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The Book of Prime Number Records

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Few mathematicians, recreational or otherwise, lack an affection for the prime numbers and their properties. With the added charm that not many areas have fewer applications, this is one that has seen significant advances made by "amateurs." In particular, the contributions of Harvey Dubner and Samuel Yates (JRM veterans) are given extensive coverage and, for anyone who wishes to learn about the "state-of-the-art," this is a must read.
One item that is continually emphasized is the number of properties that are almost certainly true, but no one really has a good idea how to prove. Particularly enjoyable is the repeated assertion that proofs are continually being refined, adjusted, shortened and otherwise cleansed. While it is true that mathematical realities remain constant, often lost in the shuffle is the alternate reality that a correct proof is not the last word. There is so much work that remains to be done, including new results of old results.
The level of difficulty mimics a wildly undulating function. Some material could be comprehended by a smart high schooler, and others require a patient (re)reading with likely side trips to the reference shelf. That is just a tribute to the thoroughness of the presentation.
Closing with a 100-page bibliography of material for further study, this book is where anyone with an interest in the primes should begin.

Published in Journal of Recreational Mathematics, reprinted with permission.