NTIC More on Prime Numbers

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?

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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

π (x)

more rigorously.

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There are lots of resources beyond this for exploring primes! One interesting resource is Numberphile's YouTube channel for prime videos. Paulo Ribenboim has several well-known books about them, such as The Little Book of Bigger Primes [E.4.17].

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But for usability, I have to mention one of the best web sites about primes. This is the Prime Pages, 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’ 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.

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Summary: More on Prime Numbers

What else can we say about prime numbers? This chapter collates some of the most interesting questions.

In Section 22.1 we see some exciting action in asking who wins various prime races!
The next section states and gives examples of many facts about primes in sequence, including Dirichlet's Theorem on Primes in an Arithmetic Progression and the Green-Tao theorem on sequences in primes.
How many Types of Primes do you know? One of the most intriguing questions is why so many of the questions in this section are completely unanswered.

The Exercises gives practice in searching for interesting patterns in the primes.