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Here’s why we will never run out of 16-digit credit and debit card numbers

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Americans have, on average, more than three credit cards each. Many also have debit cards, flexible spending cards and other accounts that are all associated with a unique 16-digit number that enables transactions.

Plus, most popular virtual payment methods now use so-called tokenization, which means that there are additional unique numbers tied to your account. Each card you have loaded into Apple Pay, for example, is tying up three 16-digit combinations, since the watch and phone each use a unique tokenized number.

“We have way more card account numbers than we ever did before,” said Heather McGuire, senior program manager for CO-OP Financial Services, which helps credit unions leverage technology. “You could potentially have four or five different 16-digit account numbers tied to one account.”

Ongoing data breaches mean that firms are re-issuing thousands of cards every year and some have also begun issuing different account numbers to joint account holders in order to reduce replacement costs after breaches.

With all of these new numbers, is it possible that we’ll eventually run out of unique numbers to use?

“This [question] comes up every few years,” said Kris Carrera, senior vice president, financial services product development, global retail payments, at FIS, a financial services technology firm. “But we’re not going to run out.”

The potential 16-digit credit card combinations provide far more account numbers than could ever be used, according to Cris Poor, a mathematics professor at Fordham University. Poor says the 16-digit card numbers have 10 quadrillion possibilities.

By comparison, the world population is a mere 6 billion.

“So each person in the world could have more than a million potential credit numbers, and I don’t know anybody who has anywhere near that many credit cards,” Poor said.

To understand why we’re not going to run out of numbers, you need to know how the distribution of credit card numbers works.

All card numbers guidelines are laid out by the International Organization for Standardization and the American National Standards Institute, which also sets standards around things such as the size and shape of credit cards. The first digit signifies the network and industry, so for example, all Visas start with a “4,” while AmEx cards start with a “3.” That allows the merchants to identify who is ultimately responsible for payment of charges.

The first digit, along with the five that follow it, are collectively known as the Bank Identification Number, or BIN. They’re assigned to the individual payment networks (Visa, MasterCard, etc.), which then distribute them to card issuers (Bank of America, Wells Fargo, etc.).

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So the six digits on every Chase Sapphire card, for example, would be the same as would the first six digits of every Capital One Venture Rewards Card. The next nine digits on your card are given out to individual users by the issuers, and are unique to your account.

That means that each issuer has millions of individual consumer account numbers that they can distribute.

“Typically, a financial institution wouldn’t want to exhaust all the numbers in their range, though,” said Lou Grilli, AVP Product Development with Trellance, a credit union service organization. “They want to hold onto some to re-issue, and for growth or if they decide to add another card number to the family.

“Realistically, they giving out about 50 percent of their numbers would be acceptable, and most BINs out there are only around 10 percent utilized,” he added.

Even so, the networks don’t want to see their BIN capacity tested. MasterCard BINs always started with the number 5, but in 2017, the network began issuing a 2 series of cards in order to increase the number of available cards and numbers.

The number of available card numbers is not finite, either, since issuers can recycle old accounts numbers that have been closed for a certain period of time, issuing them with a new card number and a new CVV (card verification value).

Issuers don’t have any control over the last digit on your credit card, which is known as the “check digit.” It’s calculated via a formula devised by mathematician Hans Peter Luhn. The formula uses the other 15-digits for the card and allows processors to instantly know whether a number is legit, or whether it’s been entered incorrectly due to either error or fraud.

There are also several other numbers on your card that help merchants identify you and verify the number. The expiration date and the security code also help merchants and processors authenticate a card.

— By Beth Braverman, special to CNBC.com

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