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## 12M Digit Prime Number Sets Record, Nets \$100,000232

coondoggie writes "A 12-million-digit prime number, the largest such number ever discovered, has landed a voluntary math research group a \$100,000 prize from the Electronic Frontier Foundation (EFF). The number, known as a Mersenne prime, is the 45th known Mersenne prime, written shorthand as 2 to the power of 43,112,609, minus 1 . A Mersenne number is a positive integer that is one less than a power of two, the group stated. The computing project called the Great Internet Mersenne Prime Search (GIMPS) made the discovery on a computer at the University of California, Los Angeles (UCLA) Mathematics Department."
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## 12M Digit Prime Number Sets Record, Nets \$100,000

• #### Actually the 47th (Score:5, Informative)

<eldavojohn@@@gmail...com> on Thursday October 15, 2009 @11:45AM (#29758193) Journal

The number known as a Mersenne prime, is the 45th known Mersenne prime, written shorthand as 2 to the power of 43,112,609, minus 1

Wikipedia lists it as [wikipedia.org] the 47th known prime.

• #### Re: (Score:2)

It is the second largest prime: Both of all primes and Mersennes. It is not, as the summary states, the "largest such number ever discovered"
• #### Re:Actually the 47th (Score:5, Funny)

on Thursday October 15, 2009 @01:52PM (#29759955)

It is the second largest prime: Both of all primes and Mersennes.

Wow, does that mean we're close to discovering the largest prime?

• #### Re: (Score:2)

Yep, there' only one more left - just multiply all the ones we have and subtract 1. Err... and multiply all the ones we have and add 1. Crap, now there's more prime numbers to multiply.

• #### Re: (Score:3, Informative)

Is it strange to anyone else that this number can be written as 2 to the 43,112,609 minus 1, and 43,112,609 is itself...
• prime
• furthermore, a Germain prime
• the hypotenuse of a pythagorean triple (with 13003809 & 41104720)
• the sum of two squares (3880 & 5297)

This number itself has a lot of notable properties, besides generating another prime when plugged into the ol' 2-to-the-n-plus-1 thing...

• #### 45th in order of discovery (Score:4, Informative)

on Thursday October 15, 2009 @12:45PM (#29759033)
The article is correct by order of discovery- it was the 45th Mersenne prime to be discovered (on August 23, 2008.) Two smaller Mersenne primes were discovered later, on September 6, 2008 and April 12, 2009, which are also included in the Wikipedia table.
• #### Re: (Score:2)

How did they miss 2?

• #### Re: (Score:2)

What are these numbers good for? Is there a reason, other than the love of math, that a non-profit which accepts donations would pay \$100,000 for this?
• #### Re: (Score:2)

computing friggen large numbers isn't as easy as it appears. Consider the fact that your computer contains a discrete(limited) number of bits, and the processor can operate on about 64 bits at a time (depending on architecture). Try putting 2^100 into a scientific calculator, it will probably overflow (can't represent a number that large). 2^43,112,609 is a huge, huge, number.

• #### Re: (Score:2)

There are many many many applications for a large prime...stronger encryption being just one. Google is your friend.
• #### Sounds cool, but... (Score:3, Insightful)

<(moc.liamg) (ta) (eiuolyeknomg)> on Thursday October 15, 2009 @11:49AM (#29758267)

Call me a n00b, but I'm unsure there are any ways to use this newfound information about prime numbers.

Next time good ol' (2^43,112,609 - 1) comes up in conversation, I'll make sure to impress everyone with my new knowledge, but other than that, I feel no smarter for having read this article.

• #### Re:Sounds cool, but... (Score:5, Funny)

on Thursday October 15, 2009 @12:00PM (#29758417)

n00b

• #### Re: (Score:3, Funny)

Call me a n00b, but I'm unsure there are any ways to use this newfound information about prime numbers.

Next time good ol' (2^43,112,609 - 1) comes up in conversation, I'll make sure to impress everyone with my new knowledge, but other than that, I feel no smarter for having read this article.

You think you feel bad? Talk to the guy who just signed that \$100,000 check for this...

• #### Re: (Score:3, Interesting)

Talk to the guy who just signed that \$100,000 check for this...

...who works for EFF.

So what's their interest in this? Is it cryptography related?

• #### Re:Sounds cool, but... (Score:4, Informative)

by Anonymous Coward on Thursday October 15, 2009 @01:11PM (#29759377)

Think about how easy it is for a computer to multiply together (2^43112609 - 1) and (2^13466917 - 1).

Then think about how long it would take a computer to identify the factors of the resulting number, given that it is composed of two primes with twelve and four million digits, respectively.

Cryptography is all about simple math operations that can be performed one way, but cannot be easily and quickly reversed without knowing a secret (in my example, one of the original primes).

• #### Re: (Score:2)

It's not easy for a computer to multiply those two numbers! You would have to perform 2^56582998 multiplications (on a 64-bit processor) and as many additions... That would take pretty much literally forever.

• #### Re: (Score:2)

Um... the primes in question are just a long list of ones.

• #### Re: (Score:2)

So what's their interest in this?

That's what I was wondering, so I peeked [eff.org]. Initially when I saw this article, I was a bit disturbed, since people don't donate to the EFF for this purpose--that's what contributions to research organizations and universities are for. However, it turns out the money comes from a private individual specifically for this purpose; the EFF merely administers the award. It's free publicity for 'em in a good cause, a Good Thing by my reckoning.

• #### Re: (Score:2)

It's a separate donation fund managed by the EFF. They're not stealing from our brave soldiers fighting the RIAA and the government.

• #### Re: (Score:2)

Call me a n00b, but I'm unsure there are any ways to use this newfound information about prime numbers. Next time good ol' (2^43,112,609 - 1) comes up in conversation, I'll make sure to impress everyone with my new knowledge, but other than that, I feel no smarter for having read this article.

So as long as you know that water is wet, the sky is blue, and the Sun goes around the Earth you are content?

• #### Man, oh, man... (Score:5, Funny)

on Thursday October 15, 2009 @11:50AM (#29758283) Homepage
The biggest prime number I know is 8675309. I'll have to tell Jenny about this new one.
• #### Re: (Score:2)

Damn you Tommy Tutone!

• #### Re: (Score:2)

What about 2 ^ 2079460347? You know, the odds that you can get rescued while floating in outer space by a passing Heart of Gold.

• #### Re: (Score:2)

That's clearly not a prime number! The "2 ^" gives it away!
• #### Re: (Score:2)

But the best prime "number" (encoded of course) is 5t34k.

• #### I'm way late to this thread (Score:2, Funny)

by Anonymous Coward

(2^43,112,609 - 1)th post!

• #### A Question (Score:2)

What is it about Mersenne Primes that makes finding a new one worth \$100k? Is there an intrinsic value to the number or is it just one of those things that are so hard to do, like running a world's record hundred meters, that the effort and talent to do it merits a rewarded?
• #### Re: (Score:2)

The more digits that prime numbers have, the further apart adjacent primes are. If you imagine the value of a prime number represents the distance along a coastline in terms of centimeters, then you would only need a few billion to cover the entire length of a continent, and adjacent prime numbers would be separated by a few hundred metres.

These Mersenne prime numbers are hundreds of digits long, so as a distance that would be measured in light years, nor metres or kilometres. There just isn't the computati

• #### Re: (Score:2)

The more digits that prime numbers have, the further apart adjacent primes are.

That's not actually true. As numbers get larger you'll get longer composite runs, but you'll still find prime constellations between some of those runs. If what you say was true, the twin prime conjecture would be closed with a "Myth: BUSTED!" sticker on it, instead of open with overwhelming evidence in its favor.

• #### Re: (Score:2)

I think what he meant is that on average adjacent primes get further apart (see prime number theorem [wolfram.com]).

• #### Re: (Score:2)

What is it about going to the Moon that makes it worth spending \$20 billion? Advances in pure mathematics aren't done for immediate benefit, they are done on the off chance that the new "discovery" might be useful some day, like non-Euclidean geometry. In this case, it was more of an incentive to develop the algorithms and computing power necessary to deal effectively with the problem space. Hopefully this provided insights into how other large, intractable problems may be solved.
• #### Re: (Score:3, Interesting)

I think \$100,000 is roughly how much, in electricity costs, it costs to run the many, many computers for 5-10 years needed to grind out this particular number. Plus maintenance and taxes. You could pretty much say this research was done "at cost".

• #### Whoever added the "founditontheground" tag... (Score:3, Insightful)

on Thursday October 15, 2009 @12:22PM (#29758729) Journal
...is a freaking genius. I can't stop laughing. I tip my hat to you, good sir/ma'am.
• #### What a wasted opportunity (Score:5, Funny)

on Thursday October 15, 2009 @12:32PM (#29758863)

• #### Re:What a wasted opportunity (Score:5, Funny)

on Thursday October 15, 2009 @12:54PM (#29759153)

yeah, brilliant idea. next day's headline would be "Five Mathematicians Slain in Argument Over Division of Prize Money"

• #### Re: (Score:2)

yeah, brilliant idea. next day's headline would be "Five Mathematicians Slain in Argument Over Division of Prize Money"

Why? It's not like the prize is in Yen.

• #### I'm pissed! (Score:4, Funny)

on Thursday October 15, 2009 @12:45PM (#29759023)
Now that everyone knows this number, I have to change my luggage combination again. Thanks for nothing EFF!
• #### So what is it? (Score:2)

What is the awesome number? The summary makes a big deal about this number but doesn't include it! WtF?

• #### Re: (Score:2, Informative)

There is a link in TFA to the number. It gives an abbreviated version first, but links to the full number as well:

• #### Re: (Score:2)

I hope you were going for funny here, although I am curious as to how much RAM firefox would eat trying to display a page displaying a 12 million digit long string.

• #### Re: (Score:2)

Before: 140 MB used
Several minutes and 1 maxed CPU core later: Jumping between 250 MB and 300 MB used before I gave up and closed the tab.

• #### Re: (Score:2)

i was.

Yeah, that would be h00t. Lemme see what happens to IE....

170MB. Wow.

• #### Amazing coincidence (Score:2)

The number, known as a Mersenne prime, is the 45th known Mersenne prime, written shorthand as 2 to the power of 43,112,609, minus 1

That's amazing. I've got the same combination on my luggage!

• #### Various useful details (Score:4, Interesting)

on Thursday October 15, 2009 @01:34PM (#29759687) Homepage

The project GIMPS that is mentioned in the title uses a distributed computing system to search for Mersenne primes. They use a modified form of the Lucas-Lehmer test http://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test [wikipedia.org] where they use a Fast Fourier Transform to be able to do the large multiplications efficiently.

We care about Mersenne primes because they correspond to even perfect numbers. If one has a Mersenne prime 2^p -1 then (2^p-1)(2^(p-1)) is an even perfect number. This was proven by the ancient Greeks. Euler then proved much later that every even perfect number is of this form. The oldest two unsolved problems in mathematics are whether there are infinitely many even perfect numbers and whether there are any odd perfect numbers. Thus, every time we discover a new Mersenne prime we get a new even perfect number. And if we can ever get enough insight to resolve whether or not there are infinitely many Mersenne primes then we can resolve one of the oldest unsolved problems in all of mathematics.

• #### I'm glad it's voluntary (Score:2)

From TFA:

A 12 million digit prime number, the largest such number ever discovered, has landed a voluntary math research group a \$100,000 prize from the Electronic Frontier Foundation (EFF).

I'd hate to learn that EFF is using slave labor.

• #### Thank goodness it's voluntary (Score:5, Funny)

on Thursday October 15, 2009 @01:47PM (#29759887) Homepage Journal

A 12-million-digit prime number, the largest such number ever discovered, has landed a voluntary math research group a \$100,000 prize from the Electronic Frontier Foundation (EFF).

"Voluntary" math research group? Is there any other kind?

I'm trying to imagine an "involuntary" math research group, and all I'm getting is scenes from dystopian science fiction ... or possibly a scene from the life of Léon Theremin [wikipedia.org].

• #### Re: (Score:2)

In this case I presume that voluntary is referring to the fact that people do this as a hobby. The Great Internet Mersenne Prime Search is run by volunteers, not people doing research as academics or such.
• #### My irony must be rusty (Score:2)

Well, sure. I was shooting for droll irony -- must've aimed low.

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