# Twin Prime Conjecture

• Posted 01.10.06
• NOVA scienceNOW

Prime numbers—those that can only be divided by themselves and one—bear a mystery. Why do primes tend to pair up? Five and seven, for example, are prime, as are 41 and 43, and 101 and 103. For millennia, mathematicians have wondered: Does this continue no matter how high one counts? As this video and its original song reveal, a mathematician has just given us an answer to this age-old enigma.

Running Time: 03:00

## Transcript

### TWIN PRIME CONJECTURE

PBS Airdate: January 10, 2006

ROBERT KRULWICH: Our next story concerns prime numbers. It's a mystery that's been around for 2,300 years, since the days of the great mathematician Euclid.

Now a prime number, for those of you who have forgotten, is a number which can only be divided by itself and one. And there is this curious thing about primes. They seem for some reason to clump together. So if you start with 5, you'll notice that 5 is very close to 7. And then the next prime's 11 right next to 13, and then 17 very close to 19. And Euclid wondered, well do they just go on like this clumping and clumping forever? No matter how high you count?

Well, a mathematician has just given us an answer. And we thought the answer so intriguing that it was worth a song. So here it is, "Euclid's Twin Prime Conjecture" performed by our singing reporter, Rob Morsberger, for an audience of mathematicians.

ROBERT MORSBERGER (Singing):

Prime is the number
That is only divisible by itself and one.
They have no other factors,
Though they may have their detractors.
They are kind of fun.

MEL NATHANSON:

They have no detractors, everyone loves a prime.

ROBERT MORSBERGER(Singing):

'Cause they like to come in pairs,
with a number in between.
Just like 5 skip 7, 41 skip 43.
The name of our lecture, is "The Twin Prime Conjecture."
Primes will pair into infinity.

MAN:

11 skip 13.

KEVIN O'BYRANT:

17 skip 19.

ROBERT MORSBERGER (Singing):

Empirically we know,
This pattern reappears, however high we count.
Will it keep on skipping just like this?
Or somewhere down the line
Will it peter out?

TOM MORGAN:

No, we think it's going to go on forever, but no one knows.

ROBERT MORSBERGER (Singing):

Euclid first proposed this around 300 B.C.,
But none's ever proved it, in all of history.
Well this year Daniel Goldston, from the U of San Jose,
Says the pattern will continue,
In this skippy kind of way.

MEL NATHANSON:

His results certainly suggest it.

ROBERT MORSBERGER:

Goldston didn't prove the conjecture.

CARLOS MORENO:

ROBERT MORSBERGER:

A major advance. He did show that primes appear close together.

KEVIN O'BYRANT:

Kind of big skips.

GREG CHUDNOVSKY:

Gaps.

ROBERT MORSBERGER (Singing):

Gaps! A big step in the right direction.
They like to come in pairs, with a number in between.
11 skip 13, 101 skip 103.
The name of our lecture,
Is "The Twin Prime Conjecture."
Primes will pair into infinity.

## Credits

### Twin Prime Conjecture

Executive Producer
Samuel Fine
Executive Editor
Robert Krulwich
Senior Series Producer
Vincent Liota
Senior Producer
Robe Imbriano
Producers
Julia Cort
Carla Denly
Robe Imbriano
Dean Irwin
Vincent Liota
Mary Robertson
Win Rosenfeld
Editors
Ben Ehrlich
Nathan Hendrie
Robe Imbriano
Vincent Liota
Win Rosenfeld
Supervising Producer
Andrea Cross
Development Producer
Kyla Dunn
Program Editor
Steve Trevisan
Associate Producers
Anthony Manupelli
Mary Robertson
Win Rosenfeld
Ayo Babatunde
Shimona Shahi
Unit Manager
Candace White
Production Secretary
Ayo Babatunde
Compositing
Yunsik Noh
Production Assistant
Robbie Gemmel
Music
Rob Morsberger
NOVA scienceNOW Series Animation
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Chris Borghesani
Brian Dowley
Tom Fahey
Vikram Gandhi
Robert Hanna
Michael Hunkley
Sound Recordists
Paul Austin
Vikram Gandhi
Mike Karas
Dennis McCarthy
Gilles Morin
Alex Sullivan
Audio Mix
John Jenkins
Animation
Mitch Butler
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Picket Design
Pie Design
Special Thanks
Clifford Cunningham
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The New York Number Theory Seminar
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Paula S. Apsell

NOVA scienceNOW is a trademark of the WGBH Educational Foundation

This material is based upon work supported by the National Science Foundation under Grant No. 0229297. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Image credit: (prime numbers) © NOVA/WGBH Educational Foundation

## Participants

Robert Krulwich
Rob Morsberger
Correspondent

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