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Adam Spencer: Why Are Monster Prime Numbers Important?

Mar 15, 2019
Originally published on March 15, 2019 4:57 pm

Part 5 of the TED Radio Hour episode Don't Fear Math.

About Adam Spencer's TED Talk

Adam Spencer is fascinated by prime numbers. These seemingly simple numbers can be found in monster sizes—the latest being almost 25 million digits long.

About Adam Spencer

Adam Spencer originally chose to pursue a law degree and a PhD in Pure Mathematics before he shifted course to pursue radio.

Spencer was the breakfast host on 702 ABC Sydney for 8 years where he talked about the news, the weather, and math.

Spencer is the author of several books including The Number Games, Big Book of Numbers, and World of Numbers. He is the first ever Science and Mathematics Ambassador at the University of Sydney.

Copyright 2019 NPR. To see more, visit https://www.npr.org.

GUY RAZ, HOST:

Today on the show, ideas about the beauty of math and the people who love it. And for eight years, at 3:20 in the morning, Adam Spencer would roll out of bed and go to work.

ADAM SPENCER: Three hours every day - 6 o'clock till 9 o'clock - news, traffic, weather, the very best music and a healthy serve of mathematics to get you on your way.

RAZ: Adam hosted the most-listened-to morning radio talk show in Australia. And every chance he'd get, he'd talk about math.

SPENCER: Darwin, sunny and 32 degrees. That's two to the power of five.

(SOUNDBITE OF MUSIC)

RAZ: In 1996, Adam was actually working toward a doctorate in pure mathematics when he won a stand-up comedy contest for a national radio station. He thought working in radio was a better idea at the time, so he dropped out.

SPENCER: I'd like to say in a room of randomly selected people, I'm the maths genius. In a room of maths PhDs, I'm as dumb as a box full of hammers.

RAZ: These days, Adam makes his living writing and talking about math because Adam Spencer is one of those people who's always loved numbers. Here's more from Adam on the TED stage.

(SOUNDBITE OF TED TALK)

SPENCER: I cast my mind back when I was in second grade. As we came up towards lunchtime, our teacher Ms. Russell said to the class, what do you want to do after lunch? I've got no plans. It was an exercise in democratic schooling, but we were only 7. 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 would 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, 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)

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

RAZ: Do you think that you just had that switch in your brain that was like, yes, math. I love it. It's awesome.

SPENCER: It's a really difficult question 'cause with me, it goes back so far that I don't even remember if I had to try all that hard. But I do remember that having loved it, I did more and more. Like practically anything, it is a practice thing. And because it's a subject with that finite correct, incorrect sort of line, it is the thing where, to an extent, you can teach yourself. You know if you're getting it right. You're not teaching yourself bad habits. And I just loved it more than anyone else I knew.

(SOUNDBITE OF TED TALK)

SPENCER: 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. 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.

RAZ: Prime numbers - let's just remind everybody what a prime number is.

SPENCER: OK. So six is not prime...

RAZ: Right.

SPENCER: ...Because we can break it down into six equals two times three. Seven is prime because seven is one times seven, but you can't break it into any smaller multiplying building blocks. So the primes are the sort of building blocks that all the other numbers come out from. If I throw you a number - if I say 26 - well, turns out that's not prime.

RAZ: Nope.

SPENCER: It's two times 13. OK. What about 29?

RAZ: Yep.

SPENCER: That is prime. You can't break it down. Every number has to be prime or composite. Primes go on forever. There is no final, biggest prime number. A beautiful mathematician called Euclid proved that thousands of years ago. So it makes sense. In any given time, there must be a largest prime number that we know about. And my TED talk back in 2013 was the history of the largest prime numbers we've detected. Initially, it was all just humans doing phenomenal things with their brains. And I was going to say pen and paper - not even pen, you know? Quill...

RAZ: Quill, yeah.

SPENCER: ...And ink and chalk and things like that with equations pulling down that are just unbelievable to think a human mind could come up with free of any device.

(SOUNDBITE OF TED TALK)

SPENCER: This is the great Swiss mathematician Leonard Euler. In the 1700s, other mathematicians said he is simply the master of us all. Euler discovered, at the time, the world's biggest prime - two to the 31 minus one. It's over 2 billion. You think that's big. We know that two to the power of 127 minus one 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. The massive prime numbers all follow a cute little formula. I'll give you a really easy example.

RAZ: Sure.

SPENCER: Let's take two, and let's multiply two by itself three twos. Two times two is four, times two gets us to eight. Let's take away one from that. So we had two times two times two, take away one is seven, which just happens to be a prime number.

RAZ: Yeah.

SPENCER: All the massive prime numbers we've ever detected are of the form two multiplied together heaps of times, take away one. And the latest one that we uncovered in December of last year - take the number two. Write down not one two, not three twos, like I had earlier. Write down 82,589,993 twos. You end up with a 24-million-digit-long number.

RAZ: Wow.

SPENCER: And we know that single number is prime as confidently as we know the number seven is prime.

(SOUNDBITE OF MUSIC)

SPENCER: I just think that's just mind-numbingly beautiful.

(SOUNDBITE OF TED TALK)

SPENCER: My laptop at home was looking through four potential candidate primes myself as part of a networked computer hunt around the world for these large numbers. The discovery of that prime was similar to the work people are doing in unraveling RNA sequences, in searching through data from SETI and other astronomical projects.

We live in an age where some of the great breakthroughs are not going to happen in the labs or the halls of academia but on laptops, desktops, in the palms of people's hands who are simply helping out for the search. But for me, it's amazing because it's a metaphor for the time in which we live, when human minds and machines can conquer together.

(SOUNDBITE OF MUSIC)

RAZ: So right now, as we're sitting here talking on the radio, you've got a computer in your house that's just, like, you know, looking for prime numbers.

SPENCER: Yeah. There's a project called GIMPS. The more technical, mathematical name is Mersenne - M-E-R-S-E-N-N-E - from a guy who researched a monk back in the 1600s of all things. And so GIMPS is the Great Internet Mersenne Prime Search. Anyone can do this. You take your laptop and download the GIMPS software. It will give you a candidate prime. And in the background, while your computer's doing nothing else, it will just search.

Now, it would take four to six weeks before it comes back and says yes or no. And you're almost always going to be disappointed and told no. But if you think about the amount of super computing power that is just sitting on people's desks, in their man caves, in the office at work over the weekend, on their phones, just unused - there are problems out there we want solved. And the GIMPS prime search is just a great, little, nerdy example of that.

RAZ: All right. So there are people looking for these monster prime numbers. And the latest one was discovered by this guy Patrick Laroche, right?

SPENCER: Yeah. Laroche is the latest one, yes.

RAZ: What's the point? Like, what's the practical application of a prime number?

SPENCER: Big-sized prime numbers - 20 digits long, those sort of things - underpin all Internet security. And the reason that you can use your credit cards online, et cetera, is to do with algorithms based on very large prime numbers. And the best sort of practical application for large numbers like this is they're a great way to test the speed and accuracy of potential new computer chips. If my laptop is working on a Pentium 15BZ and I think that's the greatest chip in the world, and you say, well, I've come up with the double Pentium 13X - OK.

Well, let's ask them the same simple question with the same eight lines of code. And let's let the computers go and decide for us. Now, if your one comes back in only three weeks and it solves something that took my computer five weeks, you've got yourself a really fast, impressive, new computer chip. So speed and accuracy testing of computer chips these days - well worth it.

And it's also just another small piece in the deeper puzzle. One of the reasons we're so attracted to prime numbers is they're so basic. They're so fundamental. We know nothing about them. Some of the most famous problems - unsolved problems in the history of mathematics are to do with the distribution of prime numbers, the amount of prime numbers you have after a certain point and things like that. So any small step towards understanding them more, I think, is a good thing.

RAZ: That's Adam Spencer. He's the first-ever ambassador of science and mathematics for the University of Sydney in Australia. You can find his full talk at ted.com.

(SOUNDBITE OF FILM, "SCHOOL OF ROCK")

JACK BLACK: (As Dewey, singing) Math is a wonderful thing. Math is a really cool thing. So get off your ath (ph). Let's do some math, math, math, math, math, math.

(SOUNDBITE OF MUSIC)

RAZ: Hey. Thanks so much for listening to our show on math this week. If you want to find out more about who was on it, go to ted.npr.org. And to see hundreds more TED Talks, check out ted.com or the TED app.

Our production staff at NPR includes Jeff Rogers, Sanaz Meshkinpour, Jinae West, Neva Grant, Casey Herman, Rachel Faulkner, Diba Mohtasham, James Delahoussaye, Melissa Gray and J.C. Howard with help from Daniel Shukin. Our intern is Katie Monteleone. Our partners at TED are Chris Anderson, Colin Helms, Anna Phelan and Janet Lee. I'm Guy Raz. And you've been listening to ideas worth spreading right here on the TED Radio Hour from NPR. Transcript provided by NPR, Copyright NPR.