(a) The definition of BankAccount in the code that follows uses the Luhn checksum method to validate the account number.

The account number may be provided as an integer or as a string (possibly with spaces or hyphens delimiting groups of numbers):

>>> from bank_account2 import BankAccount
>>> BankAccount('John Brown', 7298-904')
<bank_account2.BankAccount at 0x103fc1350>

>>> BankAccount('John Brown', 7298905)
...
ValueError: Invalid account number

(b) An interest-free overdraft is implemented in the CurrentAccount class below as well; a change has been made to the base class's BankAccount method to output negative balances cleanly.

>>> from bank_account2 import CurrentAccount

>>> account = CurrentAccount('John Brown', '729-8904', 0, 500)
>>> account.deposit(400)

>>> account.withdraw(350)

>>> account.check_balance()
The balance of account number 729-8904 is $50.00

>>> account.withdraw(200)

>>> account.check_balance()
The balance of account number 729-8904 is -$150.00

>>> account.withdraw(600)
$600.00 exceeds the single transaction limit of $500.00

>>> account.withdraw(500)

>>> account.check_balance()
The balance of account number 729-8904 is -$650.00

>>> account.withdraw(500)
Insufficient funds

The modified code is:

class BankAccount:
    """A abstract base class representing a bank account."""

    currency = "$"

    def __init__(self, customer, account_number, balance=0):
        """
        Initialize the BankAccount class with a customer, account number
        and opening balance (which defaults to 0.)

        """

        self.customer = customer
        self.set_account_number(account_number)
        self.balance = balance

    def set_account_number(self, account_number):
        if not self.verify_account_number(account_number):
            raise ValueError("Invalid account number")

        self.account_number = account_number

    def verify_account_number(self, account_number):
        """Verify the account number, returning True if it is valid."""

        ccl = [int(d) for d in str(account_number) if d not in ("-", " ")]
        for i in range(len(ccl) - 2, 0, -2):
            ccl[i] *= 2
            if ccl[i] > 9:
                ccl[i] = 1 + (ccl[i] - 10)
        checksum = sum(ccl) % 10
        return not checksum

    def deposit(self, amount):
        """Deposit amount into the bank account."""
        if amount > 0:
            self.balance += amount
        else:
            print("Invalid deposit amount:", amount)

    def withdraw(self, amount):
        """
        Withdraw amount from the bank account, ensuring there are sufficient
        funds.

        """
        if amount > 0:
            if amount > self.balance:
                print("Insufficient funds")
            else:
                self.balance -= amount
        else:
            print("Invalid withdrawal amount:", amount)

    def check_balance(self):
        """Print a statement of the account balance."""

        s_sign = "-" if self.balance < 0 else ""
        print(
            f"The balance of account number {self.account_number} is"
            f" {s_sign}{self.currency}{abs(self.balance):.2f}"
        )


class CurrentAccount(BankAccount):
    """A class representing a current (checking) account."""

    def __init__(
        self,
        customer,
        account_number,
        annual_fee,
        transaction_limit,
        balance=0,
        overdraft_limit=1000,
    ):
        """Initialize the current account."""

        self.annual_fee = annual_fee
        self.transaction_limit = transaction_limit
        self.overdraft_limit = overdraft_limit
        super().__init__(customer, account_number, balance)

    def withdraw(self, amount):
        """
        Withdraw amount if sufficient funds exist in the account and amount
        is less than the single transaction limit.

        """
        if amount <= 0:
            print("Invalid withdrawal amount:", amount)
            return

        if amount > self.balance + self.overdraft_limit:
            print("Insufficient funds")
            return

        if amount > self.transaction_limit:
            print(
                f"{self.currency}{amount:.2f} exceeds the single transaction"
                f" limit of {self.currency}{self.transaction_limit:.2f}"
            )
            return

        self.balance -= amount

    def apply_annual_fee(self):
        """Deduct the annual fee from the account balance."""

        self.balance = max(0.0, self.balance - self.annual_fee)