I did not know — until I read Gamma (page 168) — that there actually is a formula for generating th prime number by directly plugging in . The catch is that it’s a mess:
where the outer brackets represent the floor function.
This mathematical curiosity has no practical value, as determining the 10th prime number would require computing different terms!
When I researching for my series of posts on conditional convergence, especially examples related to the constant , the reference Gamma: Exploring Euler’s Constant by Julian Havil kept popping up. Finally, I decided to splurge for the book, expecting a decent popular account of this number. After all, I’m a professional mathematician, and I took a graduate level class in analytic number theory. In short, I don’t expect to learn a whole lot when reading a popular science book other than perhaps some new pedagogical insights.
Boy, was I wrong. As I turned every page, it seemed I hit a new factoid that I had not known before.
In this series, I’d like to compile some of my favorites — while giving the book a very high recommendation.