There is a lot of negative commentary on this thread (thanks HN for always providing such valuable feedback), but I'd like to point out what I think is useful and positive with Prime.
First, health is inherently social. When you're sick, do you tell your loved one (boy/girlfriend, spouse, parent, close friends, etc?). Of course you do. You want them to know that you might need their care for a few days, that you might have to miss some events that you'd planned together, that you might need help going to the pharmacy to pick up some meds, etc. More serious health issues are even more social. Name one person you know who has suffered from a severe medical condition who has not told their loved ones. When my close family and friends are ill or going in for checkups that are potentially not routine, I want to know immediately what happened. If my loved one were to be drastically ill, I would want to know everything about their condition, the test results, the doctors' reports, the latest research, etc. Surely the HN community understands the desire to geek out over knowledge (health knowledge) and Prime aids that.
Furthermore, I recently suffered some major personal health issues. When I was in the midst of a flurry of doctors visits and medical procedures, my family and friends were all very curious to know what was happening and if they could help out, etc. I was already exhausted by the doctors' visits, and sharing the result of every test and exam with dozens of people was really straining for me. I was extremely lucky to have people near me who could assist me in spreading the word to the people who cared, but this whole "sharing information" problem would have been perfectly solved with Prime. I intentionally did not share any of my health information on Facebook, because I didn't trust Facebook's data privacy and sharing policies. While health is social, it's still private. But Prime may solve this.
For more routine procedures, I can see Prime being very useful. Did my elderly grandmother get her flu shot yet? Check. What was the result of my father's latest checkup about his cholesterol level? Easy to know.
Beyond "social", Prime provides centralized repo for all your medical data. Remember Mint? Remember how everyone gave up their bank passwords to a web-based service so they could see pretty charts and better budget and manage their finances? Remember how Mint took that information and sold ads and upsells against it? Yeah. Right. That's what is happening with medical data, too. Someone (Prime, perhaps) is going to be the one to collect all this information in one place, make it easy to read and understand, and become "the Mint of health data". I would bet on this. The world of health data is too fragmented to not be consolidated sometime soon.
The issues Prime faces are not small: first, ingesting data, and second, earning their users' trust.
I wish them the best of luck.