This chapter is entirely devoted to prime numbers. I've just realized that the chapters alternate between progressing the plot and rambling about some element of Christopher's characterization.
He begins by saying that he's given the chapters prime numbers instead of cardinal numbers because he likes prime numbers. I already figured that from his earlier claim that he knows all of them up to 7,057, but it's nice to have it spelled out, I guess.
Speaking of prime numbers, the one associated with this chapter is 19, in case you've lost track. I'm going to keep pretending they're numbered normally.
Anyway, then he tells us how to find the prime numbers.
First you write down all the positive whole numbers in the world.
Numbers aren't exactly "in" any physical location. Also, you can't write down all of them unless you have an infinite amount of free time.
[snip table full of numbers]
Then you take away all the numbers that are multiples of 2. Then you take away all the numbers that are multiples of 3. Then you take away all the numbers that are multiples of 4 and 5 and 6 and 7 and so on. The numbers that are left are the prime numbers.
No, you don't. Once you've taken away all the multiples of 2 and 3, you can't take away the multiples of 4 and 6 because they're already gone. You take away all the numbers that are divisible by something else, but if you try to describe the process in terms of specific numbers, you're liable to end up making the mistake we see here. If he's so precise and he likes prime numbers so much, he should know this.
Then we get the same table with all the composite numbers stripped out, and he talks about how there's no simple formula to determine if a very large number is prime or what the next prime is, which I can't comment on.
Prime numbers are useful for writing codes and in America they are classed as Military Material and if you find one over 100 digits long you have to tell the CIA and they buy it off you for $10,000. But it would not be a very good way of making a living.
This claim is all over the internet, apparently originating from this book. It seems to be false. Posters on the linked Snopes thread speculate that it was based on the Electronic Frontier Foundation's awards for large primes. There is such a thing as illegal primes, which are used in cryptography (specifically digital rights management), but they have nothing to do with the CIA.
Given that one has to bend the facts heavily to arrive at Christopher's claim, where did he get the idea? If he's so interested in prime numbers, you'd think he'd know better. He'd also understand the above points about multiples of 2 and 3 and the impossibility of writing down all the natural numbers. He should have been a precise character, but the only kind of precision he displays is the magical, Spock-like knowledge of quantities he could not have measured; everything else is mediocre or downright sloppy. Haddon has a feeble grasp on the concept of precision.
Separately, I don't like the way this paragraph is structured. The first sentence is too long and too unpunctuated, and the second is a fragment. I'd at least break the first into two. This is all par for the course, naturally.
Prime numbers are what is left when you have taken all the patterns away. I think prime numbers are like life. They are very logical but you could never work out all the rules, even if you spent all your time thinking about them.
Thus ends the chapter. This quote is somewhat well-known and is supposed to be all deep and profound, but I don't agree with it. Life is not "very logical". It is ruled by the random complexities of underlying reality and the arbitrary whims and rules of humans. The rules of life are in constant flux, while the rules of prime numbers are clear and unchanging, sitting motionless and unseen until they are discovered. The rules of numbers simply are, whereas the rules of life are based as much on human notions as on reality.
Many think they have the perfect metaphor for life, but nothing is like life except life itself.