1. Reverse the order of the card number's digits.

2. Double every second digit, starting from the first digit (which is now the second digit of the reversed number).

3. If any doubled value is greater than 9, subtract 9 from it (alternatively, add the digits together; e.g., 12 becomes 1 + 2 = 3).

4. Sum all the digits (including both doubled and undoubled digits).

5. Check if the sum is divisible by 10. If it is, the card number is valid.

Let’s check if the following card number is valid: 4539 1488 0343 6467

1. Reverse it: 7646 3430 8841 9354

2. Double every second digit: 7, 12, 4, 12, 6, 6, 3, 6, 8, 16, 4, 2, 9, 6, 5, 8

3. For doubled values greater than 9 (12, 12, 16), add their digits: 7, 3, 4, 3, 6, 6, 3, 6, 8, 7, 4, 2, 9, 6, 5, 8

4. Sum: 70

5. Since 70 is divisible by 10, the card number is valid.

Here's a simple Python code to check if a credit card number is valid using the Luhn algorithm:

def luhn_check(card_number):
    digits = [int(d) for d in str(card_number)][::-1]
    checksum = sum(digits[0::2]) + sum(sum(divmod(2 * d, 10)) for d in digits[1::2])
    return checksum % 10 == 0

# Example usage
card_number = "4539148803436467"
print("Valid" if luhn_check(card_number) else "Invalid")

Here is a C implementation of the algorithm:

#include <stdio.h>
#include <string.h>
#include <ctype.h>

// Function to validate a Visa card number using the Luhn Algorithm
int isValidVisaCard(const char* cardNumber) {
    int length = strlen(cardNumber);
    int sum = 0;
    int isSecond = 0;

    // Traverse the card number in reverse
    for (int i = length - 1; i >= 0; i--) {
        int digit = cardNumber[i] - '0';

        if (isSecond) {
            // Double every second digit
            digit *= 2;
            if (digit > 9) {
                // Subtract 9 if the doubled value is greater than 9
                digit -= 9;
            }
        }

        // Add digit to the sum
        sum += digit;
        // Toggle the isSecond flag
        isSecond = !isSecond;
    }

    // If the sum is divisible by 10, the card number is valid
    return (sum % 10 == 0);
}

int main() {
    char cardNumber[20];
    printf("Enter the Visa card number: ");
    scanf("%19s", cardNumber);

    if (isValidVisaCard(cardNumber)) {
        printf("The card number is valid.\n");
    } else {
        printf("The card number is invalid.\n");
    }

    return 0;
}

Based on the Luhn algorithm, this code will output whether the credit card number is valid or invalid.

Generating a valid credit card number involves adhering to the structure and validation checks used by credit card companies, primarily the Luhn algorithm. Here’s how to generate a valid credit card number (without real-world use, as actual issuance requires official channels).

1. Choose a Bank Identification Number (BIN): The first 6 digits of a credit card (the BIN) identify the issuing bank. For example:

1. VISA typically starts with 4.
2. MasterCard numbers often start with 51-55.

For this example, we’ll use a generic BIN: `4539 14` (representing a VISA card).

2. Generate Remaining Digits Except the Checksum: After the BIN, generate random digits for the rest of the card number, leaving the last digit blank for now. VISA and MasterCard usually have 16 digits, so we’ll generate 9 more digits.

3. Calculate the Checksum with the Luhn Algorithm:

1. Apply the Luhn algorithm to calculate the checksum digit (the last digit), which will make the number valid.

Here’s a Python code that generates a valid credit card number:

import random

def generate_credit_card():
    # Start with a sample BIN (6 digits)
    bin_number = [4, 5, 3, 9, 1, 4]  # Example BIN for VISA
    # Generate the next 9 random digits
    card_number = bin_number + [random.randint(0, 9) for _ in range(9)]
    
    # Calculate the Luhn checksum for the first 15 digits
    def luhn_checksum(card):
        digits = card[::-1]
        checksum = sum(digits[0::2]) + sum(sum(divmod(2 * d, 10)) for d in digits[1::2])
        return checksum % 10

    # Calculate the last digit to make the number valid
    check_digit = (10 - luhn_checksum(card_number)) % 10
    card_number.append(check_digit)

    return ''.join(map(str, card_number))

# Generate a valid credit card number
print(generate_credit_card())