The generation and composition of bank card numbers (such as credit or debit card numbers) usually follows the international standard ISO/IEC 7812, which mainly includes the following parts: 1. Major Industry Identifier (MII) and Issuer Identifier (IIN/BIN): • MII: The first digit of the bank card number, which is used to indicate the industry to which the card belongs. For example, 4 usually represents Visa cards, and 5 is more common in MasterCard. • IIN/BIN: Usually composed of the first 6 digits, it is used to identify the specific issuer. These 6 digits combine the MII and the following digits to clearly indicate which bank or financial institution issued the card. 2. Personal Account Identifier (Account Number): After the IIN, the next few digits (the length varies depending on the issuer) are used to uniquely identify the cardholder's account. For 16-digit card numbers, this part usually consists of digits 7 to 15; however, some card numbers may have different lengths (such as 13 or 19 digits). The overall purpose is to ensure the uniqueness of the account number. 3. Check Digit: The last digit of the card number is the check digit, which is used to verify the validity of the entire number. The check digit is usually calculated using the Luhn algorithm, which can detect common input errors. Let's take a fictitious 16-digit card number as an example to illustrate how to use the Luhn algorithm to calculate the check digit: Assume that the first 15 digits of the existing card number are: 4 5 3 9 8 7 6 5 4 3 2 1 0 9 8 The calculation steps are as follows: Step 1: From right to left (excluding the check digit), mark the position of each digit in turn. Usually, the rightmost digit (i.e., the 15th digit) is marked as position 1, the next digit is position 2, and so on. Note: In the Luhn algorithm, every other digit (i.e., all digits in even positions) is usually processed. Step 2: "Double" all digits in even positions (starting from the right): For example: The digit in position 2, the digit in position 4, the digit in position 6, and so on are doubled in sequence. If the doubled number is greater than 9, subtract 9 (which is equivalent to adding up all its digits). Assume that, counting from the right, the digits in the even positions are A, B, C, ..., and the values are obtained after doubling and adjusting; (When giving a practical demonstration here, we need to list the digits in each position one by one) Step 3: Add all the digits (the processed even position digits and the unchanged odd position digits) and record them as the sum S. Step 4: Calculate the check digit D so that S + D is a multiple of 10. In other words, D = (10 - (S mod 10)) mod 10. : (If S mod 10 is originally 0, the check digit is 0) Let's take a simple example (the numbers are for illustration only, the following process shows how to operate): Suppose the first 15 digits of the card number are: 4 5 3 9 8 7 6 5 4 3 2 1 0 9 8 We first give each digit and its position from right to left (position 1 is the rightmost): Position 1: 8 Position 2: 9 Position 3: 0 Position 4: 1 Position 5: 2 Position 6: 3 Position 7: 4 Position 8: 5 Position 9: 6 Position 10: 7 Position 11: 8 Position 12: 9 Position 13: 3 Position 14: 5 Position 15: 4 Next, process the digits in the even positions: Position 2: 9 → 9×2 = 18 → 18 is greater than 9, so 18 - 9 = 9 Position 4: 1 → 1×2 = 2 Position 6: 3 → 3×2 = 6 Position 8: 5 → 5×2 = 10 → 10 - 9 = 1 Position 10: 7 → 7×2 = 14 → 14 - 9 = 5 Position 12: 9 → 9×2 = 18 → 18 - 9 = 9 Position 14: 5 → 5×2 = 10 → 10 - 9 = 1 Then write out the digits in the odd positions as they were: Position 1: 8 Position 3: 0 Position 5: 2 Position 7: 4 Position 9: 6 Position 11: 8 Position 13: 3 Position 15: 4 Then sum: Sum of even positions: 9 + 2 + 6 + 1 + 5 + 9 + 1 = 33 Sum of odd positions: 8 + 0 + 2 + 4 + 6 + 8 + 3 + 4 = 35 Sum S = 33 + 35 = 68 Finally, find the check digit D so that 68 + D = 70 (that is, the next multiple of 10, 70): D = 70 - 68 = 2 Therefore, the entire card number is: 4 5 3 9 8 7 6 5 4 3 2 1 0 9 8 2 Please note: • The above example is only an academic demonstration. The actual card issuer will generate and manage the account number under strict security measures. • Different financial institutions may adjust the length of the card number and the length of the account number part according to their own rules. • Using the Luhn algorithm to calculate the check digit is a simple and commonly used method, but it is only used to check format errors and cannot prevent other security risks such as forgery. In short, the generation of bank card numbers follows international standards, and its components (card issuer identification, personal account code and check digit) ensure the uniqueness of the card number and the correctness of the input. This design not only facilitates data verification, but also provides a basis for internal management of various financial institutions.