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  • Ah yes, those university days,

  • a heady mix of Ph.D-level pure mathematics

  • and world debating championships,

  • or, as I like to say, "Hello, ladies. Oh yeah."

  • Didn't get much sexier than the Spence

  • at university, let me tell you.

  • It is such a thrill for a humble breakfast radio announcer

  • from Sydney, Australia, to be here on the TED stage

  • literally on the other side of the world.

  • And I wanted to let you know, a lot of the things you've heard

  • about Australians are true.

  • From the youngest of ages, we display

  • a prodigious sporting talent.

  • On the field of battle, we are brave and noble warriors.

  • What you've heard is true.

  • Australians, we don't mind a bit of a drink,

  • sometimes to excess, leading to embarrassing social situations. (Laughter)

  • This is my father's work Christmas party, December 1973.

  • I'm almost five years old. Fair to say,

  • I'm enjoying the day a lot more than Santa was.

  • But I stand before you today

  • not as a breakfast radio host,

  • not as a comedian, but as someone who was, is,

  • and always will be a mathematician.

  • And anyone who's been bitten by the numbers bug

  • knows that it bites early and it bites deep.

  • I cast my mind back when I was in second grade

  • at a beautiful little government-run school

  • called Boronia Park in the suburbs of Sydney,

  • and as we came up towards lunchtime, our teacher,

  • Ms. Russell, said to the class,

  • "Hey, year two. What do you want to do after lunch?

  • I've got no plans."

  • It was an exercise in democratic schooling,

  • and I am all for democratic schooling, but we were only seven.

  • So some of the suggestions we made as to what

  • we might want to do after lunch were a little bit impractical,

  • and after a while, someone made a particularly silly suggestion

  • and Ms. Russell patted them down with that gentle aphorism,

  • "That wouldn't work.

  • That'd be like trying to put a square peg through a round hole."

  • Now I wasn't trying to be smart.

  • I wasn't trying to be funny.

  • I just politely raised my hand,

  • and when Ms. Russell acknowledged me, I said,

  • in front of my year two classmates, and I quote,

  • "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."

  • (Laughter)

  • "It'd be like putting a piece of toast through a basketball hoop, wouldn't it?"

  • And there was that same awkward silence

  • from most of my classmates,

  • until sitting next to me, one of my friends,

  • one of the cool kids in class, Steven, leaned across

  • and punched me really hard in the head.

  • (Laughter)

  • Now what Steven was saying was, "Look, Adam,

  • you are at a critical juncture in your life here, my friend.

  • You can keep sitting here with us.

  • Any more of that sort of talk, you've got to go and sit

  • over there with them."

  • I thought about it for a nanosecond.

  • I took one look at the road map of life,

  • and I ran off down the street marked "Geek"

  • as fast as my chubby, asthmatic little legs would carry me.

  • I fell in love with mathematics from the earliest of ages.

  • I explained it to all my friends. Maths is beautiful.

  • It's natural. It's everywhere.

  • Numbers are the musical notes

  • with which the symphony of the universe is written.

  • The great Descartes said something quite similar.

  • The universe "is written in the mathematical language."

  • And today, I want to show you one of those musical notes,

  • a number so beautiful, so massive,

  • I think it will blow your mind.

  • Today we're going to talk about prime numbers.

  • Most of you I'm sure remember that six is not prime

  • because it's 2 x 3.

  • Seven is prime because it's 1 x 7,

  • but we can't break it down into any smaller chunks,

  • or as we call them, factors.

  • Now a few things you might like to know about prime numbers.

  • One is not prime.

  • The proof of that is a great party trick

  • that admittedly only works at certain parties.

  • (Laughter)

  • Another thing about primes, there is no final biggest prime number.

  • They keep going on forever.

  • We know there are an infinite number of primes

  • due to the brilliant mathematician Euclid.

  • Over thousands of years ago, he proved that for us.

  • But the third thing about prime numbers,

  • mathematicians have always wondered,

  • well at any given moment in time,

  • what is the biggest prime that we know about?

  • Today we're going to hunt for that massive prime.

  • Don't freak out.

  • All you need to know, of all the mathematics

  • you've ever learned, unlearned, crammed, forgotten,

  • never understood in the first place,

  • all you need to know is this:

  • When I say 2 ^ 5,

  • I'm talking about five little number twos next to each other

  • all multiplied together,

  • 2 x 2 x 2 x 2 x 2.

  • So 2 ^ 5 is 2 x 2 = 4,

  • 8, 16, 32.

  • If you've got that, you're with me for the entire journey. Okay?

  • So 2 ^ 5,

  • those five little twos multiplied together.

  • (2 ^ 5) - 1 = 31.

  • 31 is a prime number, and that five in the power

  • is also a prime number.

  • And the vast bulk of massive primes we've ever found

  • are of that form:

  • two to a prime number, take away one.

  • I won't go into great detail as to why,

  • because most of your eyes will bleed out of your head if I do,

  • but suffice to say, a number of that form

  • is fairly easy to test for primacy.

  • A random odd number is a lot harder to test.

  • But as soon as we go hunting for massive primes,

  • we realize it's not enough

  • just to put in any prime number in the power.

  • (2 ^ 11) - 1 = 2,047,

  • and you don't need me to tell you that's 23 x 89.

  • (Laughter)

  • But (2 ^ 13) - 1, (2 ^ 17) - 1

  • (2 ^ 19) - 1, are all prime numbers.

  • After that point, they thin out a lot.

  • And one of the things about the search for massive primes

  • that I love so much is some of the great mathematical minds

  • of all time have gone on this search.

  • This is the great Swiss mathematician Leonhard Euler.

  • In the 1700s, other mathematicians said

  • he is simply the master of us all.

  • He was so respected, they put him on European currency

  • back when that was a compliment.

  • (Laughter)

  • Euler discovered at the time the world's biggest prime:

  • (2 ^ 31) - 1.

  • It's over two billion.

  • He proved it was prime with nothing more

  • than a quill, ink, paper and his mind.

  • You think that's big.

  • We know that (2 ^ 127) - 1

  • is a prime number.

  • It's an absolute brute.

  • Look at it here: 39 digits long,

  • proven to be prime in 1876

  • by a mathematician called Lucas.

  • Word up, L-Dog.

  • (Laughter)

  • But one of the great things about the search for massive primes,

  • it's not just finding the primes.

  • Sometimes proving another number not to be prime is just as exciting.

  • Lucas again, in 1876, showed us (2 ^ 67) - 1,

  • 21 digits long, was not prime.

  • But he didn't know what the factors were.

  • We knew it was like six, but we didn't know

  • what are the 2 x 3 that multiply together

  • to give us that massive number.

  • We didn't know for almost 40 years

  • until Frank Nelson Cole came along.

  • And at a gathering of prestigious American mathematicians,

  • he walked to the board, took up a piece of chalk,

  • and started writing out the powers of two:

  • two, four, eight, 16 --

  • come on, join in with me, you know how it goes --

  • 32, 64, 128, 256,

  • 512, 1,024, 2,048.

  • I'm in geek heaven. We'll stop it there for a second.

  • Frank Nelson Cole did not stop there.

  • He went on and on

  • and calculated 67 powers of two.

  • He took away one and wrote that number on the board.

  • A frisson of excitement went around the room.

  • It got even more exciting when he then wrote down

  • these two large prime numbers in your standard multiplication format --

  • and for the rest of the hour of his talk

  • Frank Nelson Cole busted that out.

  • He had found the prime factors

  • of (2 ^ 67) - 1.

  • The room went berserk --

  • (Laughter) --

  • as Frank Nelson Cole sat down,

  • having delivered the only talk in the history of mathematics

  • with no words.

  • He admitted afterwards it wasn't that hard to do.

  • It took focus. It took dedication.

  • It took him, by his estimate,

  • "three years of Sundays."

  • But then in the field of mathematics,

  • as in so many of the fields that we've heard from in this TED,

  • the age of the computer goes along and things explode.

  • These are the largest prime numbers we knew

  • decade by decade, each one dwarfing the one before

  • as computers took over and our power to calculate

  • just grew and grew.

  • This is the largest prime number we knew in 1996,

  • a very emotional year for me.

  • It was the year I left university.

  • I was torn between mathematics and media.

  • It was a tough decision. I loved university.

  • My arts degree was the best nine and a half years of my life.

  • (Laughter)

  • But I came to a realization about my own ability.

  • Put simply, in a room full of randomly selected people,

  • I'm a maths genius.

  • In a roomful of maths Ph.Ds,

  • I'm as dumb as a box of hammers.

  • My skill is not in the mathematics.

  • It is in telling the story of the mathematics.

  • And during that time, since I've left university,

  • these numbers have got bigger and bigger,

  • each one dwarfing the last,

  • until along came this man, Dr. Curtis Cooper,

  • who a few years ago held the record for the largest ever prime,

  • only to see it snatched away by a rival university.

  • And then Curtis Cooper got it back.

  • Not years ago, not months ago, days ago.

  • In an amazing moment of serendipity,

  • I had to send TED a new slide

  • to show you what this guy had done.

  • I still remember -- (Applause) --

  • I still remember when it happened.

  • I was doing my breakfast radio show.

  • I looked down on Twitter. There was a tweet:

  • "Adam, have you seen the new largest prime number?"

  • I shivered --

  • (Laughter) --

  • contacted the women who produced my radio show out in the other room,

  • and said "Girls, hold the front page.

  • We're not talking politics today.

  • We're not talking sport today.

  • They found another megaprime."

  • The girls just shook their heads,

  • put them in their hands, and let me go my own way.

  • It's because of Curtis Cooper that we know,

  • currently the largest prime number we know,

  • is 2 ^ 57,885,161.

  • Don't forget to subtract the one.

  • This number is almost 17 and a half million digits long.

  • If you typed it out on a computer and saved it as a text file,

  • that's 22 meg.

  • For the slightly less geeky of you,

  • think about the Harry Potter novels, okay?

  • This is the first Harry Potter novel.

  • This is all seven Harry Potter novels,

  • because she did tend to faff on a bit near the end.

  • (Laughter)

  • Written out as a book, this number would run

  • the length of the Harry Potter novels and half again.

  • Here's a slide of the first 1,000 digits of this prime.

  • If, when TED had begun, at 11 o'clock on Tuesday,

  • we'd walked out and simply hit one slide every second,