 Thank you all very much. Most of you probably do know me from Breakfast Radio, but before I got onto that I was—I still am, and I always will be—a mathematician. For anyone who's been bitten by the numbers bug, you'll know that it bites early and it bites deep. For me, I was in second grade at Baronia Park Public School. Teacher Ms Russell said as we came into lunch one day, you too? What do you want to do after lunch today? I've got no plans. It's over to you. It was an exercise in democratic schooling, which was pretty cool. We were seven and made a series of ridiculous suggestions for how we could occupy ourselves through the afternoon. Finally, a frustrated Ms Russell said to one student, that won't work. That would be like trying to put a square peg into a round hole. I thought about it for a couple of seconds, put my hand up. She said, yes, Adam, and I said, but miss, surely if the diagonal of the square is less than the diameter of the circle, well, the square peg will pass quite easily through the round hole. It'll be like putting a piece of toast through a basketball hoop, wouldn't it? There was that same awkward silence for a couple of seconds before Stephen Capper, one of the cool kids in class who was sitting next to me, lent over and punched me really hard in the head. Now, what Stephen was saying was, look, Adam, you are at a critical juncture in your life here, my friend. You can keep sitting here with us, or any more of that sort of talk, you'll be sitting over there with them. I took a moment, I looked at the roadmap of life and ran off down the street marked geek as fast as my chubby, asthmatic little legs would carry me. I was in love with numbers from the youngest of ages. I used to say to my friends that numbers are the musical notes with which the symphony of the universe is written. And I was saying that for years before I even discovered that one of the greats, René Descartes, said very similar, the universe is written in mathematical language. I was thinking of suing him, but I think he said it before me. Today we're going to hunt for one of those amazing, beautiful musical notes. We're talking prime numbers. Don't freak out. Six is not prime because it's two times three. Seven is prime because we can't break it down into smaller factors. It's simply one times seven. Three things to know about prime numbers. One is not a prime number. Happy to explain why later. Two, there's an infinite number of primes. They go forever and ever. The great mathematician Euclid proved that 300 BC. And three, as mathematicians, we've always wondered, well, what's the biggest prime number we do know of at any moment in time? And all you need to remember from all of high school maths to follow me today is this. When I say two to the power of five, I'm talking about multiplying two by itself, two times two times two times two times two, five times. So two to the power of five, 32 minus one, 31, happens to be prime. And for reasons I won't go into, most of the monster primes we've ever discovered are of this form. Two, multiplied by itself a prime number of times, take away one. Now, two to any prime minus one isn't automatically prime. Two to the 11 minus one is 2047. You don't need me to tell you. That's 23 times 89. But two to the 13 minus one, two to the 17 minus one, two to the 19 minus one, they're all prime numbers. And this search has obsessed some of the great mathematicians. Leonard Euler, so great that other mathematicians said he is the master of us all. A man so amazing they put him on European currency back before that was an insult, proved The two to the 31 minus one, it's over two billion, he proved it's prime. What the heck, we know the two to 127 minus one. A monster number, 39 digits long. In 1876, a guy called Lucas proved this was prime with nothing more than pen and paper. Word up, L-dog, what an amazing achievement. But as with so many sciences, the long-come computers and the game changes entirely. The largest prime we currently know, take two and multiply it by itself 43 million, 112,609 times, take away one. You've got a number that's almost 13 million digits long. Here's just a thousand of those digits. If I was to show you this entire number, I'd have to put up a screen this large every second of every minute, of every talk you'll hear for this afternoon or three and a half hours, including interval, and I would just manage to show you that number. And as I stand here, I know it's prime as confidently as I know that seven is from. I find that beautiful, I find that almost sexually exciting. I know many of you say Adam, we're happy for you, but why should we care? I'll give you two reasons. First of all, testing massive primes is a simple and beautiful way to test the power and speed of potential new computer chips. But secondly, this prime is found as part of an international search. While I'm here talking to you at home, my computer is part of the GIMPS project, searching for giant primes. In the same way that other people around the world on their laptops, on their workstations, are searching through data for RNA patents, are searching for signs of extraterrestrial life. Distributed computing over the next ten years will see scientists around the world looking at your laptop, looking at your workstation, looking at your computer and saying, I want its grunt. I want it to find things for me. Some of the great discoveries of the next twenty years will happen on your computer, on your laptop in the palm of your hand. But for me, it's enough that this beautiful, beautiful number, this magical note was lying out there and has been since the dawn of creation. And finally, we found it with the power of the human mind. I think my friend Dave Cart would probably put it this way. To find a number like that, to find that musical note is the essence of human being. We think and therefore, we are. Thanks a lot.