42nd Mersenne Prime Confirmed

Jazzer_Techie writes "The possible Mersenne Prime discovered last week has now been confirmed. This prime has 7,816,230 digits, which makes it not only the largest Mersenne Prime, but also the largest prime of any kind ever discovered. For those who don't want to take time to read the article, the prime is 2^25,964,951 - 1."

2^25,964,951 - 1

[Joey Patterson]

Can anyone post those digits in case the site gets /.'ed?

Re:2^25,964,951 - 1

[mrspecialhead]

Here's an Exclusive Binary Preview!

11111111111111111111111111111111
11111111111111111111111111111111
11111111111111111111111111111111...

--Your free demo has expired. For access to the rest of this content, please subscribe!--

Re:2^25,964,951 - 1

[Eric Smith]

My web site has the full expansion in binary [brouhaha.com]. It's over 25 megabytes, so please don't download it unless you really need it.

Re:2^25,964,951 - 1

[TheSHAD0W]

Hope your web server has gzip and/or bzip compression...

M42.gz.gz.base64

[Morosoph]

Homegrown, gziped twice, and base 64 encoded :-)

begin-base64 644 M42.gz.gz
H4sICOMCIUIAA000Mi5nei4A7dw9jgEBAAXgGbZ gI1Yi0SiMZDoamy00Cgqd
RKMWvUPYKOmdgMQB9Jxis7XolEr i7woKId9XvfId4OWVJqnUNlFuBcnOz3ew
3/wGV6NocdoVlp8 BAAAAAAAAAPDiRv/jZHgL0fmv3e0BAAAAAAAAAK9u8JX9
uI8 Cjv1i89llAAAAAAAAAICHzRv1+LYFyB3Oq8rwmRcFvJF1nK+mM 7PaNLwA
+SBAu5ViAAA=
====

Re:2^25,964,951 - 1

[DJStealth]

Can you post the 2's compliment of that? :)

Re:2^25,964,951 - 1

[bird603568]

actually its 25964951 :)

Re:2^25,964,951 - 1

[KinkifyTheNation]

So can I...

2^25,964,951 - 1
Voila!

Torrent

[TorrentNinja]

Here is a torrent of the prime number.. it's 25MB..

M42.torrent [simplecache.com]

Some good times testing bandwidth :)

Re:Torrent

[kyhwana]

Oops, look like the tracker is down. Anyone have another tracker/.torrent?

Re:2^25,964,951 - 1

[neurophys]

Just started my PC to compute it:
echo "2^25964951-1"|bc -l>prime

If you put 'time' in front, the system will tell you how long it takes.

Just checked that 2^1000000 took about 8,5s, but it is not linear. I expect it to take some 15 minutes one my AMD64

Re:2^25,964,951 - 1

[maxwell demon]

No problem. I just asked the C compiler, and it told me the result is 25964948.

Re:2^25,964,951 - 1

[penguinoid]

Can anyone post those digits in case the site gets /.'ed?

In binary, it's just a fucking lot of 1's (25,964,951 of them, almost 26 megabytes). If you could even count them all to be sure it's right, I'd be incredibly impressed. In decimal it's still really huge and looks incredibly complicated.

Comment removed

[account_deleted]

Comment removed based on user account deletion

PARENT NOT FLAMEBAIT (GIMPS:name of project)

[Anonymous Coward]

GIMPS is the name of the project that apparently was responsible for finding this, so the parent was a joke, not flame bait.

Re:Man.

[halivar]

Those math freaks sure are a bunch of GIMPS.

All I know is this: Stephen Hawking is married to a real woman and I'm not.

OMG

[computerme]

No Way!!

2^25,964,951 - 1.

Is my password! Oh Man, I guess everyone knows it now....

Re:OMG

[penguinoid]

In what base? If it is in binary you wouldn't be able to get it past the lameness filter.

Re:OMG

[confused philosopher]

"2^25,964,951 - 1.
Is my password! "

Really? That's the password on my luggage! Now I have to get my dark sith to change it for me!

And useful, too!

[Eric Smith]

Now we can use the 41st and 42nd for a 50 megabit RSA key.

to put this into perspective

[sgant]

To put this into real-world perspective, if you had 1 dollar for every digit in the number, you would have 7,816,230 dollars!

Wow...

Re:to put this into perspective

[kanweg]

So??

Bill G.

Re:And useful, too!

[Alsee]

Isn't that kinda overkill?
I'm going to use 2 as the second prime.

-

Its the answer!

[Rs_Conqueror]

This is the 42nd one? I wonder if that means anything...

Re:Its the answer!

[igny]

Clinton must be proud.

Re:Its the answer!

[zoloto]

THIS IS THE Answer to life, the universe and everything [google.com]

!!! YES! Douglas Adams would be proud!

Re:Its the answer!

[freitasm]

The OP was obviously referring to the Question... But what is the question now?

[For you others, check Hitchiker's Guide to the Galaxy]

Re:Its the answer!

[Bake]

Relax, obviously they haven't found the Answer yet. Otherwise the universe would once again have been replaced by something even more bizzare and inexplicable. :-)

Participate in the search

[Drooling_Sheep]

GIMPS [mersenne.org] (Great Internet Mersenne Prime Search

They have Windows, Linux, FreeBSD, and OS/2 clients.

Re:Participate in the search

[LinuxHam]

You have the right idea [worldcommunitygrid.org] , but why limit yourself?

42!!!

[MicroBerto]

This one contains all the information to the meaning of life, the universe, and everything!

Re:42!!!

[maxwell demon]

Looking at the binary representation, I conclude: Life, the universe and everything are all one, just repeated many times.

Re:42!!!

[maxwell demon]

I think it was something along the line of "What is the product of the sixth and the nineth Mersenne Prime?"

Why?

[Ensign Regis]

I'm not trying to be a troll here, but of what possible value is a really big prime number? Is there any practical value to it, or is it just an interesting bit of trivia?

Re:Why?

[irokitt]

...of what possible value is a really big prime number?

I believe the search for Mersenne primes continues solely for the purpose of impressing women in bars. No, I don't think it would work either.

Re:Why?

[MC68000]

The best reason for large Mersenne prime numbers that I can think of is that it gives data for mathematicians to formulate conjectures. There are many consequences to theoretical breakthroughs in the field of prime numbers, especially in the field of encryption, as the RSA algorithm requires large prime numbers.

Note: This new prime number by itself is USELESS for encryption. There are only 42 Mersenne numbers, so they can't be used because there are insufficiently many.

Re:Why?

[Ayaress]

Maybe there are an infinite number, but there are 42 found. I'd list them here, but at least one of them is seven million digits and my 8 key is broken.

Re:Why?

[skybird0]

The question of the number of Mersenne primes is open. It might very well be finite.

Re:Why?

[Skiron]

A lot of it is to do with number theory research. No one knows the extent of prime numbers, nor indeed an algorithm to find them.

Re:Why?

[MC68000]

There actually are very good algorithms for finding primality. It has reached the point where proving a number prime is MUCH easier than finding any factors of it.

There are two types. One is deterministic, and will give you absolute proof that the tested number is prime. The other type is probability based. These are more popular. The most widely used is known as the Miller-Rabin test. It is known to be absolutely correct for all n 3*10^16. For larger n, it will never report a composite to be prime, but there is a small (around 10^-20) chance the "prime" number will be composite. There are no known prime numbers that Miller-Rabin reports to be composite.

In the case of Mersenne numbers, it's a different story. There is a deterministic algorithm called the Lucas-Lehmer test. This will determine whether 2^p-1 is prime with O-notation p! The catch of course is that it only works for Mersenne numbers.

Re:Why - algorithm

[Skiron]

'algorithm' was wrong to use. I meant 'formula' in that numbers need to be tested to be prime, you cannot deduce by applying a known interation - hence why it takes such a long time to compute proof of a possible candidate.

Re:Why?

[Coryoth]

It has reached the point where proving a number prime is MUCH easier than finding any factors of it.

Primality is in P in fact. It is just not a very conveniently low exponent (about O(n^9) dropping to about O(n^6) for most cases) so porbablistic algorithms are still the popular way to go.

Jedidiah.

Re:Why?

[cryptor3]

There are no known prime numbers that Miller-Rabin reports to be composite.

I'm certain that you can prove that no prime numbers will ever be reported composite by the definition of the test, but I don't have any number theory texts around me. I'm sure you can just look it up online. Or probably in Schneier's Applied Cryptography, too.

If it didn't do that, the test would be useless.

Re:Why?

[fredrikj]

For larger n, it will never report a composite to be prime, but there is a small (around 10^-20) chance the "prime" number will be composite.

Actually you got that first statement the wrong way around (and the second one right; they're in conflict with each other if you think about it). The Miller-Rabin test may report a composite to be prime, but may never report a prime to be composite.

Also, the chance is (1/4)^n, where n is the number of bases you test the number against. So if you choose more bases, t

Re:Why?

[fredrikj]

Nope, I'm right. (In fact, I've written a program implementing the Miller-Rabin test myself.)

If you read the Wikipedia article, you'll see:

It can be shown that there always exists a strong witness for any odd composite n, and that at least 3/4 of the values for a are strong witnesses for the compositeness of n.

Also Mathworld [wolfram.com] says:

If N multiple independent tests are performed on a composite number, then the probability that it passes each test is 1/4^N or less.

And according to this page [abdn.ac.uk]:

Choose k i

Re:Why?

[onemorechip]

It has reached the point where proving a number prime is MUCH easier than finding any factors of it.

Unless the number in question is composite. In that case, it is MUCH easier to find factors of it, than to prove that it is a prime.

Re:Why?

[AnyoneEB]

But proving a composite number to be prime is impossible, so any possible task would be easier. The grandparent was a joke. Laugh.

Re:Why?

[Sneftel]

It has reached the point where proving a number prime is MUCH easier than finding any factors of it.

Great! Now all we have to do is find a way to prove that ALL numbers are prime, and our factoring needs will be a thing of the past!

Re:Why?

[sylvester]

My recollection of Miller-Rabin is that, for each iteration, it returns either "Composite" or "Probably prime."

With each iteration, you increase a power of 1/2 that your "unknown" number is actually prime. So if it makes it through 20 iterations, it's 1/2^20 that it's composite, and 1 - 1/2^20 that it's prime.

I'm not sure where the grandparent got his 10^-20 number.

Re:Why?

[azaris]

The density of primes is well known by the Prime Number Theorem. To find them in practice takes simply lots of tries and probabilistic tests to weed out the composites. The problem with primes is not finding them but finding the prime factors of an arbitrary integer.

Re:Why?

[adrianbaugh]

You can prove not only that there is an algorithm to find the primes, but there is an algorithm to find any sequence of numbers you care to produce. It's a really ugly formula though (and generates lots of spurious negative answers), and not particularly interesting. See "The Music of the Primes" (search on Amazon or somewhere) for details.

Re:Why?

[max born]

Perhaps that's why there's no Nobel Price for mathematics.

Re:Why?

[thelenm]

of what possible value is a really big prime number?

Here's one possible value: 2^25,964,951 - 1.

Might not be the 42nd largest

[MarkByers]

It is confirmed that it is a prime, but it hasn't yet been confirmed that it is the 42nd largest prime, because some numbers have not been checked.

From TFA:

However, note that the region between the 39th and 40th known Mersenne primes has not been completely searched, so it is not known if M20,996,011 is actually the 40th Mersenne prime.

Re:Might not be the 42nd largest

[Eric Smith]

Of course it's not the 42nd largest prime. It's not even the 42nd largest known prime. It is the largest known prime.

It is easily proven that there ISN'T a 42nd largest prime, because there isn't a largest prime.

Re:Might not be the 42nd largest

[Vicsun]

What the parent meant was that it's not verified it's the 42nd mersenne prime. It's currently the largest one known, but it is possible there's another mersenne prime between the 41st and 42nd, making this the 43rd.

Re:Might not be the 42nd largest

[man_ls]

Primes are odd. Odds * Odds = Odd, + 1 = Even. Even is impossible of being prime.

Nice try though ;)

Re:Might not be the 42nd largest

[pmjordan]

Except for the very first prime number, which is 2, of course. Which makes the whole thing odd again.

~phil

Re:Might not be the 42nd largest

[man_ls]

I hereby move that the number 2 be stricken from the Integers, thus correcting my misstatement.

Re:Might not be the 42nd largest

[flynt]

Replace "largest" with "Merseene" and your sentence would be correct. It is the largest known prime. It is a Mersenne prime. It is not the largest prime number, since there is no largest prime number. It may or may not be the 42nd Mersenne prime since they might have missed some in between (still checking). There, I think that's all the facts.

Re:Might not be the 42nd largest

[maxwell demon]

It's certainly the 42nd Mersenne number which has been found to be prime (i,e, if sorting the Mersenne primes for the date when they have been found to be prime, then this one is at position 42). Note that future discoveries won't change that (except if any "known" Mersenne primes turn out not to be prime, i.e. if there was an error in the testing), the next Mersenne prime to be identified will be the 43rd, even if it's smaller.

Mersenne GIMPS FAQ

[bigtallmofo]

The FAQ for this endeavor can be seen here [mersenne.org].

One glaring ommission from the FAQ is "Why participate in this?" I guess if you have to ask why, there's no point in asking.

Re:Mersenne GIMPS FAQ

[spoonyfork]

One glaring ommission from the FAQ is "Why participate in this?" I guess if you have to ask why, there's no point in asking.

You're right, compared to protein folding, cancer research, and other research projects there is no good reason to run GIMPS. Heck even SETI@home could return something useful. But there are a couple reasons to do it:

• One reason is money. The EFF put up a $100,000 [mersenne.org] prize for the discovery a 10 million digit prime.
• Another reason is developing new algorithms and enhancing existing on

Re:Mersenne GIMPS FAQ

[mblase]

One glaring omission from the FAQ is "Why participate in this?" I guess if you have to ask why, there's no point in asking.

Finding new and interesting numbers is the mathematical equivalent of climbing Mt. Everest -- you do it because they are there.

I wonder

[opusman]

Maybe Paris Hilton could use this prime to encrypt her phone book next time?

Re:I wonder

[AvantLegion]

>> Maybe Paris Hilton could use this prime to encrypt her phone book next time?

Use the number of men she's been slammed by to encrypt her cell phone data? BRILLIANT!

Largest known perfect number?

[The Wookie]

So does this make (2^25,964,951 - 1) * (2^25,964,950) the largest known perfect number?

Re:Largest known perfect number?

[MC68000]

yes. There is a theorem due to Euclid that every even perfect number (a number which is the product of all of its divisors except itself) is of the form
(2^n-1)*2^n. The given form does not apply to odd perfect numbers, but it is unknown whether any odd perfect numbers exist.

Re:Largest known perfect number?

[Eric Smith]

Does the theorem also prove that every integer of the form (2^n-1)*2^n is a perfect number?

Re:Largest known perfect number?

[CarlDenny]

You mean a number which is the *sum* of all of its divisors except itself.

A number which is the product of all its divisors except itself is, well, any product of exactly two primes.

Re:Largest known perfect number?

[Fortress]

Euclid only proved that any integer of the form ((2^n)-1)*2^n is a perfect number when (2^n)-1 is prime.

Years later, Euler proved that every even perfect number is of this form, i.e. there are no even perfect numbers not of this form.

Wikipedia reference [wikipedia.org]

Next Mersenne Prime

[Anonymous Coward]

I predict that the next one that will be found will be the 43rd. You heard it here first!

"Not only" the largest Mersenne prime ...

[gvc]

The top three previously known primes were Mersenne. Here's a list [utm.edu]. At the time they were discovered, almost all largest Mersenne primes have held the record for biggest prime until being edged out by another Mersenne prime. I am not sure when a non-Mersenne last had that status, but it is a rare occurrence.

Looking for Mersennes is "picking the low fruit" when it comes to prime hunting so I question the phrasing "Not only is it the biggest Mersenne .."

What would have been remarkable would have been if the new largest prime were *not* a Mersenne.

Re:"Not only" the largest Mersenne prime ...

[jeffwolfe]

I am not sure when a non-Mersenne last had that status, but it is a rare occurrence.

391581*2^216193-1 was the largest known prime from 1989 to 1992. Before that, the last non-Mersenne record was 1951-1952. A complete list can be found here [utm.edu].

Re:"Not only" the largest Mersenne prime ...

[gvc]

They can. It is just that Mersenne primes are fairly dense and trivial to test.

Numbers of the form k*2^n+1 are pretty dense and also easy to test, but not the gold mine that Mersennes are.

Big Deal - Javascript!!

[XanC]

I found it by leaving my browser open for a while on this page [surfeu.fi].

Re:Big Deal - Javascript!!

[bcmm]

Thank you very much for that link.
You've just brightened the day for hundreds of people.


2417 and counting...

Anybody else notice...

[joNDoty]

that the digits make a phone number?? 225-964-9511 used to dial the residence of a man in Baton Rouge, Louisiana. [whitepages.com]

Now all you get is "the number you have dialed is not a working number"

Could this be the first telephone slashdotting in history!?

Re:Anybody else notice...

[east coast]

Except perhaps 867-5309 [snopes.com].

and our final news of today...

[e**(i pi)-1]

... QWest announced to have solved their IT problems. Delayed phone connection times had appeared already in 1998 [distributed.net], when the company was called US West.

One use of Mersenne Primes...

[MAdMaxOr]

is the Mersenne Twister (MT), a pseudorandom number generator.

Pseudorandom number generators are periodic, that is they start repeating the sequence of "random" numbers, after a while. This is bad. The period of the MT is as big as the Mersenne Prime that you choose to base the algorithm on. So, if you wanted a REALLY long period, you could use this new prime. In practice, however, very few people need this long of a period.

Shift the "unsed" computational power...

[ChristianBaekkelund]

Ok, now that we've finally found prime numbers so ridiculously large as to never have any practical purpose within any of our lifetimes, can we stop running the GIMPS screen saver, and move over all that computational power to something that might actually help mankind (within our lifetimes, even)?

No, not SETI@home (which is about as useful as GIMPS), can't folks please switch to something like the UD/NFCR "Screensaver Lifesaver" that processes some various highly computationally intensive biological problems (ligand fitting, etc.) related to a number of issues (these are directed at cancer research, specifically):
- http://www.chem.ox.ac.uk/curecancer.html
- http://www2.nfcr.org/site/PageServer?pagename=scre ensaver
- http://www.grid.org/download/gold/download.htm

I don't know, maybe it's just me, but when I hear of all the people running GIMPS, SETI@home, etc. etc., I feel a tiny bit sad that maybe all those unused cycles could be used towards something more useful, but not as sexy...

Re:Shift the "unsed" computational power...

[maxwell demon]

That's just because you don't know that the extraterrestrials know the cure for cancer, but will not tell us unless we tell them a large enough prime ...

Re:Shift the "unsed" computational power...

[owlstead]

Not until they created a unix variant of their grid software. And not until I can be sure my PC is not abused, and that there are no possible weaknesses in their programs. They can do this either by creating a Java client (hint hint) or making their software open source.

Damn, I thought it said...

[payndz]

...Metroid Prime. I would finally have had a new game for my Gamecube!

And a REALLY hot cup of tea...

[Ironix]

2^25,964,951 to 1 against also happens to be the finite amount of improbability needed to generate the infinite improbability drive out of thin air.

Re:prime post

[dhakbar]

#11788398

That's an even number, so your post wasn't prime. Liar!

Re:not me

[MyLongNickName]

Sorry, that isn't prime. By definition 1 is not prime.

Re:not me

[sameerdesai]

Uhuh!! 1 is not a prime number

1 is not a prime

[tetromino]

because by definition, primes are elements of your current ring that generate a proper ideal. The ideal generated by a unit element in the ring is obviously the entire ring, i,e. not proper; and in the ring of integers, 1 is most definitely a unit.

Please take a math class before posting on this subject.

Re:1 is not a prime

[wwest4]

You know, with an attitude like yours, you really missed your calling as a nerd battle rapper.

Re:Largest Prime?

[MC68000]

That is not true. The number p1*p2*....*pn+1 is either a prime, OR it has a factor that is not one of the p's. In either case, you have a new prime, which as an aside proves that there are infinitely many primes.

Re:Largest Prime?

[MacGabhain]

3 * 7 + 1 is prime?

Re:Largest Prime?

[SamBeckett]

This is actually true but only if you enumerated every single prime up to your largest:

2*3 - 1 = 5
2*3*5 - 1 = 29
2*3*5*7 - 1 = 209 = 11*19

haha just kidding. /runs away

Re:Largest Prime?

[vorpal22]

Incorrect. If 2 is not in {p1, ..., pn}, then clearly for all i in {1, ..., n}, pi is odd since pi is a prime number not equal to 2. Thus, p1 * ... * pn is odd, and p1 * ... * pn + 1 is even, and hence, has a divisor, 2, and is not prime.

Want pi now!

[tepples]

No, it's a Wobbl and Bob section, of course! Go watch an episode [jolt.co.uk] or two or three point one four; when come back bring Pi.

Chudnovsky Brothers?

[Schwarzchild]

I wonder if Darren got his idea for the movie PI based on the exploits of two mathematicians who built a supercomputer in their spare bedroom and computed PI to billions of digits. The story was in the New Yorker but it is now here [barryland.com].

Re:Darren Aronofski section?

[hunterx11]

And Requiem for a Dream [imdb.com]. True, only two movies, but I certainly look forward to seeing his next.

Re:Darren Aronofski section?

[CastrTroy]

Yes, sometimes the best movies come from directors who don't put out 3 movies a year. Look at Tarantino, Kubrick, Tim Burton, as well as many others i'm probably forgetting.

Re:I have the next largest prime after this one

[Colonel Cholling]

Very clever, except not all numbers of the form 2^n-1 where n is prime are themselves prime.