Unknown Quantity. Like Unknown Quantity, it is a book about the history of math. Specifically, it's about the Riemann Hypothesis, how it came to be, and what it actually means.
The Riemann Hypothesis is the greatest unsolved problem in mathematics, at least according to the subtitle. It makes a statement about a function (which is described in the book) that has a deep connection with the prime numbers (which is also explained in the book). If you're the kind of person who reads math books, then you've likely already heard of the Riemann Hypothesis. It's one of the six remaining unsolved Millennium Prize puzzles, so proving it to be true or false will make you a million dollars richer.
Prime Obsession is divided into two parts. The odd-numbered chapters are math-heavy, and the even-numbered chapters focus more on history. This is done so that a reader who's just into math can only read the odds, and a reader who's just into history can only read the evens. I don't really like this split; I preferred the structure in Unknown Quantity, where both areas were present throughout the entire book. The split between the chapters removes the interesting math from the interesting stories of the mathematicians. As a more math-leaning person, I found the even chapters a bit slow. Because the people and their stories were not connected with their ideas, a lot of the people become forgettable to me.
All in all, though, I did like the book. Derbyshire explains everything clearly and takes time to ensure that the reader understands what's going on. This is the first source I've found which explains the zeta function's connection to the primes in a way that's clear and satisfying (although it does take a while to get there). I also like that, when Derbyshire does skip a few steps in the math, he takes a moment to explain that and why he is doing so. If you're curious about what this whole "Riemann zeta" business is about, then Prime Obsession is the book to read.
P.S.: You should also watch this video by 3Blue1Brown, which is about visualizing the zeta function. You can consider it a supplement to chapter 13, or you can just watch it because it's pretty.