Prime Challenge Sends Mathematicians On Infinite Search

University of New Hampshire professor Yitang Zhang announced this week that he has come close to solving a centuries-old problem: proving the twin prime conjecture. Host Scott Simon gets an explanation from Weekend Edition Math Guy Keith Devlin of Stanford University.

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SCOTT SIMON, HOST:

A University of New Hampshire professor announced this week he's come close to solving a centuries-old problem proving something called the twin prime conjecture. We asked our math guy - Keith Devlin, of Stanford University - to join us, as he does now from their studios. Keith, thanks very much for being with us.

KEITH DEVLIN: Thanks, Scott. Nice to be with you again.

SIMON: Nice to be with you. And first, I didn't know there was such a thing as close in math. I mean, my seventh grade would have been a lot different had I known that.

DEVLIN: There is indeed close and this story is interesting because for this one close turns out to be within 70 million. It's about prime numbers, the whole numbers that are only divisible by themselves and one, so 2, 3, 5 and 7, the primes less than 10, and 4, 6, 8 are the non-primes less than 10. The twin prime conjecture is a curiosity and it says that there are infinitely many pairs of primes which are just separated by two.

For example, 3 and 5, 11 and 13. They're prime numbers and they're just two apart. So you've got these pairs of primes, but the conjecture is that there are infinitely many of them. It's not a world-shattering result, but it's a mathematically interesting result simply because it's a challenge. This is sort of a Mount Everest question that you just want to solve because it's out there.

But some very famous and powerful mathematicians over the centuries have tried to prove this and come up short until this new result by Yitang Zhang, which says that there are actually infinite many pairs of primes which is separated by no more than about 70 million. But remember, to the lay person, $70 million sounds like a lot of money. To Bill Gates, $70 million is small change.

So mathematicians who are used to thinking in terms of infinity, the fact that there's any finite bound is huge.

SIMON: With respect for what the professor has done, or should I put it almost done, how does it make our life richer?

(LAUGHTER)

DEVLIN: This probably doesn't. It's always very difficult to make conjectures. I mean, back in the 19th century, one of the most famous people in number theory, who did a lot of work on prime numbers, said that the work he did would never have applications. Well, now that work is the basis of the encryption systems that run the whole of the Internet. So we should be very cautious about saying anything to do with prime numbers doesn't have applications.

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SIMON: Keith Devlin, our math guy, speaking with us from Stanford. Thanks so much.

DEVLIN: OK, my pleasure, Scott.

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SIMON: This is NPR News.

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