Introduction

This is not an essay on credit cards per se. If that's what you're looking for, I recommend Joe Ziegler's excellent series Everything You Ever Wanted to Know about Credit Cards. This essay has a narrower focus -- to explore the anatomy of your credit card number, and to provide Java source code which determines if a given credit card number might be valid.

Specifications for credit card numbering have been drawn up by the International Standards Organization (ISO/IEC 7812-1:1993) and the American National Standards Institute (ANSI X4.13). These eminent organizations refuse to make their publications freely available on-line, and so the following information on the format of credit card numbers comes largely from an Internet Engineering Task Force (IETF) draft by Donald E. Eastlake 3rd, "ISO 7812/7816 Numbers and the Domain Name System (DNS)" (draft-eastlake-card-map-08, expires August 2001), available at the time of this writing at http://www.globecom.net/ietf/draft/draft-eastlake-card-map-08.html. I have not linked to this URL, because individual versions of IETF drafts are notoriously ephemeral.

Digit numbering in this essay is left to right. The "first" digit, therefore, means the leftmost digit.

Major Industry Identifier

The first digit of your credit card number is the Major Industry Identifier (MII), which represents the category of entity which issued your credit card. Different MII digits represent the following issuer categories:

MII Digit Value	Issuer Category
0	ISO/TC 68 and other industry assignments
1	Airlines
2	Airlines and other industry assignments
3	Travel and entertainment
4	Banking and financial
5	Banking and financial
6	Merchandizing and banking
7	Petroleum
8	Telecommunications and other industry assignments
9	National assignment

For example, American Express, Diner's Club, and Carte Blanche are in the travel and entertainment category, VISA, MasterCard, and Discover are in the banking and financial category, and SUN Oil and Exxon are in the petroleum category.

Issuer Identifier

The first 6 digits of your credit card number (including the initial MII digit) form the issuer identifier. This means that the total number of possible issuers is a million (10 raised to the sixth power, or 1,000,000).

Some of the better known issuer identifiers are listed in the following table:

Issuer	Identifier	Card Number Length
Diner's Club/Carte Blanche	300xxx-305xxx, 36xxxx, 38xxxx	14
American Express	34xxxx, 37xxxx	15
VISA	4xxxxx	13, 16
MasterCard	51xxxx-55xxxx	16
Discover	6011xx	16

If the MII digit is 9, then the next three digits of the issuer identifier are the 3-digit country codes defined in ISO 3166, and the remaining final two digits of the issuer identifier can be defined by the national standards body of the specified country in whatever way it wishes.

Account Number

Digits 7 to (n - 1) of your credit card number are your individual account identifier. The maximum length of a credit card number is 19 digits. Since the initial 6 digits of a credit card number are the issuer identifier, and the final digit is the check digit, this means that the maximum length of the account number field is 19 - 7, or 12 digits. Each issuer therefore has a trillion (10 raised to the 12th power, or 1,000,000,000,000) possible account numbers.

If we consider the large number of potential customers and usurious interest rates charged by issuers, there is obviously a lot of money to be made in the credit card industry. In more civilized ages, people believed that usury was a grievous offense contrary to nature or a mortal sin, not an acceptable business practice (Aristotle, Politics 1.10; St. Thomas Aquinas, De Malo 13.4; Dante, Inferno 11.94-111; etc.).

Check Digit

The final digit of your credit card number is a check digit, akin to a checksum. The algorithm used to arrive at the proper check digit is called the Luhn algorithm, after IBM scientist Hans Peter Luhn (1896-1964), who was awarded US Patent 2950048 ("Computer for Verifying Numbers") for the technique in 1960. For details about Luhn's life, see

• Biography on the American Society for Information Science and Technology's Web site, at http://www.asis.org/Features/Pioneers/luhn.htm.
• Notes compiled by Susan K. Soy on "H.P. Luhn and Automatic Indexing" at http://www.gslis.utexas.edu/~ssoy/organizing/l391d2c.htm

Thanks to Aleksandar Janicijevic for directing me to information about H.P. Luhn.

The most succint description of the Luhn algorithm I have found comes from the hacker publication phrack 47-8: "For a card with an even number of digits, double every odd numbered digit and subtract 9 if the product is greater than 9. Add up all the even digits as well as the doubled-odd digits, and the result must be a multiple of 10 or it's not a valid card. If the card has an odd number of digits, perform the same addition doubling the even numbered digits instead."

The bit about even and odd is a little confusing. The main point is that you don't want to double the check digit, and this can easily be done by starting with the check digit, going backwards, and doubling every other digit. See the source code below for details.