At the moment, Prime doesn't exist on the mobile-optimized version of the site. And 'mobile' in this context means, smartphone. We had planned to implement this by early December. But the demand has proven great enough that we're rejiggering the schedule and now plan to have it completed by the end of this month.
Once that happens, you'll get the same Prime features and experience on your iPhone or Android as on the website. Same features, custom layouts and dramatically reduced or possibly no ads at all (we're still figuring out that last part).
The Hive itself still won't be available on your iPhone or Android phone. That's a good deal more complicated for a series of technical reasons. But the rest of the Prime experience, including a rocket fast ad-free iphone/android version, should be in your hands shortly.
Questions? Send them to us at tpmprime (at) talkingpointsmemo.com