How To Generate *Valid* Credit Card Numbers

What do the credit card numbers mean and how are they generated?

I need to start with a disclaimer: Do not use any credit card numbers, except your own, to buy things off internet. It’s wrong and it’s illegal. The purpose of this post is *not* to create fraudulent workable card numbers. It is to explain the math and the science behind those numbers that most of us see day in and day out; and hence this post should be viewed from a purely academic perspective.

Typical credit card anatomy

Before we understand how credit card numbers are generated, here is a brief explanation of what a typical credit card number means.

• Out of the 16 numbers on a typical credit card, the set of first 6 digits is known as the issuer identifier number (read this for details), and the last digit is known as the “check digit” which is generated in such a way as to satisfy a certain condition (the Luhn or Mod 10 check). “Luhn check” is explained later in this post. The term sounds intimidating, but it’s really a very simple (and elegant) concept.
• Taking away the 6 identifier digits and 1 check digit leaves us with 9 digits in the middle that form the “account number”.
• Now, there are 10 possible numbers (from 0 to 9) that can be arranged in these 9 places. This gives rise to 10⁹ combinations, that is, 1 billion possible account numbers (per issuer identifier).
• With each account number, there is always an unique check digit associated (for a given issuer identifier and an account number, there cannot be more than one correct check digit)
• Amex issues credit cards with15 digits. The account numbers in this case are 8 digit long.

What is the “Luhn” or “Mod 10″ check?

In 1954, Hans Luhn of IBM proposed an algorithm to be used as a validity criterion for a given set of numbers. Almost all credit card numbers are generated following this validity criterion…also called as the Luhn check or the Mod 10 check. It goes without saying that the Luhn check is also used to verify a given existing card number. If a credit card number does not satisfy this check, it is not a valid number. For a 16 digit credit card number, the Luhn check can be described as follows:

1. Starting with the check digit, double the value of every second digit (never double the check digit). For example, in a 16 digit credit card number, double the 15th, 13th, 11th, 9th…digits (digits in odd places). In all, you will need to double eight digits.
2. If doubling of a number results in a two digit number, add up the digits to get a single digit number. This will result in eight single digit numbers.
3. Now, replace the digits in the odd places (in the original credit card number) with these new single digit numbers to get a new 16 digit number.
4. Add up all the digits in this new number. If the final total is perfectly divisible by 10, then the credit card number is valid (Luhn check is satisfied), else it is invalid.

When credit card numbers are generated, the same steps are followed with one minor change. First, the issuer identifier and account numbers are assigned (issuer numbers are fixed for a given financial institution, whereas the account numbers are randomly allocated – I think). Then, the check digit is assumed to be some variable, say X. After this, the above steps are followed, and during the last step, X is chosen in such a way that it satisfies the Luhn check.

This part is a bit confusing and takes some time to understand. However, don’t get stuck here…continue reading through the examples below and you will figure out what this is all about.

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Credit card numbers valid or invalid?

Have you ever wondered if those numbers on the fake plastic or cardboard credit cards that come with the “preapproved” offers are real or imaginary? If they are not valid, how do you know it?…Just apply the Luhn check and all the those fake credit cards will invariably fail.Here is an example of a VISA credit card (look at the expiry date – 01/09 ..it’s still valid ! )

Note that the credit card number starts with “4″…so it is indeed a VISA issued credit card (VISA cards start with “4″ and MasterCard/Maestro cards start with “5″). Now, let us apply the Luhn algorithm to this card. To make it easier on you guys, I have created a schematic of the steps towards the Luhn check (below) for this card number 4552 7204 1234 5678:

• In this case, when we sum up the total, it comes to 61 which is not perfectly divisible by 10, and hence this credit card number is invalid.
• If such a credit card number is ever generated, the value of the check digit would be adjusted in such a way as to satisfy the Luhn condition. In this case, the only value of the check digit, that will create a valid credit card number, is 7. Choosing 7 as the check digit will bring the total to 60 (which is perfectly divisible by 10) and the Luhn condition will be satisfied. So the valid credit card number will be 4552 7204 1234 5677.

Let’s try another example, this time with a MasterCard.

Again, performing the Luhn check on this credit card number, we have:

• The total comes to 65 which is not perfectly divisible by 10. Hence this credit card number is invalid.
• In this case, a valid credit card number will result only if the check digit is 8. This will bring the total to 70 which is perfectly divisible by 10. So the valid credit card number will be 5490 1234 5678 9128.

Closing remarks

If I still have your attention, here are some additional thoughts. In the context of this post, by the term “valid”, I mean “mathematically valid”. A mathematically valid credit card does not mean a “working” credit card. The Luhn formula validates only the credit card number; it does not validate the expiry date and/or card security code (CVV, CVC). Plus, as discussed before, the 9 digit account number will yield 1 billion combinations; so the chances of getting a working credit card number are very remote. It should also be noted that, this validation is usually employed at the transaction end; which means that numbers that do not satisfy the Luhn check are not forwarded to the card issuer and the transaction is terminated. If you have a fake credit card which satisfies the Luhn check, it will go through at the transaction end, but the card issuer will most likely catch the mischief. So don’t go about trying to use these numbers to buy stuff.

Just to be clear on this, I don’t expect comments like these (check out the source of this comment):

hey. im hearing good things about your site! i need some money to jump start my poker career. Probably about 40-100$ would do. i dont have a credit card to use and it pisses me off because i know i could beat the majority of the people online. please help

If you intend to post such comments, at least be extremely funny.

So you think you can separate out valid and invalid account numbers now? Here are a couple of trial numbers for you:

• 5491 9469 1544 4923 – Valid or invalid? If invalid, what should have been the correct check digit to make it valid?
• 4539 9920 4349 1562 – Valid or invalid? If invalid, what should have been the correct check digit to make it valid?

Sudoku fans will quickly figure out multiple valid combinations of the above numbers. If you don’t want to do the math, here are some ready made valid (”test”) credit card numbers from Paypal.By the way, the Luhn check is also valid for debit card numbers.I am still in the learning phase with this topic and trying to further understand how people use (or misuse (?)) such information. If you have some insight in this matter, please feel free to share it with us.If you liked what you read above, go ahead and subscribe to this blog to get more updates. It’s easy – just click on one of the buttons below and get the feed.

Credit Card

Credit Card

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Shopping

Shopping around for a credit card can save you money on interest and fees. You’ll want to find one with features that match your needs. This information can help you

Understand the features of credit cards
Compare credit card features and costs
Know your rights when using your credit card
File a complaint if you have a problem with
your credit card

How will you use your credit card?

The first step in choosing a credit card is thinking about how you will use it.

If you expect to always pay your monthly bill in full–and other features such as frequent flyer miles don’t interest you–your best choice may be a card that has no annual fee and offers a longer grace period.

If you sometimes carry over a balance from month to month, you may be more interested in a card that carries a lower interest rate (stated as an annual percentage rate, or APR).

If you expect to use your card to get cash advances, you’ll want to look for a card that carries a lower APR and lower fees on cash advances. Some cards charge a higher APR for cash advances than for purchases.

What are the APRs?

The annual percentage rate–APR–is the way of stating the interest rate you will pay if you carry over a balance, take out a cash advance, or transfer a balance from another card. The APR states the interest rate as a yearly rate.

Multiple APRs

A single credit card may have several APRs:

One APR for purchases, another for cash advances, and yet another for balance transfers. The APRs for cash advances and balance transfers often are higher than the APR for purchases (for example, 14% for purchases, 18% for cash advances, and 19% for balance transfers).

Tiered APRs. Different rates are applied to different levels of the outstanding balance (for example, 16% on balances of $1–$500 and 17% on balances above $500).

A penalty APR. The APR may increase if you are late in making payments. For example, your card agreement may say, “If your payment arrives more than ten days late two times within a six-month period, the penalty rate will apply.”

An introductory APR. A different rate will apply after the introductory rate expires.

A delayed APR. A different rate will apply in the future. For example, a card may advertise that there is “no interest until next March.” Look for the APR that will be in effect after March.

If you carry over a part of your balance from month to month, even a small difference in the APR can make a big difference in how much you will pay over a year.
Fixed vs. variable APR

Some credit cards are “fixed rate”–the APR doesn’t change, or at least doesn’t change often. Even the APR on a “fixed rate” credit card can change over time. However, the credit card company must tell you before increasing the fixed APR.

Other credit cards are “variable rate”–the APR changes from time to time. The rate is usually tied to another interest rate, such as the prime rate or the Treasury bill rate. If the other rate changes, the rate on your card may change, too. Look for information on the credit card application and in the credit card agreement to see how often your card’s APR may change (the agreement is like a contract–it lists the terms and conditions for using your credit card).

How long is the grace period?

The grace period is the number of days you have to pay your bill in full without triggering a finance charge. For example, the credit card company may say that you have “25 days from the statement date, provided you paid your previous balance in full by the due date.” The statement date is given on the bill.

The grace period usually applies only to new purchases. Most credit cards do not give a grace period for cash advances and balance transfers. Instead, interest charges start right away.

If you carried over any part of your balance from the preceding month, you may not have a grace period for new purchases. Instead, you may be charged interest as soon as you make a purchase (in addition to being charged interest on the earlier balance you have not paid off). Look on the credit card application for information about the “method of computing the balance for purchases” to see if new purchases are included or excluded. Information on methods of computing the balance is in the section “How is the finance charge calculatedHow is the finance charge calculated?

The finance charge is the dollar amount you pay to use credit. The amount depends in part on your outstanding balance and the APR.

Credit card companies use one of several methods to calculate the outstanding balance. The method can make a big difference in the finance charge you’ll pay. Your outstanding balance may be calculated

Over one billing cycle or two,
Using the adjusted balance, the average daily balance, or the previous balance, and
Including or excluding new purchases in the balance.

Depending on the balance you carry and the timing of your purchases and payments, you’ll usually have a lower finance charge with one-cycle billing and either

The average daily balance method excluding new purchases,
The adjusted balance method, or
The previous balance method.

Minimum finance charge

Some credit cards have a minimum finance charge. You’ll be charged that minimum even if the calculated amount of your finance charge is less. For example, your finance charge may be calculated to be 35¢–but if the company’s minimum finance charge is $1.00, you’ll pay $1.00. A minimum finance charge usually applies only when you must pay a finance charge–that is, when you carry over a balance from one billing cycle to the next.

What are the fees?

Most credit cards charge fees under certain circumstances:

Annual fee (sometimes billed monthly). Charged for having the card

Cash advance fee. Charged when you use the card for a cash advance; may be a flat fee (for example, $3.00) or a percentage of the cash advance (for example, 3%)

Balance-transfer fee. Charged when you transfer a balance from another credit card (Your credit card company may send you “checks” to pay off the other card. The balance is transferred when you use one of these checks to pay the amount due on the other card.)

Late-payment fee. Charged if your payment is received after the due date

Over-the-credit-limit fee. Charged if you go over your credit limit

Credit-limit-increase fee. Charged if you ask for an increase in your credit limit

Set-up fee. Charged when a new credit card account is opened

Return-item fee. Charged if you pay your bill by check and the check is returned for non-sufficient funds (that is, your check bounces)

Other fees. Some credit card companies charge a fee if you pay by telephone (that is, if you arrange by phone for payment to be transferred from your bank to the company) or to cover the costs of reporting to credit bureaus, reviewing your account, or providing other customer services. Read the information in your credit card agreement to see if there are other fees and charges.

What are the cash advance features?

Some credit cards let you borrow cash in addition to making purchases on credit. Most credit card companies treat these cash advances and your purchases differently. If you plan to use your card for cash advances, look for information about

Access. Most credit cards let you use an ATM to get a cash advance. Or the credit card company may send you “checks” that you can write to get the cash advance.

APR. The APR for cash advances may be higher than the APR for purchases.

Fees. The credit card company may charge a fee in addition to the interest you will pay on the amount advanced.

Limits. Some credit cards limit cash advances to a dollar amount (for example, $200 per cash advance or $500 per week) or a portion of your credit limit (for example, 75% of your available credit limit).

How payments are credited. Many credit card companies apply your payments to purchases first and then to cash advances. Read your credit card agreement to learn how your payments will be credited.

How much is the credit limit?

The credit limit is the maximum total amount–for purchases, cash advances, balance transfers, fees, and finance charges–you may charge on your credit card. If you go over this limit, you may have to pay an “over-the-credit-limit fee.”

What kind of card is it?

Most credit card companies offer several kinds of cards:

Secured cards, which require a security deposit. The larger the security deposit, the higher the credit limit. Secured cards are usually offered to people who have limited credit records–people who are just starting out or who have had trouble with credit in the past.

Regular cards, which do not require a security deposit and have just a few features. Most regular cards have higher credit limits than secured cards but lower credit limits than premium cards.

Premium cards (gold, platinum, titanium), which offer higher credit limits and usually have extra features–for example, product warranties, travel insurance, or emergency services.

Does the card offer incentives and other features?

Many credit card companies offer incentives to use the card and other special features:

Rebates (money back) on the purchases you make

Frequent flier miles or phone-call minutes

Additional warranty coverage for the items you purchase

Car rental insurance

Travel accident insurance or travel-related discounts

credit card registration, to help if your wallet or purse is lost or stolen and you need to report that all your credit cards are missing

Credit cards may also offer, for a price,

Insurance to cover the payments on your credit card balance if you become unemployed or disabled, or die. Premiums are usually due monthly, making it easy to cancel if the payments are higher than you want to pay or you decide you don’t need the insurance any longer.

Insurance to cover the first $50 of charges if your card is lost or stolen. Under federal law, you are not responsible for charges over $50.

Before you sign up to pay for any of these features, think carefully about whether it will be useful for you. Don’t pay for something you don’t want or don’t need.

How do I find information about credit cards?

You can find lists of credit card plans, rates, and terms on the Internet, in personal finance magazines, and in newspapers. The Federal Reserve System surveys credit card companies every six months. You’ll need to get the most recent information directly from the credit card company–by phoning the company, looking on the company’s web site, or reading a solicitation or application.

Under federal law, all solicitations and applications for credit cards must include certain key information, in a disclosure box similar to the one shown.

APR for purchases. The annual percentage rate you’ll be charged if you carry over a balance from month to month. If the card has an introductory rate, you’ll see both that rate and the rate that will apply after the introductory rate expires.

Other APRs. The APRs you’ll be charged if you get a cash advance on your card, transfer a balance from another card, or are late in making a payment. More information about the penalty rate may be stated outside the disclosure box–for instance, in a footnote. In this example, if you make two payments that are more than ten days late within six months, the APR will increase to 23.9%.

Variable-rate information. Information about how the variable rate will be determined (if relevant). More information may be stated outside the disclosure box–for instance, in a footnote.

Grace period for repayment of balances for purchases. The number of days you’ll have to pay your bill for purchases in full without triggering a finance charge.

Method of computing the balance for purchases. The method that will be used to calculate your outstanding balance if you carry over a balance and will pay a finance charge.

Annual fees. The amount you’ll be charged each twelve-month period for simply having the card.

Minimum finance charge. The minimum, or fixed, finance charge that will be imposed during a billing cycle. A minimum finance charge usually applies only when a finance charge is imposed, that is, when you carry over a balance.

Transaction fee for cash advances. The charge that will be imposed each time you use the card for a cash advance.

Balance-transfer fee. The fee that will be imposed each time you transfer a balance from another card.

Late-payment fee. The fee that will be imposed when your payment is late.

Over-the-credit-limit fee. The fee that will be imposed if your charges exceed the credit limit set for your card.

What are your liability limits?

If your credit card is lost or stolen–and then is used by someone without your permission–you do not have to pay more than $50 of those charges. This protection is provided by the federal Truth in Lending Act. You do not need to buy “credit card insurance” to cover amounts over $50.

If you discover that your card is lost or stolen, report it immediately to your credit card company. Call the toll-free number listed on your monthly statement. The company will cancel the card so that new purchases cannot be made with it. The company will also send you a new card.

Make a list of your account numbers and the companies’ phone numbers. Keep the list in a safe place. If your wallet or purse is lost or stolen, you’ll have all the numbers in one place. Take the list of phone numbers–not the account numbers–with you when you travel, just in case a card is lost or stolen.

What can you do about billing errors?

The federal Fair Credit Billing Act covers billing errors. Examples of billing error are

	A charge for something you didn’t buy
	A bill for an amount different from the actual amount you charged
	A charge for something that you did not accept when it was delivered
	A charge for something that was not delivered according to agreement
	Math errors
	Payments not credited to your account
	A charge by someone who does not have permission to use your credit card

If you think your credit card bill has an error, take the following steps:

1. Write to the credit card company within 60 days after the statement date on the bill with the error. Use the address for “billing inquiries” listed on the bill. Tell the company
   Your name and account number,
   That you believe the bill contains an error, and why you believe it’s wrong, and
   The date and amount of the error (the “disputed amount”).
2. Pay all the other parts of the bill. You do not have to pay the “disputed amount” or any minimum payments or finance charges that apply to it.

If there is an error, you will not have to pay any finance charges on the disputed amount. Your account must be corrected.

If there is no error, the credit card company must send you an explanation and a statement of the amount you owe. The amount will include any finance charges or other charges that accumulated while you were questioning the bill.

What if the item you purchase is damaged?

The federal Fair Credit Billing Act allows you to withhold payment on any damaged or poor-quality goods or services purchased with a credit card–even if you have accepted the goods or services–as long as you have made an attempt to solve the problem with the merchant.

The sale must have been for more than $50 and must have taken place in your home state or within 100 miles of your home address. You should notify the credit card company in writing and explain why you are withholding your payment.

You may withhold the payment while the credit card company investigates your claim. If you pay the charges for the goods on your credit card bill before the dispute is resolved, you will lose your right to make a claim.