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Chapter 22 More on Prime Numbers

This chapter serves two purposes. First, there are all kinds of interesting facts ahout prime numbers, and this chapter collates some of the ones I personally find amazing. What are your favorites?
Secondly, exploring the wonderful world of primes will start us heading back toward other arithmetic functions, especially toward developing the language we’ll need to explore \(\pi(x)\) more rigorously.
There are lots of resources beyond this for exploring primes! One interesting resource is Numberphile’s YouTube channel for prime videos 1 . Paulo Ribenboim has several well-known books about them, such as The Little Book of Bigger Primes [E.4.17].
But for usability, I have to mention one of the best web sites about primes. This is the Prime Pages 2 , hosted at the University of Tennessee, Martin. It’s just amazingly full of useful information, but also quite user-friendly and usable for people with a large variety of backgrounds. In particular, the ‘Top Twenty’s Complete Index 3 ’ page has links to the top twenty of just about every prime type you can imagine, a cornucopia of information. My personal favorite is the prediction of when the first billion digit prime will surface 4 .