(NASDAQ:AMZN) is finally shedding some light on its Amazon Prime membership numbers, and the results are nothing short of remarkable. The e-commerce giant kicked off the new year by announcing that it added more than 1 million Prime members in the third week of December. On top of this, other reports claim the e-tailer now has 20 million users paying for its Prime membership, though Amazon has not yet confirmed this figure.

But Amazon did say it now has "tens of millions" of Prime members worldwide. This is especially important because Amazon Prime is the company's gateway drug. Let me explain.

The "gateway effect"
Amazon Prime is a program that entices customers to spend more (and more frequently) on by offering free two-day shipping on an unlimited number of deliveries for just $79 a year. Adding to its appeal, Amazon expanded its Prime service in 2011 to include unlimited video streaming.

Since launching its Prime service back in 2005, Amazon has refused to disclose information about the number of Prime members enrolled with the company -- until now. Amazon's blowout holiday quarter could be one reason for the sudden change of heart. After all, the world's biggest online retailer said more Prime items were shipped worldwide on Amazon's peak shipping day than ever before.

Source: Amazon.

Importantly, Amazon Prime is one of the most successful loyalty programs in retail today because it encourages customers to make repeat purchases on in order to take advantage of the unlimited free shipping that's included in their annual $79 membership fee. In fact, Prime members often spend twice as much as non-Prime shoppers and more frequently, according to research from Morningstar.

For this reason, it doesn't matter that Amazon doesn't make money on the actual membership fees, because each new Prime member is tremendously valuable to Amazon's bottom line.

Free access to Amazon's streaming library is another way in which Prime acts as a gateway drug to Amazon's other services. Today, Amazon's digital library has grown to include more than 41,000 movies and television shows, and free access to 350,000 Kindle e-books. Not to mention, Amazon's first original series, Alpha House and Betas, are also available exclusively on Prime Instant Video.

Prime numbers that will blow your mind
Here are a few facts to help investors understand the scope of Amazon's retail operations over the recent holiday quarter. The cyber-retail giant shipped enough items with Prime over the holidays to deliver at least one gift to every household in America. Customers ordered more than 36.8 million products from Amazon on Cyber Monday alone. To put that in perspective, that translates into a record 426 items per second. For investors, the obvious takeaway is that you don't want to bet against Amazon in the years ahead.