42nd Mersenne Prime Probably Discovered

RTKfan writes "Chalk up another achievement for distributed computing! MathWorld is reporting that the 42nd, and now-largest, Mersenne Prime has probably been discovered. The number in question is currently being double-checked by George Woltman, organizer of GIMPS (the Great Internet Mersenne Prime Search). If this pans out, GIMPS will have been responsible for the eight current largest Mersenne Primes ever discovered."

Comments

Uses?

[UncleJam]

What uses are there for gignatic prime numbers like this other than showing off computing power?
Encrypting?

Re:Uses?

[selectspec]

Chics dig it.

Re:Uses?

[Husgaard]

I don't the any real use for this except finding large primes.

The theory is that there is an infinite number of these numbers, but they are unlikely to prove the theory by finding them all...

Re:Uses?

[kaedemichi255]

Not to mention, it's just a side effect of the male syndrom of giant prime number envy.

Re:Uses?

[ackthpt]

Chics dig it.

Either that or their eyes glaze over and you sneak a quick peck before they slap you silly.

"ah, l'amour"

Re:Uses?

[Jeremy Erwin]

Testing distributed primality algorithms. I should have thought this was obvious.

And, no, one does not encrypt with Mersenne primes. The rarity of such numbers makes a "brute force" crypto-analysis seem rather plausible. Best to use an ordinary prime number-- there are, after all, many more of them to choose from.

Re:Uses?

[tehshen]

Yep, encrypting. Specifically, public-key cryptography, which requires two fairly-large (think hundreds of digits) prime numbers multiplied together to encrypt a message.

I pick two primes, say 3 and 5, and the product of these is 15. A message is encoded using the number 15. If you know the encoded message and the product, you can decrypt it as it only has two factors.

These things take a very long time to do, however, especially with 100-digit primes. And this new one has 33219253 of them, so decrypting could take a while.

Re:Uses?

[Mysticalfruit]

Now that I've got that working quantum computer I've proven the theory so it's now a fact...

There are an infinite number of numbers hence an infinite number of infinite primes from that set of infinite numbers.

The nice thing was that it only took a billionth of second to figure it all out.

Re:Uses?

[adeyadey]

Hi darling, ooh is that a gigantic Mersenne Prime, or are you just pleased to see me?

Re:Uses?

[ArsonSmith]

no, it just seams that way. Chick's will put out just to shut you up.

Re:Uses?

[Anonymous Coward]

but if one wants to be keul and use "the 42nd and largest Mersenne prime" as one of the two factors, the calculation becomes much easier :)

Re:Uses?

[Husgaard]

Using Mersenne primes for public cryptography is way too easily attacked - just try to first N Mersenne primes, where the Nth prime is less than the composite number.

Re:Uses?

[tehshen]

But decryption becomes much harder. Decrypting a message encoded with the 41st and 42nd Mersenne primes could become distributed computing itself ;)

Re:Uses?

[26199]

Heh... how did this get modded informative? It's no use at all for encryption. Maybe 'funny' would be a better moderation...

Re:Uses?

[Rei]

My partner majored in Mathematics; she'd probably find it neat :)

Re:Uses?

[pclminion]

Yeah, except that the Mersenne primes are well known and thus useless for cryptography -- at least, if you want any security.

Re:Uses?

[Anonymous Coward]

I goes to show you: siZE DOES MAtter....

Re:Uses?

[Tjoppen]

There ara probably as many Mersenne primes as regular primes. Thus you could just as well encrypt with Mersenne primes.

Re:Uses?

[jaoswald]

You are arguing about a different domain.

Encryption discussions have to take place in a "computing" domain, where a prime only exists if it has been computed to be prime by at least one computer somewhere in the world, and where the prime number can fit on a distribution medium.

Arguing that there are as many Mersenne primes as regular primes is only possible in a theoretical domain in which countably infinite sets can be said to exist.

Re:Uses?

[uberdave]

The X axis is infinite. So are the Y and Z axes. Therefore, there must be an infinite number of regular solids. Oh, wait! There's only five. Gee, I guess the mere fact that numbers are infinite doesn't imply that subsets of those numbers are infinite.

Re:Uses?

[owlstead]

No, encryption is out of the question, since it would take enormous computing power to get a new key (see GIMPS). As for the known keys, these are obviously not available for use. A brute force attack would take 21 rounds to complete (on average).

Using a mersenne prime for the public exponent is no problem though. Both 3 and 7 are used quite a lot for this purpose, though 65537 is used most (and this is not a mersenne prime).

Re:Uses?

[azaris]

There ara probably as many Mersenne primes as regular primes. Thus you could just as well encrypt with Mersenne primes.

Not really. Since there are so few known Mersenne primes, the problem of factoring n to find the prime factors p and q to calculate phi(n) in order to crack RSA for example is greatly simplified if either p or q is a Mersenne prime. Perform 42 divisions and you're done.

Re:Uses?

[hdparm]

Yes because 42 is not a good choice, since it's too obvious.

Re:Uses?

[Tjoppen]

I know. Notice how I typed probably in reference to the article.

Re:Uses?

[FuzzyBad-Mofo]

The theory is that there is an infinite number of these numbers, but they are unlikely to prove the theory by finding them all.

Yogi Berra, is that you?

Re:Uses?

[Anonymous Coward]

Useless is think about RSA, but not useless for cryptography. I couldn't find a good link, but look at the end of the first "page" of http://yoyo.cc.monash.edu.au/~bunyip/primes/whypri mes.htm there is a snippet about it.

Re:Uses?

[roman_mir]

Ha! My brainy beautiful girlfriend (girl) just called me and told me this: at work someone asked her what distance in parsecs will a dude be able to walk energized by a single grape.

It's something like a small constant x 10^-16 parsecs ... nuts. I wander what distance the same guy could go on a single nut... or maybe with a single nut. And he will have to cover that distance with a single nut if he continues asking her questions of this nature..

Re:Uses?

[whizzard]

The theory is that there is an infinite number of these numbers

Actually, this theory has already been proven.

Re:Uses?

[Anonymous Coward]

Only on slashdot does NOBODY know how to spell chiks.

Re:Uses?

[abradsn]

not true

Re:Uses?

[pclminion]

Wow, what an enlightening and detailed explanation.

The frickin' AC did better than that.

Re:Uses?

[cdegough]

To create jobs for math graduates who currently deliver pizza...

Re:Uses?

[Mr2cents]

Not mine, I use the 43th Mersenne prime.

Re:Uses?

[naff]

Wrong theory. That is for primes in general. "These numbers" refers to just the Mersenne primes.

Re:Uses?

[SharkJumper]

C'mon guys. Size doesn't matter, right?

Right?

SharkJumper

Re:Uses?

[jd]

However, if you pick one Mersenne prime and one non-Mersenne prime, it is impossible for anyone to prove which Mersenne prime you've picked, unless they find the non-Mersenne prime.

It reduces the problem space some, because the attacker only has to sweep through the Mersenne prime table for each of the other primes they are trying out. However, it does so at a cost. There simply aren't many ten million bit CPUs out there, and that's the sort of size you need to directly process the Mersenne primes they're finding now.

(Most computers cheat, by using Berkeley MP or GMP to simulate very very large numbers, but I personally wouldn't want to be doing lots of floating-point divisions with million-digit numbers. Intel's maths core can barely handle the
adds and multiplies used to generate and test the
primes.)

Re:Uses?

[CastrTroy]

43th? 43th? Isn't it 43rd?

Re:Uses?

[Seculus]

That's not actually the argument for why the number of primes is infinite. Rather, assume there are only finitely many prime numbers. Multiply all of them together. Add one to this number. It is easy to show that this number is not divisible by any of the finitely many primes you started with. Hence it must be a prime number as well.

Re:Uses?

[mattspammail]

And we all know that it's only the Marsupial primes are the ones that let us mathematicians get all the chixkcs.

And c'mon. Not like you couldn't find 2^21 - 1 reasons why not to like Merstupid primes. They're awesome!

Re:Uses?

[bhadreshl]

Because now Bill Gates can factor them.

Re:Uses?

[Anonymous Coward]

Actually, it doesn't have to be. It only suffices so say, that when you multiply all primes in your list, and add one, you get a number not divisable by any of the number in the list. Hence, one of TWO things can hold true:

1) The number in question really is prime, as you suggested

2) The number in question isn't prime. Then it has prime divisors, none of them in your list (because none of the primes in the list divided our new number).

In both cases, we have derived a way to find at least one new prime from any list of primes, and hence, the collection of primes is non-finite because we can always find "another one".

Re:Uses?

[Anonymous Coward]

*Factor them* - More like PATENT them!! :P

Re:Uses?

[novakyu]

Actually, this theory has already been proven.

IMNSHO, but that was the worst proof of infinite number of primes. Why introduce unique factorizability when you don't need to? Why introduce something foreign that you are not going to prove when there is absolutely no need for it?

The most elegant proof I've seen so far (but I don't know any website showing it, so I can't link to it) is this: For any given N, an integer, consider N!+1, which is greater than N (where N! is defined by N! = 1 * 2 * 3 * ... * N). If this number is divisible by no other number than 1 and N!+1, then we are done (i.e. we have proven that given any arbitrary integer, there is a prime greater than tat integer). If this number is divisible by a prime, than that prime can't be less than or equal to N, since any integer (not equal to 1) less than or equal to N divides N! (see the definition of N!) but does not divide 1. Therefore, the prime that divides N! is greater than N. QED.

This proof involves no assumption (additional to assumptions (i.e. axioms) of the set of integers) other than this (which also happens to be much easier to prove than factorizability into primes): if n divides a + b and n divides a, then n divides b as well.

Re:Uses?

[Anonymous Coward]

43th? 43th? Isn't it 43rd?

You must be thinking of 41rd.

Re:Uses?

[Anonymous Coward]

1. suppose the list of prime numbers IS really an exhaustive list
2. the multiplied list + 1, N cannot be divided by any number in the list
3. by (1) that list is the list of prime numbers, so N cannot be divided by any prime number.
4. by (3) it is prime -- contradiction.

There's no need for a construct like yours.

To suppose the number in question is not prime would be supposing our (wrong) assumption to be wrong before proving it wrong, which wouldn't be much of a help.

Re:Uses?

[Godwin O'Hitler]

Five? I can count six from here, with 4, 6, 8, 12, 20, and infinity faces respectively.

Re:Uses?

[Hank the Lion]

However, if you pick one Mersenne prime and one non-Mersenne prime, it is impossible for anyone to prove which Mersenne prime you've picked, unless they find the non-Mersenne prime.
Which will be quite easy. Divide the product you have been given by all Mersenne primes. As there are only 41/42 known, this will be very fast. As soon as the result is integer, you have found the other number.

It reduces the problem space some, because the attacker only has to sweep through the Mersenne prime table for each of the other primes they are trying out
You will work from the other side. So the problem space is reduced to 42.

There simply aren't many ten million bit CPUs out there, and that's the sort of size you need to directly process the Mersenne primes they're finding now.
In elementary school, we learned how to divide arbitrarily large numbers one digit at a time. We called it 'staartdeling', but I don't know the English word. The same algorithm can be used by any computer.

but I personally wouldn't want to be doing lots of floating-point divisions with million-digit numbers.
No need for floating point at all.

If you give me the product of a Mersenne prime and a non-Mersenne prime, I can write a computer algorithm to factor it in the order of a second or so.

Re:Uses?

[Impy the Impiuos Imp]

> What uses are there for gignatic prime numbers
> like this other than showing off computing power?

If you don't understand the following, you'll never get it: Ahhhh...Slashdot has lived up to its subtitle for the first time in a long time. =D

Re:Uses?

[tibike77]

Nah, it's just the "Answer to Life, The Universe and Every Existing Mersene Prime Number".

Wait, I mean just the 42th Mersene prime ;)

Re:Uses?

[m50d]

Giles, is that you? It does have to be a new prime, because he has stated at the start that he is assuming his list contains all the primes.

Re:Uses?

[Anonymous Coward]

> Rather, assume there are only finitely many prime numbers.
> Multiply all of them together. Add one to this number.
> It is easy to show that this number is not divisible by any of
> the finitely many primes you started with.

Easy? Euclid, who came up with the above proof, did accept enormous amounts of hand-waiving, but modern mathematicians can be much less forgiving.
To fill the holes in your proof you will, for instance, have to prove that the number you get is not one of the primes you started with. Claims like "everybody knows that if I multiply 2*3*5*...,with all factors positive integers, the result is larger than any of the factors" are not necessarily acceptable.
Mathematicians can make anything hard :-)

Re:Uses?

[Anonymous Coward]

There ara probably as many Mersenne primes as regular primes. Thus you could just as well encrypt with Mersenne primes.

Your first sentence is just plain wrong.

An infinite set can be smaller than another infinite set. Examples: Complex Numbers>Real Numbers>Whole Numbers=Fractional Numbers>Natural Numbers>Even Numbers>Odd Numbers>Counting Numbers

A mersenne prime is a mersenne number ((2^n) - 1) that is also a prime number equal to 2 raised to the power of a prime number, and the result subtracted by one. Therefore, the set of mersenne primes is demonstrably a proper subset of the primes, since (2^9) - 1 = 511 = 7*73.

While your second sentence is certainly true, there are so many fewer mersenne primes (at least in the number range we know) and they are known, so their unique value as factors is infinitely diminished. Encryption by primes relies on security through obscurity. Or to put it another way, their value to encryption could be mainly showing the primes not to choose.

Re:Uses?

[Anonymous Coward]

We called it 'staartdeling', but I don't know the English word

It's "long division"

Re:Uses?

[Anonymous Coward]

An infinite set can be smaller than another infinite set. Examples: Complex Numbers>Real Numbers>Whole Numbers=Fractional Numbers>Natural Numbers>Even Numbers>Odd Numbers>Counting Numbers

Wrong. Infinite sets are considered equal if there exists an bijective map between them. Thus 'infinite sizes' are divided only into countable and uncountable infinities. For instance, the set of rational numbers is the same 'size' as the set of whole numbers, but isn't the same 'size' as the reals. Further more you show a fundamental lack of understanding of complex numbers, which aren't a 'number set' in itself but merely a vector field over an arbitrary set of numbers (For instance, gaussian integers are a vector field over the integers.)

Re:Uses?

[CPM User]

I'm afraid that was a rumour put about by men with small ones.

Sincerely,

the girls

Re:Uses?

[Claire-plus-plus]

Hashing data stores. When you build a hash table to sort and store large data sets it is usually best to use a large prime number in the hash function.

Re:Uses?

[Anonymous Coward]

Your "because" is inconsequential.

Re:Uses?

[arodland]

Yes, but we haven't actually proved that the result of the multiplication-addition operation is prime. However, we don't have to, because if it is prime, then it's necessarily a prime that's not on the list, and if it's composite, then by the Fundamental Theorem of Arithmetic it has a unique set of prime factors, and by the way you constructed the number, none of those primes are in the list. Either way, you've found at least one prime that wasn't in the list, contradicting the claim that the list was complete.

You see? For completeness, we say "either N is prime, in which case the list is incomplete, or N is composite, in which case the list is incomplete", and save ourselves worrying about whether N is prime or not.

Re:Uses?

[m50d]

Why not just say it can't be divisible by any of the primes in the list, thus it's a new prime?

Re:Uses?

[VTBassMatt]

Because it may be divisible by a prime not already in the list. If you multiply all the known primes together and add 1, you're going to make a number much, much bigger than the biggest number in your list. It may be the case that this new number is divisible by two or more primes from the set of numbers greater than your biggest old prime.

I'm a little rusty on my discrete math, and it may be possible to prove that the new number is indeed prime, but it's easier to just say it's either a new prime OR the product of new primes (as the grandparent poster was doing).

Re:Uses?

[Anonymous Coward]

Most mathematics which has practical uses today was discovered long before the use was found. There may not be any use for it now, but check back in 250 years and see then.

Re:Uses?

[wcanevari]

no way this works for finding a new prime.... multiply and number of prime numbers (which are all odd) and you get an odd number... add 1 and you get an even number, and even numbers (except for the integer 2) are never prime.

Re:Uses?

[rbrito]

One of the most obvious uses for having tasks like this is to understand better the problems and to develop better algorithms.

In Computational Complexity's terms, we like to design "efficient" algorithms.

One of the criteria used to say if an algorithm is efficient or not is to measure the time it takes to execute in terms of the size of its input.

We are usually concerned with designing faster algorithms (especially when we have to deal with huge inputs --- that's one of the things that people have in mind when they say "scalability) and if we have algorithms that help expose details of the problem being solved, it will only help us to design faster algorithms.

And these techniques may, with some adaptation, be used for solving other problems, not only the problem in question.

I hope that this helps you understand why some people are always concerned with developing good algorithms and also testing them in practice.

If you are interested in knowing more about the design of algorithms, please don't hesitate to ask.

Re:Uses?

[Anonymous Coward]

But 2 is a prime number, so you multiply all the odd primes by the only even prime (2) and you get an even number. Adding 1 to this will be an odd number again.

Re:Uses?

[highfreq2]

2 is always in the list of primes. Your point that any odd number + 1 can no longer be odd, is exactly what is behind this proof. Any n-divisible number (n not 1) plus 1 is no longer n-divisible.

Re:Uses?

[tbjw]

Step 4 is incorrect. The fact you are looking for is the fundamental theorem of arithmetic, which says that every positive integer can be factorised into a product of prime numbers (uniquely up to reordering of factors). Plainly the number N would contradict this fact, so it does not exist, so it cannot be constructed, so there are not finitely many primes.

It is incorrect to say that a positive integer that cannot be divided by any prime is prime, since there is only one such number, 1, and it is not prime. Every prime is divisible by itself.

Re:Uses?

[tbjw]

If it were possible to prove this number were prime, we would have a fantastic way to generate new primes. Take all the primes you know, multiply them and add one. Voila! new prime!

Of course, since the set "all known primes" is not mathematically distinguishable from any subset of primes, it would have to be true that any number which is of the form pqr...z+1 where p,...,z are primes is prime. Of course, this fails, as you can see taking (2)(3)(5)(7)(11) + 1 = 30031 = (59)(509).

Re:Uses?

[VTBassMatt]

I was trying to use the first 5 primes as an example when I posted the previous comment. The problem is that (2)(3)(5)(7)(11) is 2310, and 2311 really is prime. Not sure where you got 30031 from, but it's nice to know that someone else was thinking down the same paths as me. =)

Re:Uses?

[bedessen]

Why would a mountaineer care if someone sets a record for highest mountain climbed? Why would an explorer care if someone pioneered a part of the antartic where no human has ever been? Why would a spelunker care if someone found a new cave that has never been seen before? The same reason that mathematicians and hobbiest prime-hunters care about finding the largest known mersenne prime.

It has no immediate practical value, but it's always interesting when something new is discovered, especially when it's something that is the largest of its kind.

Re:Uses?

[m50d]

But there are no primes not in the list, because the list is a list of *all* the primes. So you don't need to worry about it being divisible by two or more primes from the set of numbers greater than your biggest old prime, because there are no primes in that set, because the original list is the list of all primes.

Re:Uses?

[VTBassMatt]

>[T]here are no primes in that set, because the original list is the list of all primes.

That's easily proven false. The most trivial example is: take the list of all known primes up to three: 2, 3. Multiply these together and add 1: 7. Now there's a prime in the set between the biggest old prime and the new number.

This example obviously doesn't demonstrate the entire principle since 7 is in fact a prime. The point everyone in this thread is making, though, is that just because you generated 7 by multiplying up some consecutive primes and adding 1 doesn't inherently make it a prime, but it does still prove that there are infinitely many primes.

Hope this doesn't come across as flamebait; it's not intended as such.

Re:Uses?

[m50d]

Yes, because {2,3} isn't the list of all primes. However, if that were the list of all primes, as is being assumed in this proof, there could be no primes between 3 and 7.

Re:Uses?

[novakyu]

Therefore, the prime that divides N! is greater than N. QED.

Oops---I meant "Therefore, the prime that divides N!+1 is greater than N."

Re:Uses?

[arodland]

30031 is (2)(3)(5)(7)(11)(13) + 1; I guess the grandparent just missed one :)

Re:Uses?

[Class Act Dynamo]

That is not a reason there are an infinite number of primes. The simplest proof is that if there were some largest prime, P, after which there are no more, then we could multiply all the primes together, including P. If we add 1 to this new number, we know it is prime, larger that P, and not divisible by any of the other primes. That is a contradiction, therefore there is no largest prime number.

Of course...

[rackhamh]

... the moment they discovered the 42nd prime, the world was immediately destroyed to make way for an intergalactic superhighway.

Re:Of course...

[micromoog]

Now that was a prime rib!

Re:Of course...

[captjc]

But, then we will find that the answer to the question of Mathematics is the 42nd Mersenne Prime. Later it will be discovered by some Ape Descendant and a hitchhiking researcher for an wholly remarkable electronic book with the words "Don't Panic" inscribed on the cover in large friendly letters, that the question of Mersenne Primes is "What do you get when you multiply the sixth Mersenne prime by the ninth Mersenne prime. which will prove that Mathematics is fundamentally screwed up.

Re:Of course...

[pv2b]

Actually, a quick glance at the listing of the prime number clearly showed that the number is divisible by 3.

Oh well. At least the world won't be destroyed now.

Re:Of course...

[JonLatane]

Really, now? Where did you find the number, exactly, since, quoth the article:

the exact exponent of the new find has not yet been made public

All that's been verified is that its exponent is between 24,036,584 and 33,219,253. If you don't know the exponent for the Mersenne number then you obviously can't tell what it is, now can you? So, uh, how could you tell it's divisible by 3? Assuming you're trying using the good old "add the digits" method, I think it's worth noting that this number has between 7.2 and 10 million digits, making that method effectively useless, especially with a "quick glance."

Re:Of course...

[pv2b]

Assuming you're trying using the good old "add the digits" method, I think it's worth noting that this number has between 7.2 and 10 million digits, making that method effectively useless, especially with a "quick glance."

Heh. You understood the punchline and yet completely failed to get the joke at the same time. Congratulations.

Re:Of course...

[Hoch]

If you mean the number 181, then you are wrong. It was discovered a long time ago.

Re:Of course...

[Anonymous Coward]

You okay after that post? Walk it off, man.

Re:Of course...

[Anonymous Coward]

Heh. You understood the punchline and yet completely failed to get the joke at the same time. Congratulations.

Was there a punchline? That was a joke? Now that's funny.

The real magic number

[Anonymous Coward]

42

Could it be?

[Anonymous Coward]

Could this be the one? the answer to the question of life, the universe.... and everything!

I never thought I'd say this...

[Paladin144]

...but those GIMPS kick ass.

You just know...

[Anonymous Coward]

If this pans out, GIMPS will have been responsible for the eight current largest Mersenne Primes ever discovered.

Being able to say that sentence was the reason they named the project the way they did.

Great. Now what is it???????

[solafide]

Tell us what it is!!! We can't confirm it either until he says what it is!

Congratulations George! Now what use is this? In cryptology? But how?

Re:Great. Now what is it???????

[ravenspear]

Tell us what it is!!!

Would you like that in decimal or binary?

Re:Great. Now what is it???????

[Anonymous Coward]

Binary is pretty easy. The number is:

11111...1111

where "..." means some number of 1s.

Re:Great. Now what is it???????

[ArsonSmith]

The biggest problem with cryptology right now is the inability to factor large prime numbers. Once we have the computeing power to do so cryptology strength will be increased greatly.

Re:Great. Now what is it???????

[Anonymous Coward]

Actually, factoring a prime number is pretty damn easy.

Re:Great. Now what is it???????

[ArsonSmith]

Not if they are really big, I mean REALLY BIG!!! Like way over a hundred

Re:Great. Now what is it???????

[Anonymous Coward]

Ha ha ha!! This is great!

You missed the boat... prime numbers are called prime numbers because they have no factors... Did you not learn this in high school? Or are you 12?

Re:Great. Now what is it???????

[Anonymous Coward]

Here, I'll show you how to factor an extremely large prime. Set p to be any prime number (small or large). The following are a list of factors for p:

1, p

That is all... Wasn't hard either.

Re:Great. Now what is it???????

[lytenyn]

Well, actually ..

I think, factoring primes shouldn't be that hard.
Even if they're _really_ big :)

Re:Great. Now what is it???????

[jdhutchins]

Factoring a large prime number, we'll call it n, is extremely easy. Its factors are n and 1, by definition. Factoring large, 'hard' composite numbers (ones that don't have obvious factors like 2 or 3, there are some other criteria as well) is the difficult problem.

Re:Great. Now what is it???????

[Albinofrenchy]

Assuming you meant "the inabiliy to factor large composite numbers," that isn't a problem in the field of cryptology as much as it is the base on which some of the strongest algorithms rest.

Re:Great. Now what is it???????

[Anonymous Coward]

Good God what are you smoking?
Each primenumber has two(2) factores: 1 and the prime.

Re:Great. Now what is it???????

[Anonymous Coward]

If you study Mathematics at a higher level, you tend to ignore the two trivial factors (the number itself and 1), and jump right to the conclusion that there are no factors. Perhaps had I said no trivial factors, there would have been less confusion.

Re:Great. Now what is it???????

[Iamnoone]

I can tell you what I think it is - M33653413
and if it is I'm gonna be kicking some ass over there because I've been nursing that thing along for a year or more and I've always had a feeling about it, it is now 82.58% through the final checks and is supposed to finish in less than a month. I wonder if they have a way to cherry pick and find ones that look promising and snipe them...

Re:Great. Now what is it???????

[vally_the_poo]

Latest news: after hours of hard working, George came out to the conclusion that this was not a mersenne prime number as it ended with 42 !!

Re:Great. Now what is it???????

[Eythian]

Microsoft is working hard on this, according to Bill Gates' The Road Ahead pg 265:

The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers.

(Yes, I know that it is simply an error. It's funny nonetheless)

Re:Would a math geek...

[haluness]

From mathworld (whose link is in the summary)

A Mersenne prime is a Mersenne number, i.e., a number of the form

2^n - 1

that is prime. In order for it to be prime, n must itself be prime.

Sheesh

[Anonymous Coward]

The number in question is currently being double-checked by George Woltman, organizer of GIMPS

And while George takes time off to double-check Mersenne primes, GIMP doesn't get any closer to the usability of Photoshop...

Re:Sheesh

[algorithm0]

i'd have to agree. wow, this /. article sure isn't delivering.

Re:Sheesh

[Anonymous Coward]

um photoshop is nice and all but you know crunching prime is funner.... photo shop make my computer sound like a yetti when useing winamp and useing it so personally i just stear clear

Re:Would a math geek...

[Smallpond]

A Mersenne number is all ones when written in binary. If its prime, it is a Mersenne prime.

If I do say so myself.

[Anonymous Coward]

Now that's a prime find!

Re:If I do say so myself.

[yogikoudou]

Now THAT is The Answer to Life, the Universe, and Everything ! Wonder what the 43rd will reveal ?

Re:If I do say so myself.

[cyriustek]

But what are the implications to the Prime Directive?

Re:If I do say so myself.

[Anonymous Coward]

Engage, Number One.

Re:If I do say so myself.

[Anonymous Coward]

This number fell backward through a temporal vortex and led to the creation of Optimus Prime. Transform and roll out!

Practical Applications/Uses?

[NitroWolf]

Can someone explain what the application/use these primes are for? Not a flame, I'm honestly curious as to what something like this could be used for, as are others, I'm sure.

Re:Practical Applications/Uses?

[mctk]

Large primes, of around 75-100 digits, are useful in encryption. Huge primes (i.e. over 7 million digits) are not currently useful in themselves, although we certainly learn more about mathemathics and computers as we try to find them.

Re:Practical Applications/Uses?

[robbyjo]

From here:

Finding new Mersenne primes is not likely to be of any immediate practical value. This search is primarily a recreational pursuit. However, the search for Mersenne primes has proved useful in development of new algorithms, testing computer hardware, and interesting young students in math.

Re:Practical Applications/Uses?

[vivin]

It's a mathematical curiosity in some cases - just to find it for the sake of finding it, or for the glory of finding it. You know, like being the first to do something cool.

Also, necessity is the mother of invention. Even if Big Primes aren't really a necessity, it has brought forth some really innovative algorithms and methods to finding prime numbers. Furthermore, it has developed newer and faster ways for multiplying integers.

In 1968, Strassen figured out how to multiply integers quickly by using Fast Fourier Transforms. Strassen, along with Schönhage improved on the method and published a refined version in 1971. GIMPS now uses an improved version of their algorithm. This improved version was developed by Richard Crandall (a longtime researcher of Mersenne Primes).

Another application of finding Prime Numbers is to test computer hardware. Since testing Primes involves a thorough excercise of basic mathematical operations, it provides a good test for hardware. Software routines from GIMPS were used by Intel to test the PII and the Pentium Pro chips before they were shipped. The search for prime numbers was also indirectly responsible for the discovery of the infamous FDIV bug on the Pentium, during the calculation of the twin prime constant (by Thomas Nicely).

Re:Practical Applications/Uses?

[Sloppyjoes7]

Uncommon and unique numbers of varying types are usually useful for mathematics in general. Usually only mathematicians know why.

Whatever the case, this must be a more useful application for CPU power than Seti@home, which is a total waste of energy. Literally.

What we need are more projects that use distributed computing for useful calculations that could further science or solve problems. Universities build giant supercomputers to help their students calculate equations and solve problems. Maybe the students should release the problems over a network, and have home users calculate the answer for them. It'd save the Universities a lot of money.

I don't think it would work for code cracking, or government projects, as these contain sensitive information.

Re:Practical Applications/Uses?

[pclminion]

Can someone explain what the application/use these primes are for?

Communicating with alien species, perhaps.

Mersenne primes have two interesting properties that might catch the attention of alien species: when written in binary, they are entirely composed of '1' bits; and, of course, they are prime.

A sure way to prove to another being that you are intelligent is to spew a bunch of numbers which all happen to be prime. The fact that they can be tranmitted using only '1' bits means the modulation is simple -- just send a series of pulses.

Re:Practical Applications/Uses?

[myowntrueself]

So... the main reason for searching for large primes is to develop better techniques for... searching for large primes?

Re:Practical Applications/Uses?

[geoffspear]

Transmitting the same binary signal over and over seems unlikely to impress anyone. You're as likely to be sending a really boring all-white image as a really big prime number.

If anything, anyone receiving the signal will wonder how you managed to build such a powerful transmitter when you haven't discovered binary numbers yet and are apparently using some sort of unary mathematics that really shouldn't work. They're bound to be disappointed when they find out you actually know about "0", but just weren't using it.

Re:Practical Applications/Uses?

[pclminion]

No, you have to transmit MULTIPLE numbers. You transmit the first Mersenne prime. Then you wait for a while. Then you transmit the next one. Wait again. Etc. It's much more efficient to send them in binary than unary (although this most recent prime would require over 2 million bits).

And just because aliens receive a signal with a bunch of strong, equally spaced pulses doesn't mean they'll automatically assume it's intelligent. There are plenty of natural cosmic phenomena which produce equally spaced pulses.

Re:Practical Applications/Uses?

[wwi]

Also used for many years to test/burn in all of the Cray supercomputers. Many thanks to Dave Slowinski!

Re:Practical Applications/Uses?

[burns210]

large prime numbers are used in encryption techniques, also.

Re:Practical Applications/Uses?

[Fizzl]

Namely in RSA.
At times I hear someone say "primes are the foundation of modern cryptography".
Not necessarily. We allready have ECC (Elliptic Curve Cryptography) to step into RSA's shoes once someone finds/maps factorizations of large primes multiples.

And this was totally off tangent :)

Re:Practical Applications/Uses?

[farnz]

The trouble with distributed computing is that not all problems can be suitably parallelised. For example, simulations are hard to parallelise; each time unit's calculations depend upon the results obtained in the previous time unit.

A supercomputer can be put to work partly because each serial element is fast, and partly because the results can be shared among nodes very quickly; think inter-node latencies in the 10s-100s of microseconds range, rather than broadband's 10s of milliseconds, and bandwidth measured in gigabits/s.

Re:Practical Applications/Uses?

[kesuki]

World domination. The practical applications of prime and prime mersennes is limitless, from good luck (7) to bad luck (which is just a prime, and not meridian) (13) primes and prime mersennes are the underpinnings of the very universe. So, by knowing more of them than anyone else, anything from immortatility, to world domination are the practical applications of prime meridians. Also just to note This is the 42nd Prime number (which also happens to be a mersenne prime as well) discovered. The list as used on 'mathworld' includes numerous prime numbers that are NOT mersennes. They are Just Prime. 2, 13, 17, 19, 87, 107 are examples of 'non mersenne prime numbers' listed on that list, and '255' is an example of a 'mersenne prime' who's number is Not prime. and thus is also not on the mathworld list.

Re:Practical Applications/Uses?

[kesuki]

Opps meridian was meant to be mersenne in the 2 instances that I missed the mistake ;) I keep trying to type 'meridian' instead of mersenne...

Re:Practical Applications/Uses?

[cfalcon]

I'm still laughing, thanks ;)

Re:Practical Applications/Uses?

[Anonymous Coward]

Boy cryptography you need to calucalte Pi to brute force! I think we'll be waiting all year to decrypt that data ;)

Re:Practical Applications/Uses?

[TiggertheMad]

However, that isn't to say that there might be some use for them in the future. Lots of stuff in math gets discovered and later proves very useful.

I believe that Eulier was the guy who developed higher dimensional geometry. Nobody did much with until this guy named Einstein came along and faund a marvelous application. (I am a math nerd. Hyper math nerds, feel free to correct or expound.)

Re:Practical Applications/Uses?

[Anonymous Coward]

Someone is smoking crack ;) okay if M2 is a mersenne Prime, then mersenne primes are not 'expressed in binary as "1's exclusively"' Wikpidia is calling M2 as mersenne prime, and the list at mathworld also lists it as one, in the same article as they make the (false) claim that all mersenne primes are binarily expressed as 1's so either 2 is 'just prime' or 2 is 'mersenne prime' and if 2 is mersenne prime then with a binary value of 10 it invalidates the claim that mersenne primes are binarilly expressed as only containing 1's so i understand how you got confused by the articles, but someone is clearly smoking crack over at math world.

Re:Practical Applications/Uses?

[localman]

This should be modded funny, right? An endless series of pulses as a sign of intelligent life? I guess Pulsars have been sending us back to back mersenne primes in binary for eons now!

Those clever devils!

Re:Practical Applications/Uses?

[IWannaBeAnAC]

Sorry, you are smoking crack, or just horribly confused.

M_n refers to the Mersenne prime comprising n 1's in binary. So M_2 is 0b11 = 3 = prime.

Re:Practical Applications/Uses?

[pilgrim23]

Indeed. Many more years ago then I care to rememeber, I was a tech working on a Cray computer during the install process. We ran a Mersenne search as part of the burn-in. I forget the number of the one we found, but I do recall I used to have a Cray poster that was from the previous Mersenne discovered; also found on a Cray burn-in. Now where di I put that dang thing...

Re:Practical Applications/Uses?

[toddhunter]

Pretty much just escaping from a Cube. Just keep them in mind

Re:Practical Applications/Uses?

[rainman_bc]

Whatever the case, this must be a more useful application for CPU power than Seti@home, which is a total waste of energy. Literally.


Yes, because Jesus said we're alone in the universe right? And the earth is only 6000 years old, and god told you to post this on /. so all the nerds out there could learn about his holy grace.

Seriously, that effort should be applauded. I don't think they'll find anything personally, but you never know...

Re:Practical Applications/Uses?

[CastrTroy]

I'm not a hyper math nerd, nor a math nerd. Actually I'm a software nerd. But I still feel compelled to correct your spelling of Euler.

Re:Practical Applications/Uses?

[kreyg]

You're as likely to be sending a really boring all-white image as a really big prime number.

Except, of course, that it can't be a rectangular image because, well, the number of pixels is PRIME.

Re:Practical Applications/Uses?

[Andrewkov]

Can someone explain what the application/use these primes are for? Not a flame, I'm honestly curious as to what something like this could be used for, as are others, I'm sure.

Chicks dig this stuff. You must be suffering from large-prime envy.

Re:Practical Applications/Uses?

[Anonymous Coward]

Yes, The hunt for big prime numbers is an time wasting program set up by our evil overloads,
so that our brights minds is distracted from making real discoveries.

Re:Practical Applications/Uses?

[Anonymous Coward]

Save bandwith by only sending the exponents (which are prime numbers themselves) of the mersenne primes would possibly prove an even higher level of intelligence.

Re:Practical Applications/Uses?

[Anonymous Coward]

Pete spent most of his evenings repairing and tuning his motorcycle. Once a friend asked him why he did that, and Pete answered: "Now that's obvious. The tuning makes her go faster, so I save time going to and from work."
"Ah, and what do you do with that extra time?"
"Tuning my bike, of course."

Re:Practical Applications/Uses?

[Anonymous Coward]

That's the funniest thing I've read all day.

Re:Practical Applications/Uses?

[tepples]

They're bound to be disappointed when they find out you actually know about "0", but just weren't using it.

One way to do this is to send each prime number in increasing order in unary followed by binary, using a half-strength pulse to represent zero.

Re:Practical Applications/Uses?

[fingerfucker]

Another copy, paste & edit Indian.

original source (where he copy & pasted from)

That website...

[daveschroeder]

...is linked in the summary.

(Last sentence, "Mersenne Primes".)

Sheesh.

Re:Would a math geek...

[IvyMike]

A prime of the form (2^n)-1. This means that in binary, it's a big string of "1"s.

The reason that mersenne primes are usually the biggest is because for primes of this form, there is a primality test (Lucas-Lehmer) that is exceedingly efficient.

Re:Would a math geek...

[chad.koehler]

A number such that: Mr = 2^n - 1 Where Mr is prime. SO for instance, 3, 7, 31 For n = 2, 3, 5 2^2 - 1 = 3 2^3 - 1 = 7 2^5 - 1 = 31

A Mersenne Prime is...

[vivin]

A mersenne Prime is a prime number that is one less than the power of two. Hence:

Mn = 2^n - 1.

Mersenne primes have a connection with Perfect Numbers (numbers that are equal to the sum of their proper divisors) where by if M is a Mersenne prime, then M(M+1)/2 is a perfect number.

Re:A Mersenne Prime is...

[ch-chuck]

and you can calculate them using the 'bc' arbitrary precision calculator in Linux - I just tried 2^6972593-1 (#38) and it took a few minutes at 99% cpu on my AMD 3200+ then printed out a BIG number.

Re:A Mersenne Prime is...

[Derek Pomery]

I can print it out even faster.
Here.
2^64-1 for example.
1111111111111111111111111111111111111111 1111111111 1111111111111

Oh.
You want it represented in base 10? :)

Re:A Mersenne Prime is...

[reflexreaction]

You forgot the wikipedia link though if it's true then the Wikipedia article is now out of date.

Re:A Mersenne Prime is...

[tbjw]

You can say even more. If M can be written as 2^n - 1, then M is said to be a Mersenne number. If M is also prime, then it is a Mersenne prime. For 2^n - 1 to be a Mersenne prime, n must be a prime number, since we have

2^(ab) - 1 = (2^a-1)(2^(a(b-1)) + 2^(a(b-2)) + ... + 2^(a))

For instance, 2^6-1 is (in binary) 111111 = 1001 * 111, as predicted by the above factorisation.

If p is a prime number and if 2^p-1 is a Mersenn prime, then, as was pointed out above, 2^(p-1)(2^p-1), is a perfect number. Moreover, if N is an even perfect number, then N can be written (uniquely) as 2^(p-1)(2^p-1) where p is a prime number and 2^p-1 is a Mersenne prime.

Wikipedia has a reasonably intelligible introduction to perfect numbers, and MathWorld contains a proof of why every even perfect number must have the form claimed above.

To see why M = 2^(p-1)(2^p-1) is a perfect number when p, 2^p-1 are primes, it suffices to note that s(n), the function that maps an integer to the sum of its divisors (e.g. s(6) = 1 + 2 + 3+6, s(8) = 1 + 2 + 4+8) is multiplicative in the number-theoretic sense, that is to say s(ab) = s(a)s(b) whenever a, b have no prime factors in common. Then evaluating s(M) is simply a case of evaluating it on the factors, which are relatively prime since one is a power of 2, 2^(p-1), and the other is an odd prime, 2^p-1. s(2^p-1) = 2^p-1 + 1 = 2^p (since we have a prime number), and 2^(p-1) = 2^p -1 is an easy formula that is true of all powers of 2. Hence s(M) = 2^p(2^p-1) = 2 ( 2^(p-1) (2^p-1) = 2s(M). That is to say, the sum of all the divisors of M add up to twice M, and if we leave the divisor M itself out of the sum, we see that M is a perfect number.

Re:A Mersenne Prime is...

[tbjw]

Sorry, that should be '=2M' in the very last equality.

Re:A Mersenne Prime is...

[uberdave]

That's not the perfect number (2^64-1)*(2^64). That is merely 2^64-1.

Re:A Mersenne Prime is...

[daveo0331]

It's still an easy number to print out...

FFFFFFFFFFFFFFFF0000000000000000

Re:A Mersenne Prime is...

[Anonymous Coward]

I just found a bigger prime...

FFFFFFFFFFFFFFFF0000000000000000LLLLLLLLLLLLLL

Re:good website for info

[Rosco P. Coltrane]

Wow, some work you did, lifting the link inside TFA to repost it here...

Mods these days couldn't see a karma-whore if it painted his bottom blue, put on a jester's hat and shouted "I'm a karma-whore"...

Re:Would a math geek...

[piquadratCH]

In mathematics, a Mersenne prime is a prime number that is one less than a power of two. For example, 3 = 4 - 1 = 2^2 - 1 is a Mersenne prime; so is 7 = 8 - 1 = 2^3 - 1. On the other hand, 15 = 16 - 1 = 2^4 - 1, for example, is not a prime.

From Wikipedia

Mersenne Primes? Bah!

[Guano_Jim]

Call me when a distributed computing project finds Fruit Fucker Prime.

Re:Mersenne Primes? Bah!

[Anonymous Coward]

good fucking god penny arcade sucks the shit of my fat ass

Re:good website for info

[EaterOfDog]

hahahahahaha!

Mersenne Primes - Definition

[Un-Thesis]

A Mersenne Prime is where the prime number also fulfills the equation 2^P - 1 2^2 - 1 = 3 ... 3 is a mersenne prime. 2^3 - 1 = 5 ... 5 is a mersenne prime. 2^4 - 1 = 7 ... 7 is a mersenne prime. The next one is 31 and after that 127. From there they get quite rare (only 42 known). They are VERY useful in cryptography and quantum physics...both deal with huge numbers. They are also used in some SETI applications because if you wanted to send primes, you'd probably send mersennes as these would be *very* non-random. Pratically, they're mostly used in military-grade real-time encryption in the hash keys of secured phones.

Re:Mersenne Primes - Definition

[omahajim]

How non-random can a Mersenne number be when there's only 42 (or 48, depending on how you interpret your paragraph above)? Maybe I don't understand your use of 'non-random'.

Re:Mersenne Primes - Definition

[omahajim]

Nevermind, there goes the karma, I think I read your post wrong. They would be non-random precisely because there are so few. Oh well, time to slow down the 'submit' clicking.

Re:Mersenne Primes - Definition

[jandrese]

Well, yeah, if you encode the Prime number in Binary it will not look Random at all. It will look like a giant string of 1s though... Aliens might mistake it for filler or something.

Re:Mersenne Primes - Definition

[Anonymous Coward]

A Mersenne Prime is where the prime number also fulfills the equation 2^P - 1 2^2 - 1 = 3 ... 3 is a mersenne prime. 2^3 - 1 = 5 ... 5 is a mersenne prime. 2^4 - 1 = 7 ... 7 is a mersenne prime.

Were you up late last night or something? 2^3 - 1 is NOT 5. 5 is NOT a Mersenne prime. 2^4 - 1 is NOT 7. 7 is a Mersenne prime, though. You suck at math.

Re:Mersenne Primes - Definition

[Anonymous Coward]

2^3=8 therefore 2^3 - 1 = 7 not 5

2^4=16 therefore 2^4 -1 = 15 not 7, 15 isn't prime

Re:Mersenne Primes - Definition

[Anonymous Coward]

let me rephrase, 3 is a prime, 3 is a mersenne prime. 7 is a prime, 7 is a mersenne prime. 5 is a prime, 5 is not a mersenne prime, but 2^5-1 is equivalent to a mersenne prime (31)

Re:Mersenne Primes - Definition

[Tyler Eaves]

Not Quite.

A MP in binary would look like 10000000001, where the total number of binary digits is equal to the power of two.

Re:Mersenne Primes - Definition

[cpeikert]

Pratically, they're mostly used in military-grade real-time encryption in the hash keys of secured phones.

This sounds like some gobbledegook. Most Mersenne primes are too large and too rare to have any real cryptographic significance today. Can you back up this claim at all?

Re:Mersenne Primes - Definition

[SwansonMarpalum]

Might want to check your math:

2^2 = 4
4 - 1 = 3

2^3 = 8
8 - 1 = 7

2^4 = 16
16-1 = 15

Re:Mersenne Primes - Definition

[nacturation]

You realize that the 2^n - 1 form is a mersenne prime only when the resulting number is also prime, right? In other words, mersenne primes are prime numbers which can be expressed as 2^n - 1 for some integer value n.

Re:Mersenne Primes - Definition

[vivin]

Why has the parent been modded informative?

The formula Mn = 2^n - 1 applies to ALL Mersenne Primes in the sense that all Mersenne Primes are one less than some power of two. It does not mean that for every value of n, Mn is prime.

Re:Mersenne Primes - Definition

[Anonymous Coward]

2^3 = 8
8 - 1 = 7, not 5.
5 is not a Mersenne prime.

Re:Mersenne Primes - Definition

[10Brett-T]

Why has the parent been modded informative?

Ummm... because he successfully demonstrated that 5 is not a Mersenne Prime by doing the math better than the grandparent?

Re:Mersenne Primes - Definition

[Anonymous Coward]

Did you notice that the link states that '15' is an example mersenne prime though? I think they meant 13, not 15 though.
"Mersenne numbers are numbers of the form Mn = 2n - 1, giving the first few as 1, 3, 7, 15 , 31, 63, 127, .... "

Probably silly reference

[serutan]

Reminds me of the first BlackAdder episode

Lord Percy: "The King is dead! L-"
Prince Harry [interrupting]: "Probably dead."
Lord Percy: "The King is probably dead!"

Re:Would a math geek...

[em0te]

http://mathworld.wolfram.com/MersennePrime.html
One can explain something to another,
but if said person is unable to relate to the way that one is teaching them then either:
The explainer is a horrible teacher, or, the explainee just simply doesn't understand. And i, for one, am a horrible teacher.
Which is why i say: RTFA

Spoiler alert about the number

[Anonymous Coward]

Don't read any farther if you don't like spoilers.






Seriously, don't reead any farther....






It only has two factors.

Re:Spoiler alert about the number

[Anonymous Coward]

What a worthless post. Had you wanted to be informative, you could at least have mentioned that one of the factors is "1".

Re:Spoiler alert about the number

[Anonymous Coward]

Couldn't figure that one out yourself?

Re:Spoiler alert about the number

[Anonymous Coward]

Couldn't figure that one out yourself?

Why would be reading a spoiler, if we could?

Immoral use of computing power

[Space_Soldier]

What is number going to for us? Is it going to feed us? No. It would be better if the computer power was used for cancer research or finding aliens.

Re:Immoral use of computing power

[Stanistani]

>What is number going to for us? Is it going to feed us? No. It would be better if the computer power was used for cancer research or finding aliens.

Because of course aliens will feed us...
They even will bring a cookbook with them, "To Serve Mankind."

Re:Immoral use of computing power

[JustNiz]

There are already working cures for cancer, but the FDA are sitting on them so that the drug companies can make more money selling drugs to alleviate the symptoms, not the problem.

Re:Immoral use of computing power

[Anonymous Coward]

o yeah that's useful, i can give you an alien anytime, what are you gonna do with it? eat it? that's right nothing, u look at it, freak out and crawl under the table, you nerd. no aliens for you

Re:Immoral use of computing power

[Anonymous Coward]

oh pllleeaaazzzzee I guess rendering porno movies is an immoral use of computing power.

If someone buy the computing power to discover new primes it's their right to do so.

Re:Immoral use of computing power

[redivider]

Personally, I think having a "Free iPods" link in your sig is a more immoral use of computing power than searching for prime numbers.

Re:Immoral use of computing power

[mctk]

Some guy with a "free iPOD" sig is telling me about the immoral use of computing power?

Re:Immoral use of computing power

[Anonymous Coward]

You forgot "Get some priorities, people!"

If you're going for one of the tried-and-tested classic Slashdot trolls, please stick to the script.

Re:Immoral use of computing power

[GIL_Dude]

You shouldn't waste computing power on listening to your stupid iPod either. Convert it to find a cure for AIDS or something.

Re:Immoral use of computing power

[Surt]

Nah, the goal is obviously to find a technologically inferior bunch of intelligent aliens, and bring our cookbooks to their planet. Before any vegans complain, I want to point out that anything from another planet can't technically be an animal, so morally they should be fine to eat. And spicy!

Re:Immoral use of computing power

[Tjoppen]

The joke would be better had the title read "To serve man".

Where would we be today without the twilight zone?

Re:Immoral use of computing power

[Anonymous Coward]

The joke would be better had the title read "To serve man".

Naah, the aliens carring around "To serve mankind" like to think big...

Re:Immoral use of computing power

[Koiu Lpoi]

To Serve Mankind! Where is that from, I remember that from somewhere!

No, it's not an oxymoron, it's just a regular one

[Thud457]

In chicken sexing, a Mersenine prime is a hermaphroditic chick.

Re:Number Theory Professor...

[Anonymous Coward]

Unfortunately, number theory professors don't read /., they actually do work...

Woohoo! The world is saved!

[kakos]

Now that we've found the 42nd Mersenne Prime, we can cure cancer, cure AIDs, solve all NP problems in deterministic polynomial time, travel faster than light, and solve world hunger.

Thank you Great Internet Mersenne Prime Search!

One practical use of Mersenne Primes...

[William_Lee]

I'm not sure what else they're actually good for, but searching for these with Prime95 is a great way of putting the flame to your CPU.

Prime95 (which searches for these primes) really puts a load on the CPU and raises the temperature in a hurry. It's commonly used to test the stability of overclocking configurations since it stresses the chip and is able to detect if there is an error in the computation.

Generally, if you can run Prime95 for 24 hours straight, most people will consider the overclocked PC a stable configuration.

Re:One practical use of Mersenne Primes...

[slux]

I don't know if Prime95 double checks all keys but if it doesn't, that might not be a very nice idea. There'll be a chance of the overclocked CPU doing miscalculation even if it keeps running ok otherwise and you might cause the project to miss a prime.

Distributed.net has this to say on overclocking.

Re:One practical use of Mersenne Primes...

[Foddrick]

The client actually has a "torture test" option for this very reason. You can test against known results and don't actually contribute to the project.

Re:One practical use of Mersenne Primes...

[adpowers]

They do run double checks. Every time a number is computed and isn't a Mersenne Prime, it outputs a little string (can't remember the technical name). Once the double check is run (which can take a well, last time I checked there was a large time difference between the first time checks and the double checks), the server compares the strings. The numbers must be computed by different users. If the strings aren't equal, it is rereleased to have a triple check run. This process repeats until two of the outputs are equal. If a lot of your computations produce errors, it is a sign you might have a hardware problem (or overclocked too much).

Re:One practical use of Mersenne Primes...

[srichand]

I suppose when PrimeXP comes along, you'll be able to watch a movie/play/dvd/interact with people all over the world, while you're finding primes...

Client written in assembler

[Anonymous Coward]

For those of you who wondered... yes all two of you... the client (or at least the one on the GIMPS website) was written in assembler. Pretty cool.

Re:Client written in assembler

[Anonymous Coward]

Cool?? On the contrary. It uses the processor to the max and heats up the room temparature.

Re:Would a math geek...

[macaulay805]

Although I normally don't do this .. but .. if you actually RTFA, it states:

Mersenne numbers are numbers of the form Mn = 2n - 1. For example, M7 = 27 - 1 = 127 is a Mersenne number. In fact, since 127 is also prime, 127 is also a Mersenne prime.

That was a cut-and-paste job btw.

Yes!

[Anonymous Coward]

If this pans out, GIMPS will have been responsible for the eight current largest Mersenne Primes ever discovered.

In your face, Photoshop!

Re:Yes!

[oO Peeping Tom Oo]

I'm a gimp, you insensitive clod!

Re:Yes!

[Anonymous Coward]

Good one. ;)

Re:Yes!

[earthbound kid]

Their method is quite impressive. First, they made a layer with every prime number written on it. Then, they did a posterize effect, inversed the color, rasterized it, applied an outline filter, and added a second layer. On that second layer, they wrote the 42nd Mersenne Prime.

It just goes to show that Adobe has a long way to go to compete with the power of OSS.

And???

[michelcultivo]

And what this will change in our computer form or life? Will it reduce the greenhouse effect?

Two unknowns

[MaGogue]

This has not yet been confirmed, therefore there could be less than 42 known Mersenne primes.

Hovewer, according to MathWorld, there is a chance that it is not the 42nd Mersenne prime at all for another reason :

"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.."
Looks like the big math guys don't exactly know how to count at all ;)

Re:Two unknowns

[Anonymous Coward]

> therefore there could be less than 42 known Mersenne primes

Grammar Geek says:

Because the primes are countable, there are "fewer than 42" of them, not "less than 42."

So there! :)

Re:Two unknowns

[Anonymous Coward]

Eat ass, you pedant.

That brings back some memories...

[Anonymous Coward]

Back in the dark ages when I was in university, I took a class called "Mathematics and Poetry". I thought it would be a useful bird course in my senior year, but it turned out to be both interesting and challenging.

As part of the course, we studied Mersenne primes. At the time, I was dabbling in x86 assembler, and I decided to write a program to calculate the then largest known Mersenne prime number: 2^31 - 1, which worked out to 65,050 digits.

The size worked out perfectly, as in 1989 that meant it could fit into one 65KB segment on my blazing-fast 8Mhz 8088. As I recall, the runtime was about two days. The program still works--I can't remember how long it took to run on a 3Ghz P4, but I think it was just a few minutes.

I'm sure any competent programmer (read--not me) could calculate the result much faster, but at the time I was very proud of my little creation.

Re:That brings back some memories...

[djmurdoch]

As part of the course, we studied Mersenne primes. At the time, I was dabbling in x86 assembler, and I decided to write a program to calculate the then largest known Mersenne prime number: 2^31 - 1, which worked out to 65,050 digits.

I don't think it actually did bring back those memories. 2^31-1 is 2147483647. You're thinking of Mersenne prime 31, which is 2^216091 - 1.

Re:That brings back some memories...

[Anonymous Coward]

Uh, dude, 2^31-1 = 2147483647.

That's a lot less than 65050 digits.

Re:That brings back some memories...

[nojomofo]

I was working through that, too. A number 2 ^ n is certainly not going to have > n digits in decimal. This is given that the minimum value of an n digit integer is 10 ^ (n - 1). One can safely assume that 2 ^ n is smaller than 10 ^ (n - 1) for any integer n > 1.

Re:That brings back some memories...

[nizo]

Actually it did bring back memories, just not the right ones :-)

Re:That brings back some memories...

[Anonymous Coward]

Working out 2^31 -1 must have been real hard...

Let my try:
1111111111111111111111111111111b
There you go.

Re:That brings back some memories...

[Anonymous Coward]

If you knew some math, you'd know that 2^n actually has 0.30103*n decimal digits.

Re:That brings back some memories...

[naff]

That is the one I did it with. Until the pretty smoke billowed out of my no-fan-needed Mac. The parents were not amused.

Re:That brings back some memories...

[nojomofo]

Well, no. I do know some math. But I suspect that 2 ^ 2 has 1 decimal digit, not .60206. And 2 ^ 4 has 2 decimal digits, not 1.20412.

wolfram.com?

[Anonymous Coward]

I wonder if "Wolfram Research" had a trademark dispute (or at least cause for one) with the producers of "Angel".

Can't see the pattern?

[nitio]

Of course it will do all this things... it's the 42nd Mersenne Prime...

ok now , back to protien folding!

[L1nux_L0ser83]

...now that weve got this important prime number thing handled..lets get back to folding protiens...

im a geek...but damn...thats uber-geekish

Re:ok now , back to protien folding!

[Anonymous Coward]

Please note in the comment above that protien is how a faulty protein folding program decoded that protein into a word.

the trouble is

[pmike_bauer]

The number in question is currently being double-checked by George Woltman

Ok...lets see here...

5465875133124687545551258898456556......98034802

BUMMER!

Re:the trouble is

[Surt]

No no, you misunderstand. When they tell you a mersenne prime, they're giving you the exponent.

Re:the trouble is

[FnH]

All exponents of Mersenne Primes are primes too.

Re:the trouble is

[Maxite]

So if someone took a Mersenne prime and used it as an expontent to find a Mersenne prime, would the resulting number then be a Mersenne Mersenne Prime?

Re:the trouble is

[Anonymous Coward]

So 2^127-1 is Mersenne Mersenne Mersenne Mersenne Prime :-).

Re:the trouble is

[Surt]

I can't believe this got moderated offtopic. How much more on-topic could you possibly get. Maybe the moderator just didn't understand.

What an incredibly awesome...

[GatesGhost]

...waste of time, money and processing power. what kind of use would this have, other than just knowing it? its like winning a eating contest: a completely useless achievement, plus it just turns to poop.

Re:What an incredibly awesome...

[Dan Farina]

Tell that to the number theory and crypto guys.

Re:What an incredibly awesome...

[loqi]

You're right! And for that matter, what use has space travel been for us? I mean, all we ever did was go there and come back! Ridiculous! Or physics! All it ever got us was a bunch of equations!

Properties of mathematics seem to be the very underpinning of our collective reality. I'd say anything that tells us more about those properties, however esoteric they seem to be, is worth pursuing.

Re:What an incredibly awesome...

[SmokeHalo]

But that poop could eventually fertilize a garden.

Re:What an incredibly awesome...

[zx75]

Don't knock the achievements of mathematicians because you cannot concieve of an application of the results.

Public-key encryption was only developed in 1976, about 2400 years after the first known discovery of prime numbers.

I'm pretty certain the ancient Greeks at the school of Pythagoras would have been as facinated at discovering the existance of these numbers and discovering new ones as we are today with Mersenne primes. It did take around 100 years before Euclid's Elements proved that there were in fact an infinite number of primes.

Re:What an incredibly awesome...

[Anonymous Coward]

Uh, dude, you're reading Slashdot..

Re:What an incredibly awesome...

[The MESMERIC]

Parent should have been
Score:-1, Clueless

Re:What an incredibly awesome...

[PurpleFloyd]

You know, a lot of people said the same thing about the study of number theory prior to World War II. Of course, number theory turned out to be a decisive factor in the war - it allowed the Allied forces to break Axis codes and gain a clear view of the situation behind enemy lines. In both the Pacific theater (especially Midway) and the European theater, it was the esoteric field of number theory which won battles and saved thousands of lives.

What about quantum physics? Those esoteric investigations turned into the transistor and the atomic bomb; they indisputably changed the course of history forever. You almost certainly wouldn't be reading this right now if it weren't for research that, at the time it was done, seemed extremely theroretical and devoid of any practical use.

Does this mean that Mersenne primes are destined for this kind of greatness? Of course not. Still, just because something has no immediate practical value, doesn't mean it's not worth pursuing.

When will this be put into SSH or MUTE?

[Anonymous Coward]

I just want to know when will this be put into SSH and MUTE filesharing ?

Screw you AC

[Mr Guy]

If we discover aliens, I am going to eat them.

OMG! Do you know what this means!?!?!

[Eskimore_]

OMG! Do you know what this means!?!?!

.

.

No really, please tell me. I haven't a clue...

Re:OMG! Do you know what this means!?!?!

[tinkerton]

Is it a stunt for that Hitchikers guide to the Galaxy movie that will be coming out soon?

42? gimp?

[Esine]

42? the GIMP? so that must mean GIMP is answer to life, the universe and everything. (thats 42 decoded)

Here's one good reason...

[thesatch]

http://www.eff.org/awards/coop.html

Thought it takes my 1.7Ghz 3 months to test a 10mil digit prime.

OT but I'll bite..

[MikeFM]

Owwie you pain me. I can't stand using Photoshop. It's so hard to get things done that I keep switching back to GIMP. It's really a case of which you're used to. I have issues with GIMP's usability but I have just as many with Photoshop's usability. In fact I have issues with most software's usability. :)

Something`s wrong...

[Anonymous Coward]

A story on slashdot including the number 42 receives only one or two tiny comments including references to Hitchhiker's Guide to the galaxy?
Something`s wrong here ...

Re:Something`s wrong...

[SmokeHalo]

Don't panic, it's under control. Stay hoopy and you'll sass what the froods are up to.

Re:Something`s wrong...

[Anonymous Coward]

42's not cool anymore, now that it's going mainstream.

You ask why?

[SafteyMan]

Its called knowledge for the sake of knowledge. They found the number because they could. You'd think nerds would be the first to understand the nature of this discovery...

Re:You ask why?

[PDAllen]

Yes, but there are interesting things in maths and there are less interesting things.

A table of all primes up to N is very interesting, lots of things to see.

A general theorem is usually interesting.

Spending a long time finding Mersenne primes is boring. We already know just about everything we want to know about Mersenne primes; the only major open question is whether there exist infinitely many, and that can't be answered by searching. A long string of 1s is not interesting, even when there are a prime number of 1s, and even when the binary number given by that string is itself prime. It's interesting that such things exist, and that there are nice algorithms for primality, but we already know that.

Use

[northcat]

For all those posters asking about how this is useful to people: Now that we know this, our (human) knowledge has increased by this much. That's the use. Knowledge.

Re:Use

[teknomage1]

I don't think people are asking what use this is because they're implying that it's useless. Most, myself included, probably feel there's a reason that the story has been posted to slahdot and, not knowing the significance of a mersenne prime, are hoping that others will tell them.

2^31 is not anywhere near that long

[Anonymous Coward]

As most programmers would know 2^31 is the same a MAXINT on a 32 bit system. In other words, about 2 billion... not anywhere near 65 thousand digits long.

GIMPS vs The GIMP

[Anonymous Coward]

These guys should sue each other for trademark infringement.

With any luck they'd both be forced to change their name to something sensible.

Re:GIMPS vs The GIMP

[Anonymous Coward]

The Gimp was that leather-clad love slave that Maynard had to wake up? Well, in my family to "gimp" someone is to make that sequential tapping with the fingers on the skull.

I claim that this use of the word gimp is better than GIMP or GIMPS.

Re:GIMPS vs The GIMP

[Anonymous Coward]

So what if OSS brought out the (Gnu Integer Manipulation Program) Would that cause infridgement? The Gimp is just a harmless geeky tool to give Linux and Unix guys a way to undress Brittany Spears. Why should PhotoShop users have a lock on phony porn anyway! Same thing why should Mathlab have a lock on math science. When Scilab is just about the same. Trade mark infridgement law suits are for foolish corporate dolts, imitation drives competition and innovation.

Math computing tools do not need to be differentiated. Best example is Excel, a very good play on the Words and it is only a simple little hack of a spread sheet. Now if MS had chosen something like Celecalc would the inventers of Visicalc sued then and won? Not likely. My own program for math has a similar name it is;

CALCYOULATER

ByeBye

Re:GIMPS vs The GIMP

[Anonymous Coward]

One shall become GIMPbird, and the other GIMPSfox!

MOD PARENT UP

[northcat]

One of the few truly funny posts.

Prime number bear

[SoCalChris]

So how long would it take this guy to crap out the number they found?

Mixed results

[UnknowingFool]

While this is a great academic achievement . . .

Damn it! I have to change my luggage combination again. Darn you, George Woltman!

GOOD QUESTION!

[Total_Wimp]

Why this got marked troll is beyond me. Us non-mathmaticians are curious about what significance there is for categories of numbers that mathmaticians get excited about.

If an expert gets excited, there's usually a reason. It's reasonable for non experts to ask what that reason is.

TW

Re:GOOD QUESTION!

[Surt]

It's one step closer to proving there's an infinite sequence of these numbers. Just infinity - 42 more to go and the proof is complete!

In all seriousness, they are interesting mainly because they are so simple mathematically that very very early mathematicians got interested in them. But even after hundreds of years of interest among mathematicians, there's no formula for predicting them, and very little successfully proven about them.

Since they are so rare, each find is a significant advancement for those who might be interested in trying to find a pattern.

Re:GOOD QUESTION!

[Darby]

If an expert gets excited, there's usually a reason.

Except mathematicians often get excited about things that are cool only to mathematicians. If it has any uses, fine, but that's not why they do it.

Occasionally, hundreds of years later it turns out to be just what some physicist is looking for.

As far as I know, the Mersenne primes fall into the category of things which aren't useful in a practical sense.

Re:GOOD QUESTION!

[Artifakt]

What use are they?
There may or may not be patterns in the way Merseinne primes occur.
If there are any patterns in Merseinnes, we may need to find more examples than we had before we can find those patterns.
If we do find patterns, they may or may not help us find other patterns that apply to other types of large primes in more general ways.
There is no guarenteed use outside of abstract math, but there is at least a small possibility we could crack one of the really big problems in crypto starting from whatever patterns we might discover about Merseinnes.
We are spending a lot more on developing specific quantum computing applications that just may eventually lead to cracking that same problem. Given the relative budgets involved, if the Merseinne approach has even 1/1,000th of the chance of success it is still very cost effective (or we're spending way to much on quantum computing related crypto research).

Gah!

[Krakhan]

And when I saw the word prime in the title, I thought the Riemann Hypothesis might have been proven. I guess I'll have to do it myself if no one else does soon. :P

This is news?

[null etc.]

C'mon man, I found the 42nd Mersenne Prime 2 years ago with a pocket calculator. Once you know the trick, it's easy.

Re:This is news?

[Anonymous Coward]

And I assume you included the trick, but slashcode stripped it out before posting.

Re:This is news?

[null etc.]

And I assume you included the trick, but slashcode stripped it out before posting.

Nope, federal gag order.

Re:This is news?

[Anonymous Coward]

...kinky..!!

Re:This is news?

[Anonymous Coward]

94280904 M+ 0 - MR = x MR =

Well whaddya know, it overflowed!

Re:This is news?

[Artifakt]

I've found the trick, but it's too large to include in the margin of this little box Slashdot gives me. :-)

On news like that...

[SmokeHalo]

...let's have a three-day weekend (probably).

GIMPS

[Anonymous Coward]

>> If this pans out, GIMPS will have been responsible for the eight current largest Mersenne Primes ever discovered.

It's no longer politically correct to call them "Gimps", the correct terminology is now "cripples".

42

[sosuke]

the answer to life, the universe and everything is 42, thats it, we are done
http://www.google.com/search?q=the+answer+to+life% 2C+the+universe+and+everything&sourceid=mozilla-se arch&start=0&start=0&ie=utf-8&oe=utf-8&client=fire fox&rls=org.mozilla:en-US:unofficial

Re:Woohoo! The world is saved!

[Anonymous Coward]

it could be done, but i am afraid corporate greed wont let it happen unless $$$$$

On a related note

[OverlordQ]

Seventeen or Bust (a distributed attack on the Sirpinski Problem), found the fourth largest (well fifth if this one pans out) prime at the beginning of this year, which contains 2,357,207 digits.

28433 * 2^7830457 + 1

List of all of the largest primes can be found here

Re:Would a math geek...

[Anonymous Coward]

Well if you CUT it then reading TFA won't really help now, will it?

Couldn't one just transmit the number of digits?

[benhocking]

If it's all 1's (I'll trust you on this, since I haven't RTFA), then it might make sense to transmit the first 42 Mersenne primes by transmitting the number of digits in them instead of transmitting their binary representation. Now, instead of transmitting 2 million 1's, we can transmit 21 0's and 1's. Of course, this gets back to them understanding what we're transmitting. (I think it would take a lot of patience for them to interpret 2 million (give or take) 1's as being a Mersenne prime. And what happens when Vega sets and they stop receiving our transmission?)

Dont you mean..

[adeyadey]

one?

3 = 11, 7 = 111

[benhocking]

2^n-1 = 111....1

Re:3 = 11, 7 = 111

[Surt]

The real problem with using this to communicate with aliens will be deciding whether to use bigendian or littleendian encoding.

Re:3 = 11, 7 = 111

[Anonymous Coward]

Someone should mod you up. That's the funniest comment I've seen so far. The people who make the "aliens wouldn't know it from filler" comment don't understand primes. They're rather distinct objects.

Not that I think that's such a wonderful application. Just the comment isn't funny.

Re:3 = 11, 7 = 111

[Surt]

Thanks, I think you may well be the only one who got it.

Ok, I don't get it.

[scstsut]

Does this or does this not give us the question?

And if so, could a real geek explain the question to a want to be?

Re:Would a math geek...

[iamlucky13]

If its prime, it is a Mersenne prime.

11 (base 10) = 1011 (base 2) = 2^4-5 != 2^n-1

Counterexample! The Mersennes (2^n-1) and the primes form intersecting sets with their intersection being, of course, the Mersenne primes. The primes are not, as you stated, a subset of the Mersennes, nor is the opposite case true.

Organizer of Gimps?

[puppetluva]

The number in question is currently being double-checked by George Woltman, organizer of GIMPS

Somehow, I don't think that the world will be threatened by George Woltman and his organized gimps.

Overheard in the Math Dept...

[Shadow Wrought]

"OK, I've narrowed the range down to between zero and infinity. The rest is up to you..."

Re:Overheard in the Math Dept...

[Anonymous Coward]

-42

Re:Overheard in the Math Dept...

[novakyu]

"OK, I've narrowed the range down to between zero and infinity. The rest is up to you..."

Hey, that's set of positive real numbers (far smaller than the largest set of numbers defined so far)---you don't know how many times I wished I could assume that.

Oh, and yes, I do include 0 in my set of positive real numbers. I just don't like such circumlocutions like "nonnegative" number---and even worse, "nondecreasing" sequence, instead of "increasing" sequence.

Re:Overheard in the Math Dept...

[Anonymous Coward]

"OK, I've narrowed the range down to between zero and infinity. The rest is up to you..."

But professor, according to your paper from 1999, the answer is somewhere between -9 + 8i to -24 + 31i !!!. Isn't it time you stopped using Excel as a calculator ?.

Re:Would a math geek...

[Kiryat Malachi]

A Mersenne number is all ones when written in binary. If its prime, it is a Mersenne prime.

Hey. Idiot. The "it" refers to a Mersenne number, not to the set of all primes.

I.E. if it is a Mersenne number, and prime, it is a Mersenne prime. I know that the grammar of the GP was a little sloppy, but I think you owe him at least a little inference in that it was pretty obvious he was referring to the subset of primes within the set of Mersenne numbers, and not the set of primes within the integers.

Re:Would a math geek...

[neosake]

"If its prime, it is a Mersenne prime."

I think it's the other way around - a Mersenne prime is a prime, but a prime isn't always a Mersenne prime.

For example: I can think of many primes between the 2nd Mersenne (2^3 - 1 =7) and the 3rd Mersenne prime (2^5 - 1 = 31).
(e.g. 11, 13, 17, ...)

Re:Woohoo! The world is saved!

[Anonymous Coward]

You forgot "bring an end to slashdot trolling".

Re:Couldn't one just transmit the number of digits

[John Allsup]

Why Mersenne primes are entirely composed of 1's: A Mersenne prime is a prime of the form 2^n-1. A number of the form 2^n will look in binary like 100...00 with n zeros (just as 10^n has n zeros when written to base 10.) Subtract 1, and you obviously get 011...11 with n ones, and of course we ignore the leading zero.

Why not transmit the length? This just means transmitting n rather than 2^n. No reason I can see why not.

binary

[blixel]

Interestingly, this means that Mersenne numbers are simply strings of 1s when represented in binary.

I'm looking at their list of Mersenne numbers. Here is what I come up with.

2 in binary is 10
3 in binary is 11
5 in binary is 101
7 in binary is 111
13 in binary is 1101

So I'm not sure what they mean by saying that Mersenne numbers are all 1's in binary.

Re:binary

[Anonymous Coward]

Mersene Numbers and Prime number are different but overlapping sets.

Primes: 2, 3, 5, 7, 11
Mersene Numbers, 1, 3, 7, 15, 31

Notice that 3 and 7 are in both sets, hence they are Mersene Primes.

Re:binary

[Anonymous Coward]

Those aren't the numbers themselves, but rather 2 means the mersenne prime is 2^2-1, or 3, and 3 means 2^3-1, or 7, and 5 means 2^5-1, or 31, etc.

Re:binary

[mldl]

2 (as per usual) is a special case. 5 and 13 aren't mersenne numbers and therefore aren't in the list. Those numbers are the "exponent" as in 2 to the power of 5 minus 1 = 31 and 2 to the power of 13 minus 1 = 8191 are both mersenne primes and are both strings of 1 in binary.

Re:binary

[fishbowl]

>5 in binary is 101

2^5-1 = 31

31 in binary is 11111

Re:binary

[Anonymous Coward]

Those are not Mersenne numbers. Those are the coefficients.

M1 = 2^1-1 = 1 = 1
M2 = 2^2-1 = 3 = 11
M3 = 2^3-1 = 7 = 111
M5 = 2^5-1 = 31 = 11111
M7 = 2^7-1 = 127 = 1111111
M13 = 2^13=1 = 16383 = 1111111111111

Re:binary

[Anonymous Coward]

That's because your reading it wrong. In the article, p is the power of 2. The actual Mersenne prime is 2^p-1.... so 2^7-1 which is 127, is a Mersenne prime, which is a series of 1's in binary.

Re:binary

[Surt]

The mersenne primes are two to those numbers minus one. Those are the mersenne numbers, not the primes.

Re:binary

[Anonymous Coward]

Oops...M13 = 2^13-1 = 8191 = 1111111111111

Re:binary

[lucason]

Dude... You might want to check up on the defenition!! Mersenne numbers= 2^n-1 NOT: n^2-1 Get it now?

Re:binary

[Anonymous Coward]

Dude... You might want to check up on the defenition!! Mersenne numbers= 2^n-1 NOT: n^2-1 Get it now?

Dude.... You might want to read the posts of the 8 people who pointed that out before you.

Re:Would a math geek...

[Anonymous Coward]

I really hope you mean M7=2^7-1=127. 'Cuz if 27-1 = 127...I need to get a new calculator.

Full text of article

[utexaspunk]

72,881,090,798,676,481,947,445,843,876,689,972,113 ,188,382,077,838,576,766,415,271,554,183,554,023,6 81,926,442,357,773,229,141,527,132,801,050,545,169 ,980,023,429,475,382,981,277,026,411,446,450,732,1 20,206,920,761,648,530,323,773,463,358,502,551,340 ,699,145,522,328,264,108,074,466,176,204,798,818,5 91,643,822,008,785,083,299,073,103,153,980,722,122 ,415,403,264,180,661,744,484,810,522,551,289,556,1 61,305,278,379,785,516,809,393,766,311,656,230,448 ,542,351,852,881,090,798,676,481,947,445,843,876,6 89,972,113,188,382,077,838,576,766,415,271,554,183 ,554,023,681,926,442,357,773,229,141,527,132,801,0 50,545,169,980,023,429,475,382,981,277,026,411,446 ,450,732,120,206,920,761,648,530,323,773,463,358,5 02,551,340,699,145,522,328,264,108,074,466,176,204 ,798,818,591,643,822,008,785,083,299,073,103,153,9 80,722,122,415,403,264,180,661,744,484,810,522,551 ,289,556,161,305,278,379,785,516,809,393,766,311,6 56,230,448,542,351,852,881,090,798,676,481,947,445 ,843,876,689,972,113,188,382,077,838,576,766,415,2 71,554,183,554,023,681,926,442,357,773,229,141,527 ,132,801,050,545,169,980,023,429,475,382,981,277,0 26,411,446,450,732,120,206,920,761,648,530,323,773 ,463,358,502,551,340,699,145,522,328,264,108,074,4 66,176,204,798,818,591,643,822,008,785,083,299,073 ,103,153,980,722,122,415,403,264,180,661,744,484,8 10,522,551,289,556,161,305,278,379,785,516,809,393 ,766,311,656,230,448,542,351,852,881,090,798,676,4 81,947,445,843,876,689,972,113,188,382,077,838,576 ,766,415,271,554,183,554,023,681,926,442,357,773,2 29,141,527,132,801,050,545,169,980,023,429,475,382 ,981,277,026,411,446,450,732,120,206,920,761,648,5 30,323,773,463,358,502,551,340,699,145,522,328,264 ,108,074,466,176,204,798,818,591,643,822,008,785,0 83,299,073,103,153,980,722,122,415,403,264,180,661 ,744,484,810,522,551,289,556,161,305,278,379,785,5 16,809,393,766,311,656,230,448,542,351,852,881,090 ,798,676,481,947,445,843,876,689,972,113,188,382,0 77,838,576,766,415,271,554,183,554,023,681,926,442 ,357,773,229,141,527,132,801,050,545,169,980,023,4 29,475,382,981,277,026,411,446,450,732,120,206,920 ,761,648,530,323,773,463,358,502,551,340,699,145,5 22,328,264,108,074,466,176,204,798,818,591,643,822 ,008,785,083,299,073,103,153,980,722,122,415,403,2 64,180,661,744,484,810,522,551,289,556,161,305,278 ,379,785,516,809,393,766,311,656,230,448,542,351,8 52

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Re:Full text of article

[whovian]

72,881,...,351,852

We're sorry. The Mersenne prime number you dialed is not in service.

Re:Full text of article

[tilrman]

Remarkably, it's also the first even prime discovered in years.

Low memory usage for representation

[davi_slashdot]

I don't actually how they can be usefull, but you certainly can represent them with very little memory, since you can store only the p parameter and retrieve the number very easily.

Re:Would a math geek...

[winavr]

Sure. STFW

Oh, Oh, I know one, I know one!

[rumblin'rabbit]

And in the 1930's a Canadian invented a carburetor that made automobile engines 90% efficient, but it was suppressed by Big Oil so that it wouldn't reduce their profits.

And if you put wet puppies in a microwave they explode.

Know any more?

not all of those are Mersenne primes

[Anonymous Coward]

2,5, and 13 are not Mersenne primes

Re:Would a math geek...

[Anonymous Coward]

Poorly worded, but not incorrect.

A Mersenne number is any number of the form:
Mn = 2^n - 1

Any number 2^n is written in binary as a one followed by zeros. Any number of the form

2^n - 1

is written as all ones in binary. If that number happens to be prime, then it is a "Mersenne prime".

Small steps

[Duncan3]

One small step for mathematics, one giant leap for global warming :)

Please come join Folding@home, we're actually doing something worth all that waste heat. :)

Re:Small steps

[TeknoHog]

One small step for mathematics, one giant leap for global warming :)

Please come join Folding@home, we're actually doing something worth all that waste heat. :)

Oh yeah? How about using that waste heat to help fight more waste heat?

From the Climateprediction.net FAQ:

a rough calculation suggests that 100,000 computers running 24hrs/day for one year at a power consumption of 50W will contribute approximately 0.0001% of the total amount of CO2 generated in one year. This is not an insignificant amount, but seems (to us) a worthwhile investment to better understand the climate system.

My humble opinion is that Folding@Home is not the only worthwhile distributed project out there. As long as your computer is doing something useful with its spare cycles, I'm happy. Besides, what good is protein folding when our brains are coagulated due to global warming?-)

meaning of life, bah

[zenst]

All that distibuted processing power to work out how long to hold the `1` key down :)

Re:Would a math geek...

[Hawkxor]

Will somebody mod this guy down for being 1. a tool; 2. stupid; and 3. unbelievably stupid. ?

Bring Out the Gimps!

[Anonymous Coward]

A: Bring out the Gimps.
B: The Gimps are calculating.
A: Well i guess you have to stop calculate'n now won't you.

i cannot be the only person to have this thought?

if so man maybe its time i leave my gimp cage!

correct me if i'm wrong

[xmp_phrack]

most primality tests are probabilistic in nature. will the final test determine for a fact that it is a prime?

Re:correct me if i'm wrong

[Anonymous Coward]

The best general purpose primality tests are indeed probabilistic, but GIMPS uses a special purpose deterministic algorithm that checks if Mersenne numbers (those of the form 2^n-1) are prime. In fact, a general purpose algorithm would have trouble with numbers this big. I am sure this is explained in detail in their website.

Re:correct me if i'm wrong

[rbarreira]

It's called a Lucas Lehmer primality test, which only works for mersenne numbers.

Perfectly Mersenne

[spaceyhackerlady]

A Mersenne number is all ones when written in binary. If its prime, it is a Mersenne prime.

A fun sidebar to this is perfect numbers, numbers who factors (other than one and themselves) add up to the number. Ancient Greek numerology, y'know.

It's not at all difficult to show that a Mersenne Prime times the next smaller power of two is perfect. Perfect numbers thus have an interesting binary representation.

Nobody has yet proven that all perfect numbers are of this form, or even that they're all even.

...laura

Re:Perfectly Mersenne

[Anonymous Coward]

A fun sidebar to this is perfect numbers, numbers who factors (other than one and themselves) add up to the number. Ancient Greek numerology, y'know.

Sorry - the factor '1' is always included. The identity factor is not.

1 + 2 + 3 = 6

1 + 2 + 4 + 7 + 14 = 28

Try again another time.

what a waste of computing power

[Anonymous Coward]

all those flops could of been used in various cancer programs, yet some nerds go wasting it on finding a number. big fucking wow.
stupid, selfish morons.

Re:what a waste of computing power

[The MESMERIC]

i take it you don't waste your flops right?
do you devote any of your time, energy and presence to some noble chariteable cause?

i have a feeling that despite this number-theory experiment of theirs, many of the scientists and mathematicians involved contributed more to humanity, medicine, science and education than you possibly could even in some 2^42-1 years.

Re:Would a math geek...

[Anonymous Coward]

C'mon, stop fooling with me! What is a Mersenne prime? In plain english, please.

Re:Would a math geek...

[iamlucky13]

Sheesh...harsh response guys. I read it three times to make sure I wasn't misunderstanding him. I get it now, but it's still crappy grammar. Plus, my last professor always told us to get excited when we find a counterexample to a statement.

I know the next few

[caluml]

Haven't they found the one 2 up from that one yet? I cracked it the other day. It's 10921601209381283939528579258588293236501826350187 26347610732650752384751204702754081273540781523087 60187259387598287309820238560861098264011

Re:I know the next few

[Sigma 7]

Haven't they found the one 2 up from that one yet? I cracked it the other day. It's 10921601209381283939528579258588293236501826350187 26347610732650752384751204702754081273540781523087 60187259387598287309820238560861098264011

If you want to type in a random number and claim it to be prime, at least have the decency to check that it isn't divisible by 3.

A quick way of confirming this is to ensure the sum of all it's digits does not add up to a multiple of 3.

Re:I know the next few

[Anonymous Coward]

If you want to type in a random number and claim it to be prime, at least have the decency to check that it isn't divisible by 3.

And 79. And 109. And 1723. And 4003. And 37907. Well, maybe even 5269673. And 5327107. :-]

The answer is 42

[Levetron]

Is it a coincidence that The Hitchhikers Guided to the Galaxy is soon out in theaters?

I don't think so....

Not interesting

[Jussi K. Kojootti]

I'm not interested.

...if only they'd found Optimus Prime.

just remember

[Anonymous Coward]

fold for team 11314

Cryptography, likely

[jd]

Usually, primes are of interest in the field of cryptography. Specifically, it is desirable to have numbers that are the product of two gigantic primes. This is because it is extremely difficult to find out what those primes are.

What cryptographers then do with these amazing numbers is secret, but seems to involve chicken feathers.

Re:Cryptography, likely

[Hank the Lion]

Usually, primes are of interest in the field of cryptography. Specifically, it is desirable to have numbers that are the product of two gigantic primes. This is because it is extremely difficult to find out what those primes are.
Unless one of the primes happens to be a Mersenne prime. Simply divide your product by all 42 known Mersenne primes, and if the result is integer, you have found your factorization.

Re:Would a math geek...

[Canadian_Daemon]

For all of the computer geeks, recognize 2^n -1 = all 1's in binary
2^4 -1 = 15 = 1111

So this means...

[mordejai]

...nothing?

OT: Re:GIMPS vs The GIMP

[ambrosen]

One of my long term coding plans is to make a fork of the GIMP that has a sensible name, but I haven't thought of it yet. Maybe a few other alterations, too, but that'd be trickier.

B.S.

[Anonymous Coward]

List of all of the largest primes can be found here

There is no "largest prime". There cannot be a list of "largest primes".

Re:B.S.

[Anonymous Coward]

largest found you fucking grammar nazi.

Wait a minute!

[savage1r]

Isn't 42 supposed to be the answer(According to Hitchhiker's Guide)?

Inifinite number of primes

[kickdown]

This is not just a theory. It is a well-proven fact since centuries. And there is even more than one proof for it. Ever since Euler's proof other mathematicans have had a fun time (for what they think is fun) finding approx. ten elementary independent proofs for it. Why some people like finding big primes? No idea. Probably because they think they are cool then.

FYI

[Anonymous Coward]

Your sig is spam (ad for Apple).

cong.to@gmail.com

[Anonymous Coward]

cong.to@gmail.com

LOL WHAT

[Anonymous Coward]

I THink u on crack. 41st! LOL NOW

Perhaps that was a little harsh

[Anonymous Coward]

What I meant to say was: "La dee fuckin' da"

If it only stopped at 42

[Anonymous Coward]

So what was the question again? ;o)

Oh, great

[Sloppy]

Now I have to change my public/private keypair.

Better yet....

[Rufus88]

A sure way to prove to another being that you are intelligent is to spew a bunch of numbers which all happen to be prime. The fact that they can be tranmitted using only '1' bits means the modulation is simple -- just send a series of pulses.


Wouldn't it be better to send the *number* of pulses that you would send, encoded in binary?

so very interesting

[sacrilicious]

The study of such numbers has a long and interesting history

Reminds me of when Bart Simpson's 4th-grade class was forced by Principal Skinner to have their annual field trip take place at a box company (instead of the hoped for chocolate factory / fireworks outlet / circus):

Tour guide (speaking in monotone nasal voice): The story of how two brothers (and five other men) parlayed a small business loan into a thriving paper-goods concern is a long and interesting one. And, here it is: it all began with the filing of form 637/A, the application for a small business or farm...

Re: 42nd Mersenne Prime Probably Discovered

[Anonymous Coward]

Alright, the Answer to the Great Question ...
Yes ... !
Of Life, the Universe and Everything ...
Yes ... !
Is ...
Yes ... !!! ...
Forty-Two
WTF ... Forty-Two what ... ??? ...
Mersenne Primes apparently.

(apologies DA THHGTTG)

Not a Beowulf cluster

[Anonymous Coward]

Just imagine a Mersenne Prime cluster of these ...

Better use of computing power

[ulatekh]

How about digital video? I'm converting my vast videotape/LaserDisc collection to VideoCD and DVD. I could tie up a 2048-processor Linux-based supercomputer with my video processing.

Re:Would a math geek...

[Anonymous Coward]

1580,187,223 divides (10^9)^(10^9)+3.
864,000,001 divides (10^9)^(10^9)+1.
ten thousand days plus a heartbeat.