It is not just about prime number records, but it is a great history of prime numbers with the personalities involved in the development of the field. There are many number groups, series and methods named after the personalities, such as Fermat numbers, Mersenne numbers, Lucas pseudoprimes, Wilson primes and so on. All have their place in history and in working with prime numbers. While Ribenboim does not claim to be complete, he has collected an extensive amount of material on prime numbers which is quite readable. As an example of its scope, this is one of the few sources that include an explanation Waring's problem.
Many more curiosities are in the book, but there is much more than just the records and the history.
The six chapters also cover recognizing primes, functions defining primes, and the distribution of primes. The last chapter is about heuristic and probabilistic results about prime numbers. Ribenboim has a sense of humor expressed throughout the book that makes it entertaining while still being true to the mathematics. He even has haiku written by Basho included. This is a large compilation of research at the periphery of most people's interest, but it also illuminates the foundation of our electronic security and privacy.