# 45th Mersenne prime revealed

Number-porn lovers rejoice! The most ridiculously long prime number ever discovered has been verified and revealed in all its 12-million-digit glory. The enormous integer was fittingly discovered within the hallowed halls of the University of California, Los Angeles (UCLA) mathematics department as part of the Great Internet …

#### bah waste of computer power

As an avid DC enthusiast (top 2000 BOINC user) I have always felt the number projects like this one are not worth the fossil fuels they use up and pollution they create (equivalent to a very large datacenter in power use at least). I would much rather see people contribute to projects more useful to applied science in the near future such as Rosetta, WCG, F@H or even Einstein. DC does have the power to change the world and freedom of choice is great and my opinion means little but imho right now we need to focus on fighting diseases at the nano level as they affect all of us in one way or another and we are very close to conquering some of the worse scourages in human history. Crunch on baby!

#### It's certainly impressive,

but what sort of usefulness does it have?

I mean, you could never complete the series as numbers just go on forever, so surely this sort of effort being spent on something must be of value, right?

If it's just for bragging rights, or for the sake of it, then I'm very confused as to why $100,000 would be given away for it...

#### clarification

Only a positive integer can be a Mersenne number, otherwise (2^0)-1 = 0 or (2^ -1)-1 = -0.5 would be valid.

#### ...and...?

This might seem all neat and stuff, but I still have to wonder: what exactly is the point? There's not an upper limit (according to Euclid), and I don't doubt him. Does this help end hunger or cause world peace or stop (alleged) global warming?

#### What's the point?

I found some fluff in my belly button earlier. It took far less time and energy than this seemingly pointless pursuit.

#### "but there could be only one"?

... at least until the next largest is discovered, of course, assuming there is no maximum Mersenne prime, which doesn't seem unreasonable.

Besides, I don't know what all the fuss is about.. it's just eleventyone...eleventyone recurring!1!!

#### But...

... what about two to the power of two hundred and sixty seven thousand, seven hundred and nine (minus one)?

Or is that just Infinitely Improbable?

#### THATS ALOT OF DIGITS!!!!!

•A comment is required, in addition to a title, and must contain text.*

*Does this work?

#### The point

I have always understood, but perhaps incorrectly, that the point is that prime numbers are, for some reason, useful in encryption technologies. So having stupendously large ones allows for really pretty good encryption.

#### While it doesn't really matter pe se...

But for correctness, 63 isn't a prime number. 9 * 7 = 63.

#### The next one....

....may have God's name on it.

(although this is unlikely as he/she/it doesn't exist)

#### Use of primes

Well how about public key cryptography?

Of course with the fairly small number of primes that exist at this size the number of ones you'd have to test is fairly limited.

#### @ -What is the point?- people

This question is often asked, by many people, about many scientific and technical activities.

(They never ask this about artistic or other 'creative' efforts, perhaps because they don't 'understand' art but they definitely know all they need to know about science and technology)

The standard answers are out there and can be searched for and found. I could tell you, but what would be the point?

#### @clarification.

Since primes are integral, no negative power of two less one could ever be a prime anyway.

And to all the nay sayers, of course it's useful, just think of the cryptographic strength of ciphers based off a twelve million digit prime!

#### Maths?

'GIMPS said it would donate $25,000 of the prize money to charity and award $50,000 to the UCLA math department.'

OK , 25,000 + 50,000 = 75,000? so er, where's the rest of the 100,000 going?

Maybe they can't add up.?

#### @Ryan 7

It is not known whether there are an infinite number of Mersenne Primes. We're not going to find out by failing to find the next biggest one, however.

I think the original point of the prize was to encourage the development of faster supercomputers. Now that these problems are being attacked by ever-growing networks of PCs, I agree that it's a little pointless. If you want to join one of these communities of active screensavers, protein folding (Folding@home = folding.stanford.edu) is a more socially useful activity.

#### dollars per digit.

As a reward, that's not many $ per digit is it? Even online journalists have a better rate of return than that.

#### WTF??

Who gives a shit about "discovering" a 12.8 million digit number? It's always been there hiding!!!

far better to give me the cash, and I'll buy everyone a beer or two!!

#### Tough Logs?

Are all the Mathematicians at UCLA constipated ?

In which case they should just work it out with a pencil.

I have to agree with the comments here:

a) infinity by definition has no top end, therefore there will also be an infinite number of Mersenne Primes

b) does it really help us to know what they specifically are?

c) is there not something more useful they could put the computing power to - like the cancer project or any (infinite) number of more beneficial research projects - or perhaps one to combat the global warming by all that er, wasted computing power

#### (2^43112609)-1

#NUM! Entering a formula that produces a number that is too large or too small to be represented in Microsoft Excel

#### Re: Tough Logs?

"a) infinity by definition has no top end, therefore there will also be an infinite number of Mersenne Primes"

No it doesn't. Not even slightly.

"b) does it really help us to know what they specifically are?

c) is there not something more useful they could put the computing power to - like the cancer project or any (infinite) number of more beneficial research projects - or perhaps one to combat the global warming by all that er, wasted computing power"

Sheesh. Some people are so short-sighted. What do you gain by constructing a network of computers capable of testing the primality of very large numbers? Well, you might get an improved algorithm but one of the attractions of Mersenne primes is that there's a very easy(*) test. No, what you get is expertise in constructing large networks of computers for solving large, distributed problems.

What use are those? Well, read back through the comments about some of the other distributed computational projects.

And what use is knowing new Mersenne primes? What use is climbing Everest? What, cosmically speaking, is the point of the Mona Lisa?

Until quite recently there didn't seem to be much point in finding very large primes. Primes show up in all kinds of unexpected places so don't expect the use in cryptography (which depends on it being hard to find the factors of a product of two very large, unknown, primes) to be the last use.

Don't you (or anyone else) remember the laser being called a solution looking for a problem? And now look at the damn things, they're everywhere.

If you can't do something without it having an immediate and apparent application we'd live in a very boring world.

(*) For a given value of "easy".

#### @white_darkness @04:21

"While it doesn't really matter pe se... But for correctness, 63 isn't a prime number. 9 * 7 = 63".

Erm, ok, fair enough and thank you for your amazing mathematical insight.

However what are you on about?

The article said "A Mersenne number is a number that is one less than the power of two, or Mn = 2n – 1. The first few are 1, 3, 7, 15, 31, 63, and so forth (but add up quickly, as numbers tend to do). Mersenne primes are Mersenne numbers that are also prime numbers" - it does NOT attempt to say that 63 is prime. And why didn't you question the inclusion of 15?

#### @AC 09:40

a) Mersenne primes are a special case, and therefore there is no obvious reason to think that they are infinite.

Alternatively, note that the average gap between each prime increases exponentially over the smaller numbers. Extrapolating towards infinity, there must be an infinite gap between the last two primes, and therefore if the penultimate prime is finite, the last one must be greater than infinite, and therefore does not exist, making what I just described as the penultimate prime is actually the final one.

#### and it's use is???

And the purpose of having this prime is??? What is it's use? Does it have 1 or is it just curiosity? I'm sure they could go on infinately finding longer and longer primes, but is it of any use?!!

#### Wow...

...that is the second biggest Mersenne Prime I've ever seen!

Pirates, because the monkeys are listening...

#### Back again

When I were a lad studying number theory at college, it was often held to be the ultimate example of 'pure' mathematics. Elegant theorems, beautiful results, but of no possible application to the real world - and then Public Key Cryptography came along!

Of course, using Mersenne primes for PKC would be idiotic (like choosing a password of 'password'). If it's of any interest (probably not :), the common algorithms used to generate (pseudo-)random primes for PKC are known to be fallible. In << 1 in a billiion cases they will generate a non-prime (and the decryption process will fail). This is felt to be an acceptable trade-off for their significant benefits in speed of operation.

More to the point, why does the article refer to this as the 45th Mp, when (the infallible) Wikipedia gives it as the 47th?

#### @ @clarification

"Since primes are integral, no negative power of two less one could ever be a prime anyway"

I agree, but that wasn't my point. I was talking about Mersenne numbers, not Mersenne primes (a concept which white_darkness also seems to fail to grasp).

#### @MnM

"The Hitch Hikers Guide to the Galaxy says that the odds of being rescued by a passing spacecraft whilst asphyxiating in deep space are approximately 2^267,709 : 1 against.

"By a curious co-incidence this was also the telephone number of an Islington flat where Arthur Dent went to a very good party and met a very nice girl whom he totally failed to get off with...."

(Quoted from memory!)

#### @Back again

>More to the point, why does the article refer to this as the 45th Mp, when (the infallible) Wikipedia gives it as the 47th?

Because it was the 45th Mersenne prime to be discovered, but currently the 47th largest known Mersenne prime. The author of this story has presumably just awoken from a thirteen-month sleep -- see http://www.mersenne.org/primes/m45and46.htm, dated 15th September 2008. I pointed this out in an earlier post, but it seems to have been rejected by Vulture Central.

#### Oh dear -- or get a grip

"Alternatively, note that the average gap between each prime increases exponentially over the smaller numbers. Extrapolating towards infinity, there must be an infinite gap between the last two primes, and therefore if the penultimate prime is finite, the last one must be greater than infinite, and therefore does not exist, making what I just described as the penultimate prime is actually the final one."

Exponential? Are you sure? What about those pairs of primes (eg 17, 19; 29, 31)? Are there an infinite number of those? (So far as I know, that's not proven yet.)

As for infinite gaps between primes. What's 2*infinity? And if you give me a finite set of primes then I'll give you a number that doesn't have any of them as a factor -- I'll multiply them all together and add on.

As Douglas Adams almost said, "Infinity is big, you might think 2^43,112,609-1 is big but that's just peanuts to infinity." 2^(2^43,112,609-1) is pretty damn big, a lot bigger than the 45th known Mersenne prime. (And "known" because there are gaps, in which there might be other Mersenne primes).

#### @Graham Marsden

<Muntz> Ha Ha </Muntz>, quoting HHGTTG and missing this one, hand back your commentards badge :-)

Why calculate such big numbers when the answer to life, the Universe, and Everything is only 42 (after a seven and a half million years calculation).

Paris. . . . . Contrary to popular belief, Paris's favourite number is not 69... It’s a big 1

#### Bah!

This crap is "useful for cryptography"? In what universe? By the time the bloody message was encrypted and decrypted at the other end the answer wouldn't matter any more. Notwithstanding the technical issues of a key so long that no one personal computer posesses the power to represent it without losing some off the ends.

Do what thou wilt and all that, but this is the math equivalent of a tw*tdangle and is justly lambasted as such. No flying cars will be built from the "discoveries" this project reveals to the world.

#### Correction

Marin Mersenne was a Minum Friar, not a monk. So he would have been the friar around the priory, not a monk around the monastery...

#### Prime numbers and Encryption

http://www.madsci.org/posts/archives/1998-05/893442660.Cs.r.html