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Mathematicians in their prime -

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LISA MILLAR: It probably hasn't been keeping you awake at night but mathematicians have been
working around the clock and they've found their holy grail - a 13-million digit prime number.
Their success is so prestigious it comes with prize money of $US100,000.

Prime numbers like seven and 11 can only be divided by the number one or themselves and now there's
another one to add to the list and it's setting the world of mathematics abuzz.

Alison Caldwell reports.

ALISON CALDWELL: It's an amazing discovery - a new prime number with 13-million digits. To write it
out by hand would take two-and-half-months. But with a computer it doesn't take anywhere near as
long.

That's how the team at the University of California at Los Angeles found the number - by linking up
75 computers and harnessing their unused power. That allowed them to perform the enormous number of
calculations needed to find and verify the new prime.

They were among thousands of other people around the world who linked the powers of their personal
computers in the search for a higher Mersenne prime number, named after the 17th century French
mathematician Marin Mersenne.

The discovery puts the team in line to collect a prize of $US100,000 set up by the Electronic
Frontier Foundation to promote cooperative computing on the internet.

Maths genius Professor Terence Tao works on the theory of maths at UCLA. Born in Adelaide, the
33-year-old made one of the most important scientific discoveries in 2004 when he proved that prime
numbers contain infinitely many progressions of all finite lengths.

He says this latest discovery is an exciting one.

TERENCE TAO: It's good news. I'm especially happy for my home university UCLA because they were
involved in writing this prime. People have been using this challenge to find very large prime
numbers to test certain mathematical algorithms and also to test computers' ability to do huge
calculations. And this particular prime was actually a milestone. There was a small prize, I think
$100,000 for the first prime to be discovered with more than 10-million digits and UCLA's team won
that prize.

ALISON CALDWELL: Do you think there are more primes out there?

TERENCE TAO: Yeah, there are. In fact there's a very old result going back to ancient Greeks in
300BC that says that in fact there are infinitely many primes. No matter how primes you find, there
will always be another one. But that argument doesn't tell you where the primes are. It just tells
you that they're out there and actually finding primes is a lot harder than just saying that they
exist.

This is by far the largest prime that's ever been discovered. But of course there will be more if
we have faster computers and better algorithms we will find larger ones too. There are more prizes
out there for even bigger primes like a hundred-million digits and so forth.

ALISON CALDWELL: Doesn't it sort of make it a little less exciting though when the prime number was
discovered with computers, I mean compared to the old days when prime numbers were discovered by
the human brain?

TERENCE TAO: That's true. I mean most mathematicians nowadays we don't actually spend our time
calculating things like that any more because we have computers to do it. But on the other hand
these sorts of calculations are actually used for other purposes too like in cryptography.

When you encode for example if you want to make sure that your transactions on the internet are
secure or the ATM machine is secure, you encode your communications using the type of mathematics
that is also used to find these primes and so by getting better practice at doing these very large
computations we also get better confidence how to do these cryptographic algorithms properly and to
see how secure they are.

It's called the positive and negative. I mean it's no longer pen and paper type mathematics but
knowing how to use computers better is the modern world so it's relevant in that respect.

ALISON CALDWELL: Have you actually seen this 13-million digit number.

TERENCE TAO: Yes well, it's on the internet but you know you don't learn anything by seeing it. I
mean it's 10-million digits long. I don't think I would get much out of staring at 10-million
digits. I think they're planning to make a poster with all the digits in a very, very tiny font. I
think it will just have artistic value. It won't actually be of that much use.

ALISON CALDWELL: The number is the 46th known Mersenne prime and the eighth to have been discovered
at UCLA. What is it about UCLA?

TERENCE TAO: Well actually UCLA's main contribution is that we just happen to have a lot of
computers lying around. There's lots of things going on in mathematics. We don't just, you know,
find really, really big numbers. That's just one very small part of mathematics.

One nice thing about this is that you can actually explain what we've done here. A lot of
mathematics nowadays is very hard, very abstract to have explained, but you can explain what a
prime number is and you can explain what a very, very big number is.

LISA MILLAR: Alison Caldwell with that report.