_number = cc_number[:i] + str(digit) + cc_number[i + 1 :]

total += digit

# Sum up the remaining digits

for i in range(len(cc_number) - 1, -1, -2):

total += int(cc_number[i])

return total % 10 == 0

def validate_credit_card_number(credit_card_number: str) -> bool:

"""

Function to validate the given credit card number.

>>> validate_credit_card_number('4111111111111111')

4111111111111111 is a valid credit card number.

True

>>> validate_credit_card_number('helloworld$')

helloworld$ is an invalid credit card number because it has nonnumerical characters.

False

>>> validate_credit_card_number('32323')

32323 is an invalid credit card number because of its length.

False

>>> validate_credit_card_number('32323323233232332323')

32323323233232332323 is an invalid credit card number because of its length.

False

>>> validate_credit_card_number('36111111111111')

36111111111111 is an invalid credit card number because of its first two digits.

False

>>> validate_credit_card_number('41111111111111')

41111111111111 is an invalid credit card number because it fails the Luhn check.

False

"""

error_message = f"{credit_card_number} is an invalid credit card number because"

if not credit_card_number.isdigit():

print(f"{error_message} it has nonnumerical characters.")

return False

if not 13 <= len(credit_card_number) <= 16:

print(f"{error_message} of its length.")

return False

if not validate_initial_digits(credit_card_number):

print(f"{error_message} of its first two digits.")

return False

if not luhn_validation(credit_card_number):

print(f"{error_message} it fails the Luhn check.")

return False

print(f"{credit_card_number} is a valid credit card number.")

return True

if __name__ == "__main__":

import doctest

doctest.testmod()

validate_credit_card_number("4111111111111111")

validate_credit_card_number("32323")

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