Amazon typically keeps its subscriber numbers very close to its chest. That means the company isn't known for offering up firm details on how many subscribers Amazon Prime has. In March of 2013, analysts tipped that Prime could have as many as 10 million subscribers.
If that number was accurate, Amazon has doubled the number of Prime subscribers since then. Amazon CEO Jeff Bezos recently made a comment that as the company exits the holiday season it has "tens of millions" of Prime subscribers.
That statement indicates that there are at least 20 million Amazon Prime subscribers. Amazon has also bragged that it had its best holiday season ever in 2013 with over 36.8 million items ordered on Amazon on Cyber Monday alone.
Bezos saying that Prime has "tens of millions" of subscribers is as close as Amazon has come to offering up exact subscriber numbers. Amazon also noted recently that the Prime service is so popular it had to limit new sign ups in some instances to ensure service to current customers wasn’t impacted by new the surge in subscriptions. Amazon also noted that it added 1 million Prime subscribers in the third week of December.