## New Record Prime Found 112

Posted
by
kdawson

from the mersenne-is-a-gimp dept.

from the mersenne-is-a-gimp dept.

An anonymous reader writes,

*"The GIMPS project has found a new record prime. 2 ^ 32,582,657 - 1, clocking in at over 9 million digits, is a Mersenne prime, as were the last few record primes. Here is the 9-megabyte decimal expansion."*
## "Nothing to see here... (Score:3, Funny)

That's what

</tinfoil hat>

## This is like playing tabletennis alone (Score:2, Insightful)

The longer they run it the more they will find.

They are getting all the records because noone else is "trying" as hard.

Good luck that they get the 10million digits, but its just a pissing competition as far as I can see.

They win 100,000 from the EFF for breaking it, but the computational power and time wasted has to be getting close to that it

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Yeah, all that computing power could be doing something useful, like say, helping the NSA and other TLAs break encryption keys. Probably under the cover story that they're 'searching for extraterrestrial intelligence'... Yeah, like that'll ever happen..

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I run Folding@Home since my computers are on 24/7 anyway--and if it leads to a cure for cancer/leukemia/Hodgekins'/alsheimer's/whatever-ot her-cancer-related-disease, I won't mind if someone makes money off producing the cure.

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## I settled on Climateprediction.net (Score:2)

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I don't think that it's fair to say that no-one is trying as hard, as many people are, it's just a matter of quantity of effort, rather than quality of effort. GIMPS is huge (and maintains a momentum because of that - people join it because it's the biggest).

So electricity-wise, you're not just right, you're so right that you're completely wrong! (Did that make sense?) It we pretend that on average they have been running 50000 machines for

## Woo Hoo! (Score:3, Funny)

## That's amazing! (Score:5, Funny)

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## Biggest non-Mersenne prime? (Score:2, Interesting)

So what's the biggest known prime number that's not a Mersenne number? Wikipedia's "Prime number" article [wikipedia.org] states that it's a prime Proth number [wikipedia.org], but what about the biggest prime that's not of any special form? Or is that illegal [wikipedia.org] to discuss on Slashdot, a server on US soil?

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what about the biggest prime that's not of any special form?I'd tell you, but it doesn't fit in the comment limits.

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I'd tell you, but it doesn't fit in the comment limits.Just list the factors... I'm sure we can do the math ourselves.

## Not of a special form? (Score:2)

specialform? Wouldn't such a definition make the prime of a special form?## Compressibility (Score:1)

I was operating under the assumption that consensus among pure mathematicians creates the list of formulae known to produce a lot of large prime numbers from a few arguments. These include Mersenne numbers (where Mersenne(n) = 2^n - 1 for all prime n) and Proth numbers (where Proth(k, n) = k*2^n + 1 for all odd k < 2^n). I was looking for primes that aren't as compressible.

## A good definition (Score:2)

## Random data followed by an odd integer (Score:1)

Kolmogorov complexity [wikipedia.org] is an objective measure of compressibility. However, this measure is not computable.

Finding such a prime is straightforward. Take a block of true random data (which is incompressible by definition), append an odd integer, and then increase that odd integer until primality tests such as ECPP [wikipedia.org] come back true. This is the technique used

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2 => 1

3 => 2

5 => 3

7 => 4

See? 2 is the 1st prime, 3 is the second. Just make sure you haven't missed any as you get to larger primes. As a tradeoff, the compression factor eventually gets very high.

## No expert in primes or compressibility, but... (Score:2)

Truly random data definitely has a chance of being compressible. For example, there's a 1 in 2^50 chance that a random, fair Bernoulli process will generate the string /1{50}/. If I use a biased Bernoulli process, say with p=0.999, I can generate such a string with much better odds. Specifically, there's more than a 95% chance that I'd generate that string, and there's even a 37% chance that I'd generate /1{1000}/, for a string of size 1,000.

I read the piece on Kolmogorov complexity, and although it's the

## Self correction (Score:2)

Um, that's only true if the machine the program is being run on is limited to n binary states. So, for a true Turing machine, I think that actually calculating the Kolmogorov complexity is not even theoretically possible, unless the "language" specification stipulates a maximum amount of memory to u

## Stars die before halting is solved (Score:1)

I was operating under the assumption of a fair Bernoulli process. In the case of something in any way biased, the device driver will likely convert it to a lower-bandwidth fair Bernoulli process by hashing blocks of raw data and returning one output bit for several raw bits.

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Still, regardless of definitions, it would be interesting to find such a prime, or to postulate about their existence. Is there a postulate that such a prime must exist?There are infinite primes, we know that. Whether every single prime can fit into some kind of classification, though, we don't know. It's conceivable that there might be, but it seems incredibly unlikely, especially given things like the classification of all finite simple groups (most of which fall into a few neat categories and then t

## Re:A good definition (Score:4, Informative)

5, for example, is a solution to the general formula A(x^C)+D, sum(x)+C, Cx+D, and so on. (Because A, C and D are constants, they would need to be the same constants for all primes you apply the expression to. Otherwise, you've not really generalized or simplified anything.) It is easy to show this has an infinite number of special solutions - pick any value of C and for any equation with D in it, simply subtract/add the necessary value to give you the prime you want.

The original question, then, is whether there is any prime number (other than the three special cases listed) for which {E}

Let us define something else, which is #({E}

(It is easy to prove that there exist two primes which have no general form in common, as that is simply the same as the proof that no general equation for primes exists.)

This leads to interesting possibilities - "islands" of primes that are totally disconnected from all other primes, "peninsulas" where you almost have an island but some perfect subset of the cloud does have a general form in common with other primes, "mountains" where you have a massive number of general forms totally in common with a large number of primes, and so on.

If you were to draw out the interrelationships between primes as a topology, what do you see? A random blob? A sea of islands? Multiple large masses that are otherwise disconnected? If islands, or multiple disconnected continents, exist in prime number space, does this mean that prime numbers aren't a single, definable set of numbers at all, but multiple concepts that should (in general) not be treated as the same at all? Will the map indicate that we can generalize the definition of prime number in a useful way, that the concept can be usefully extended and meaningfully applied outside of the natural numbers?

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Ed

## Might be arbitrary enough (Score:2)

## FTA (Score:1)

Perfectly Scientific, Dr. Crandall's company which developed the FFT algorithm used by GIMPS, will make a poster you can order containing the entire 9.8 million digit number. It is kind of pricey because accurately printing an over-sized poster in 1-point font is not easy!And to think, all I had was a Ghostbusters poster when I was growing up.

## You know what would be funny? (Score:2)

## Re:You know what would be funny? (Score:4, Funny)

## Re:You know what would be funny? (Score:5, Informative)

Seeing as 2^n is [1 followed by n 0's] in binary, and [1 followed by n 0's] minus 1 is [(n-1) 1's], this number in binary will just be 32,582,656 1's, which isn't decodeable as an MP3.

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## Know what... (Score:2)

## Come on there (Score:1)

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Basically, mersenne primes are of the form (2^p)-1, where p is a prime. The reason that these numbers seem to keep turning up as really big primes is that there is a very special test which checks if just this type of number is prime. The Mersenne project is searching it's way through all possible candidates to see if it can find some big primes.

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Mersenne numbers are of the form 2^N - 1, which is essentially a binary string of N consecutive 1's. For example, the tenth Mersenne number - aka M(10) - is 2^10 - 1, which is 1023. The binary representation of 1023 is 1111111111.

The answer to your question is on the GMPS homepage [mersenne.org]:

## Or... (Score:2)

How about if I released it as a record? Would it then become illegal?

I can't believe it would sound any worse than the rubbish kids are listening to today

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If they announced finding a new large prime number, and then later realized the number was even, and they hadn't noticed that.Even funnier -- they name it "Optimus."

## It's nice to see, but... (Score:1)

I mean, Dnet have pretty much proved that any encryption key less than 64 bits is hopelessly insecure (ISTR they're working on 72 bits at the moment), and they did the Optimal Golomb Rulers search, but what possible use does all this stuff have? Are we just looking for things that are neat, but have no use in the real world?

Folding@Home is still pretty neat th

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## Re: (Score:3, Informative)

Folding@Home is still pretty neat though - the whole "use your spare CPU cycles to (potentially) find cures for various nasty things"I think you should have said:

Folding@Home is still pretty neat though - the whole "use your spare CPU cycles to (potentially) find cures for various nasty things

and enrich the patent portfolios of drug manufacturers"HTH HAND

-R

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At least finding ETs doesn't involve enriching some MegaHuge PharmaCo's patent portfolio...

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## Expand it yourself (Score:4, Informative)

If you want to expand the number on your machine, run this:

perl -Mbignum -e 'print 2**32582657 - 1'If it takes too long for you, you can also have perl print an approximation:

perl -e 'print 2**32582657 - 1'## Re: (Score:2)

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It's running in the background on my home linux router, an older AMD XP 2700+. Already up to 334157 and the load is only 2.50. Wonder how long it will take until I get to 2^32582657? ;)

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Then, all i have to do is edit the executable file and put $x=(1895693 +1) to pick up where I left off.

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You're not checking even numbers are you?

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I have it running for whole three hours now, still no result.

relevant info from

model name : AMD Opteron(tm) Processor 248

cpu MHz : 2193.796

cache size : 1024 KB

bogomips : 4377.80

## Pfft. Doesn't stand a chance... (Score:4, Funny)

trueprime...OPTIMUS PRIME!## The Actual Number (Score:4, Informative)

## clicks text link... (Score:1, Funny)

*head explodes*

## Awww (Score:2)

## Huh? (Score:1)

My question is, can someone describe to me in SIMPLE terms what a Mersenne prime is?

Do we really do math where we need to discover prime numbers this big? I mean, its like trying to compute pi. I mean, once you take PI out a few decimal places, its as accurate as most people need it. Do we really need super computers that do nothing better with their time than calculate this kind of stuff?

I am sorry if I sound ignorant, but i

## Re: (Score:2)

f(x)=(2^x)-1. "f(x)" is prime. Another way of thinking about it is like this. In binary representation, all the bits are set to "1". There are a few of these for small

x, but as it gets larger, the primes are few and far between. One of the issues in mathematics is figuring out if there is a "last" Mersenne prime. Is there one so big there isn't one larger of this special form? I doubt it, but nobody can prove it one way or## Re: (Score:3, Funny)

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Hey everyone! Let's massacre the parent! Bonus karma points to the one who can shoot down the suggestion the best!

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I say bonus karma points to this guy:

http://slashdot.org/comments.pl?sid=196548&cid=16

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Go figure., gotta love math

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I thought that all numbers in the form 2^n -1 are prime - If I am correct, what's so new about this number? -NicolasNope, most of them aren't:

(2^3)-1 = 8 - 1 = 7 (prime)

(2^4)-1 = 16 - 1 = 15 (not prime, 3, 5)

(2^5)-1 = 32 - 1 = 31 (prime)

(2^6)-1 = 64 - 1 = 63 (prime)

(2^7)-1 = 128 - 1 = 127 (prime)

(2^8)-1 = 256 - 1 = 255 (not prime, 3, 5)

etc..

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Prime1*Prime2-2? (so long as neither one of them is '2')

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Trust me. If it was this easy, we'd have heard of it long ago.

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7 * 5 = 35

35 - 2 = 33

33 = 3 * 11

2 * 5 = 10

10 - 2 = 8

8 = 2 * 4

7 * 11 = 77

77 - 2 = 75

75 = 5 * 15

Just to cite a few.

## *ahem* (Score:2)

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Also, for a number to be a Mersenne prime, the 'n' from 2^n-1 must be prime (according to Mathworld [wolfram.com]).

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Take 2^4 - 1 = 15 = 3 * 5

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So for 2^n-1 to be prime, n itself must be prime.

Quick proof - consider the values of 2^i modulo (2^a-1) for i=0..n,

You'll notice that 2^0 == 2^a == 2^(2a) ==

i.e. 2^n-1 == 0 (mod 2^a-1)

Note, however, that it's a necessary condition, but is not sufficient.

There are plenty of prime p such that 2^p-1 is not prime.

See http://www.primepages.org/ [primepages.org]

FatPhil

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Ok, to actually be helpful here instead of being the 16th person to say 15 isn't prime (seriously, you should all be marked redundant) maybe the parent was thinking of 2^(2^n)+1, which is a Fermat Prime [wikipedia.org]. Unfortunately, not even Fermat Primes are actually prime, Fermat just thought they were when he discovered them.

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