Mining For The 'Prime' Jewels Of Numbers The world's largest prime number clocks in at nearly 13 million digits. It's a type of number called a Mersenne, and mathematicians are using the Internet to outsource the computing power to find them, number-crunching away to find one that's even larger.

#### Mining For The 'Prime' Jewels Of Numbers

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Mining For The 'Prime' Jewels Of Numbers

# < Mining For The 'Prime' Jewels Of Numbers

#### Mining For The 'Prime' Jewels Of Numbers

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RENEE MONTAGNE, Host:

NPR's Joe Palca reports.

JOE PALCA: Well, let's say you wanted to write that out on a piece of paper, and you write 10 digits per inch.

(SOUNDBITE OF CALCULATOR PRINTING)

PALCA: So, that's 12,978,189 divided by 10 digits per inch divided by 12 inches per foot divided by 5,280 feet per mile. And the answer is...

(SOUNDBITE OF CALCULATOR PRINTING)

PALCA: It was discovered last summer as part of something called GIMPS.

MONTAGNE: GIMPS is the great Internet Mersenne prime search.

PALCA: Turns out, Mersenne primes are the easiest to find, and Woltman has written a free, downloadable program to search for them.

MONTAGNE: It takes about two or three weeks to test a single number, and everybody's plugging away trying to find yet another prime number.

PALCA: They've been doing it for 13 years and found 12 so far.

D: The main obstacle in proving these numbers prime is just doing the arithmetic with numbers that size.

PALCA: Chris Caldwell is a mathematician at the University of Tennessee at Martin. Caldwell says there's a formula to test if a large number is a Mersenne prime, but it's computationally intense.

D: Not only do you have to multiply a 13 million-digit number times a 13 million-digit number, you have to do that about 13 million times. And then that just takes a tremendous amount of computation.

PALCA: So, what's the big deal here? Why are some people so anxious to find the next largest Mersenne prime? I've asked several people, and the response is generally the same: because.

(SOUNDBITE OF LAUGHTER)

PALCA: I wasn't about to let him off the hook that easily, so he expanded a bit.

D: Mersennes, in a way, are kind of like a large diamond. When I go to Washington - I took my kids to see the Hope Diamond.

PALCA: The 45-carat diamond sits in a special case in the National Museum of Natural History, usually with crowds around it.

D: Nobody there looking at the Hope Diamond ever asks, you know, why did somebody bother to dig it up? Or, what is it good for? You know, even though it really isn't good for much other than to just hang there and people to look at. And in many ways, the Mersennes play that same role - that they really are the jewels of number theory.

PALCA: So, if it's the first quarter or sooner, I win, and if it's the second quarter or later, he wins.

D: Let me think.

PALCA: You thinking?

D: Yeah, I'm thinking. I think I'm going to go with George.

PALCA: Joe Palca, NPR News, Washington.