The information provided below is for academic and knowledge popularization purposes only and should not be used for any illegal activities. Do not try to use these rules to generate numbers that can be used for fraud or cheating. Bank card (or credit card) numbers actually follow public structures and verification rules. Here is a brief introduction: ─────────────────────────────── 【1. Basic structure of card number】 Most bank card numbers (such as credit card numbers) usually consist of three parts: a. Issuing bank identification number (IIN or BIN): usually the first 6 digits, indicating the issuing institution. For example, Visa cards usually start with "4", and Mastercard often starts with "51~55" or "2221~2720". b. Personal account number part: This part of the digits varies depending on the product and is used to identify the card holder's account, usually several digits in the middle. c. Check digit: The last digit, calculated by the Luhn check algorithm, is used to prevent input errors. ──────────────────────────────── 【2. Introduction to Luhn checksum algorithm】 Luhn algorithm is a simple checksum algorithm. The steps are usually as follows (taking counting from right to left as an example): 1. Starting from the rightmost side, mark the position of each digit in turn. 2. For each even position (or odd position in some descriptions, depending on whether counting from left or right), multiply the number by 2. 3. If the product is greater than 9, subtract 9 (or add the digits of the product, that is, 12 → 1+2=3); 4. Sum all the processed digits and add the unprocessed digits. 5. If the sum is divisible by 10, the checksum passes. The last digit is the check digit selected to ensure this condition. For example: Suppose you have a card number with the first 15 digits as follows: 4 0 0 0 0 0 1 2 3 4 5 6 7 8 9 (here "400000" may be the BIN, "12345678" is part of the account identifier, which depends on the number of digits allocated by the specific issuing bank) You need to calculate the 16th digit (check digit), method: a. According to the Luhn algorithm, process each digit from the back to the front (different implementations may have slight differences, here only the general process is described). b. Get a sum S such that (S + check digit) mod 10 = 0. The check digit is 10 - (S mod 10). When S mod 10 is 0, the check digit is 0. ──────────────────────────────── 【3. Some well-known “test” number examples】 Special attention should be paid to the following sample numbers: The following sample numbers are only for public testing purposes or to demonstrate algorithms. They do not represent actual valid bank accounts and should not be used in real scenarios. For example, the following numbers are often used in the test environment of payment systems: • Visa test card number: 4111111111111111 • Mastercard test card number: 5105105105105100 • American Express test card number: 378282246310005 These numbers all meet the Luhn checksum and comply with the common number beginning rules of their respective issuers, but they are only valid in the sandbox (test) environment. ──────────────────────────────── 【4. How to “generate” a sample number】 Suppose we want to generate a 16-digit card number similar to Visa. The steps are as follows: ① Select BIN: For example, we select “400000” (Note: the real card issuing bank BIN is assigned by each bank, this example is only for demonstration) ② Generate the middle 9 digits (for a total of 15 digits, excluding the check digit), which can be generated randomly. For example, “123456789”. ③ Concatenate them to get a 15-digit number: 400000123456789 ④ Use the Luhn algorithm to calculate the last check digit. – Let’s take a simplified example (Note: the following calculation is only for demonstration and has not been strictly verified): a. Suppose that after processing 400000123456789 according to the Luhn rule, the check remainder obtained is 6 (that is, (S mod 10) = 4, then the check digit = 10 – 4 = 6). b. The final card number is: 4000001234567896 (During the actual calculation, please strictly follow the steps of the Luhn algorithm to calculate digit by digit to ensure that the check digit is correct.) ──────────────────────────────── 【5. Summary】 The generation rules of bank card numbers (or credit card numbers) mainly rely on: – Determine a legal BIN (prefix, representing the issuing institution) – Generate a personal digital sequence of a specified length – The last digit is determined by the Luhn check algorithm to ensure the correctness of the number The above are the basic principles and common examples of bank card number generation. Once again: This information is only for understanding and academic discussion, and any attempt to use these rules for illegal purposes is against the law.