The information described below is for public, academic and educational purposes only and should not be used for illegal purposes. The composition and verification of credit card numbers are public information. The following are some basic principles to help understand its structure and verification logic. [1. Structure of credit card numbers] Credit card numbers are usually composed of the following parts: A. Major Industry Identifier (MII) The first digit indicates the industry to which the card number belongs. For example: • 1 and 2: Aviation/Transportation Industry • 3: Travel and Entertainment (such as American Express usually starts with 34 or 37) • 4 and 5: Banks and Financial Institutions (Visa usually starts with 4, MasterCard starts with 51-55) • 6: Mainly used for issuing to retailers and other financial institutions (such as Discover cards start with 6011, 65, etc.). B. Issuer Identification Number (IIN, also known as BIN) Usually the first 6 digits, this part identifies the issuing institution and the type of card. Different banks or card brands have unique number segments. C. Personal account number identification Starting from the 7th digit to the second to last digit (the specific length depends on the card format), this part is usually allocated by the issuing bank to the customer to identify the cardholder's account. D. Check digit The last digit (the 16th or 15th digit, depending on the length of the card number) is used to check whether the entire number conforms to specific rules. It is mainly calculated using the Luhn algorithm. [2. Check digit generation (Luhn algorithm)] The Luhn algorithm is a simple check algorithm used to detect spelling or input errors in numbers. The main steps are as follows: (1) Starting from the rightmost digit of the number (the digit to the left of the check digit), process every other digit in turn. For example: If the number is D₁ D₂ … Dₙ, where Dₙ is the check digit, then starting from Dₙ₋₁, multiply every other digit by 2. Note: If the product is greater than 9, add the digits in the product (equivalent to subtracting 9). (2) Add all unprocessed digits to the processed digit. Take the sum S as an example. If S modulo 10 is 0, the number is valid; otherwise, the check digit should be equal to (10 - (S mod 10)). [3. Example] Take a (fictitious, for illustration purposes only) Visa card number as an example. Visa cards usually have 16 digits and start with 4. Assume that some of the digits are distributed as follows: The first 15 digits are known to be: 4 12345 67890123 = 4 | 12345 | 67890123 (This is just an example. The actual number is generated by the issuing bank). Steps to calculate the check digit (assuming that the digits are numbered from 1 to 15 from left to right): 1. Starting from the right, double the digits before the 15th digit (the last digit of the number, not yet determined) (starting from the second to last digit, every other digit). 2. For example, suppose the second to last digit, fourth digit, etc. are doubled and then corrected according to the rules (for numbers greater than 9, subtract 9 or directly add the digits). 3. Sum all the digits and let the total be S. 4. Check digit calculation: Let check digit = (10 - (S mod 10)) mod 10. For example, suppose a certain number (not representing real data): Preliminary number (15 digits): 4 5678 1234 5678 912 After processing, S = 67 (for example), then the check digit should be (10 - (67 mod 10)) mod 10 = (10 - 7) mod 10 = 3. The final complete number is: 4 5678 1234 5678 912 3 Note: The above numbers are only examples. The actual card number is generated by the issuing institution according to its own rules. 【4. Summary】 • Credit card numbers are composed of MII, IIN (BIN), cardholder account number and check digit. • Check digits are usually calculated using the Luhn algorithm to help detect input errors or spelling errors. • Understanding these principles can help understand the design of credit card numbers, but any attempt to illegally generate or defraud based on these principles is illegal. I hope this information can help you understand the basic structure and check mechanism of credit card numbers. If you have other questions, please feel free to ask!