 Let's move on now to the integer lists, and this is just a little bit of fun really, but it's an opportunity for children to see enormous integers, which are actually increasingly important of course in real life. Powers of 2 just literally goes through the usual sequence, but it very quickly gets out of hand. And there's a bunch of things that are worth stopping on, for example, 2 to the power of 10, 1 to 2, 4, that's the kilobyte that we now know it, which of course is not 1,000, 2,024. Then you've got the chessboard problem, grain of sand being doubled and doubled and doubled, and who could say this is a huge, great number now? And on it goes to just giant numbers. So that of course is why who wants to be a millionaire works so well, because the doubling process is so powerful. Let's go back to where we were, the prime numbers, so it's a bit surprising that there are so many prime numbers, I mean here we are, we've only got up to 300, 400, and we're only in thousands of prime numbers, so that's an interesting fact. Then having a look at the Massen primes, these are numbers which, it's 2 to the power of a prime number, take away one as another prime number, but it sometimes works and it sometimes doesn't. So that's obviously, this is the thing to be curious, I'm always curious to know how Euler managed to prove in 1772 that this one was prime, it's a pretty amazing feat, and there were lots of other attempts which didn't get anywhere. These ones were not found until they had calculators to actually do the mechanical work, and then we had these being produced, they're still pretty large numbers, and there we go. So there's one where the electronic calculators came along, the number started to get absolutely enormous, and now they are indeed giant, and the last one to be found is 2 to the power of this Q-trait number here, which is over 12 million digits. And well, why? And some of these links are worth looking at, and there's a link at the beginning which I think you'll quite enjoy, this Java applet here, and this enables you to put just about any number in and see if you can guess it's prime factorization before the computer does, and here it is, so we can put any number we like, and if we want it to be prime, it needs to end in 1, 3, 5, or 7, let's try that, and there we are, that's the prime factorization, it's three times that, it's not three-point, and let's do 100 times that, let's see what happens, that's a run of 100, and did we find any primes in that run? Yes, there's one, there's another one, staggering power of calculation going on here, and I have absolutely no idea how it's done or where it's done even, that would be interesting. So that's the machine primes, and otherwise you've also got Pythagorean triples, Pascal's triangle, and some factorials too.