Okay, so now that the initial hype of "Primadonna" has died down, and I've been able to listen to it all day, I feel I can give a proper review.
First. let me just start off by saying that "Primadonna" has already proved that it is the song to really open the doors to Marina's career. With an incredibly positive reception at first listen, a WW Trending Topic, and over 100 people visiting this thread at the time of the premiere, this song is just perfect to really garner the public's attention and for the name 'Marina & The Diamonds' to be thrown into people's minds.
Now, Marina's vocals. Flawless. Perfect. Magnifico. 10/10. What else can I say? Marina knows what she wants (the world), and her voice during the verses reflect that. "Buy a big diamond ring for me / get down on your knees for me / pop that pretty question right now baby" Marina commands, to who I assume is one of the many boys she hangs out with who would drop everything do tend to her needs. Her voice during the verses are assertive, witty, and sassy. For the hooks and chorus, however, her voice is tinged with regret and a longing for a happier life. The ability to sound so assertive and then change to regret/longing is nothing short of impressive.
Production. Dr. Luke, Cirkut, and Diplo. "Ugh, why would Marina work with such a generic producer?" This might be one of the thoughts running through your mind when first hearing that Marina and Dr. Luke are working together (it was one of the things running through my head, too), but this track is an amazing mix of everything Marina and everything Luke. Yes, this is probably her most commercial single to date (although "Radioactive" might have something to say about that), but the song still manages to capture Marina's 'essence'. The fun woman who brings different aspects of personalities to every song she records. "Primadonna" might be commercial, but it is not generic. A stripped back chorus that features a guitar, piano, and not much else (as opposed to 'anthemic', fist pumping choruses found in your average Britney or Katy track) paired with Marina's wonderful vocals, makes a delightful combination. This is one of the tracks flaws, however. After the banging verses (which, by the way, what other songs right now put all the danceable parts of the production in the verses?), the chorus disrupts the flow of the song a little too much for my liking. The chorus works well as an intro, but a chorus along the lines of the very last chorus in the song would be a better fit for the other choruses throughout this track. There is so much greatness in this track, though, that a little mishap in the chorus can be overlooked. Looking into the song even further, the production of the second verse and second hook is much better than the production in the first verse/hook. There are very subtle differences, which might not be able to be heard on the first few listenes. In the second verse, we hear a little flicker in the beat (no, it's not just a flaw of the radio rip), and in the second hook, we hear extra backing vocals by Marina that can't be found in the first hook. This part of the review may be pointless, but I think not many people would be aware that these differences exist, and I find them very interesting. I give the production a 8.5/10.
Lyrics. Marina is a fabulous songwriter! "Primadonna" describes a feeling that I'm sure most of us have gone through in our lives - wanting people to just bow down to us just because we are so awesome. Although on the surface it might just sound like a track about someone who gets anything they desire, we also hear Marina talk about how sad (to the core, core, core) this lifestyle makes her, in which she has to "fill the void with celluloid". How coincidental that the song that could make her a star is a track about wanting to be a star. 9/10.
Overall, my score for the entire track is 9/10. One of Marina's better tracks, and makes me so much more excited to hear the rest of Electra Heart. I'm a very, very happy Diamond.
But I feel you, sis. I don't think I have heard any song from her that could top IANAR. 
