# New Record Prime Found

#### kdawson posted more than 7 years ago | from the mersenne-is-a-gimp dept.

112
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... (2, Funny)

## tygerstripes (832644) | more than 7 years ago | (#16103302)

That's what

</tinfoil hat>

## Slow news day? (-1, Troll)

## Noxal (816780) | more than 7 years ago | (#16103318)

## Re:Slow news day? (2, Funny)

## Aladrin (926209) | more than 7 years ago | (#16103534)

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

## LiquidCoooled (634315) | more than 7 years ago | (#16103338)

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 itself.

## Re:This is like playing tabletennis alone (1)

## NotQuiteInsane (981960) | more than 7 years ago | (#16103439)

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..

## Re:This is like playing tabletennis alone (1)

## QuantumG (50515) | more than 7 years ago | (#16103459)

## Re:This is like playing tabletennis alone (1)

## $RANDOMLUSER (804576) | more than 7 years ago | (#16103621)

## Re:This is like playing tabletennis alone (1)

## LehiNephi (695428) | more than 7 years ago | (#16104790)

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-o

## Re:This is like playing tabletennis alone (0)

## Anonymous Coward | more than 7 years ago | (#16105623)

## Re:This is like playing tabletennis alone (1)

## BKX (5066) | more than 7 years ago | (#16105828)

## Re:This is like playing tabletennis alone (1)

## freakmn (712872) | more than 7 years ago | (#16106200)

## Re:This is like playing tabletennis alone (1)

## fatphil (181876) | more than 7 years ago | (#16103937)

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 the last 10 years, this prize amounts to 0.2c per machine year.

FatPhil

## Woo Hoo! (3, Funny)

## nystagman (603173) | more than 7 years ago | (#16103355)

## int? (0)

## Anonymous Coward | more than 7 years ago | (#16103414)

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

## johnfink (810028) | more than 7 years ago | (#16103419)

## Re:That's amazing! (0)

## blinder (153117) | more than 7 years ago | (#16103497)

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

## tepples (727027) | more than 7 years ago | (#16103460)

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?

## Re:Biggest non-Mersenne prime? (2, Insightful)

## Anonymous Coward | more than 7 years ago | (#16103765)

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.

## Re:Biggest non-Mersenne prime? (2, Funny)

## nacturation (646836) | more than 7 years ago | (#16105003)

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? (1)

## benhocking (724439) | more than 7 years ago | (#16103837)

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

## tepples (727027) | more than 7 years ago | (#16103963)

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 (1)

## benhocking (724439) | more than 7 years ago | (#16104116)

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

## tepples (727027) | more than 7 years ago | (#16104298)

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 to find the first prime that may be illegal to publish [wikipedia.org] .

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

## djshaffer (595950) | more than 7 years ago | (#16104463)

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... (1)

## benhocking (724439) | more than 7 years ago | (#16104670)

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 theoretically a well-defined measure (given a particular programming language or other form of interpretation), in practice it's doubly exponentially difficult to calculate. I'd have to generate every possible program of size less than n (where n is the actual Kolmogrov complexity) in order to verify that n is in fact the Kolmogrov complexity. Worse yet, for those programs that don't halt (and are of size less than n), I'll have to know that they don't halt. (Despite the well-known issues with the halting problem [wikipedia.org] , this can actually be done trivially for a program of maximum size n if you have a machine of state size 2^n (for a binary language) and a lot of patience.)

## Self correction (1)

## benhocking (724439) | more than 7 years ago | (#16104869)

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 use (perhaps relative to the size of the string being examined). In my opinion, this is not an unreasonable expansion of the definition, however. E.g., if it requires 2 Gigs of RAM and/or hard drive space to compress a 10,000 bit number down to a 1,000 bit program, I'm not sure if it's fair to say that the complexity is only 1,000 bits.

## Stars die before halting is solved (1)

## tepples (727027) | more than 7 years ago | (#16104943)

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.

"A lot of patience"? Living organisms have little patience in this universe. True, halting is computable for linear bounded automata, but not in the human lifetime or even in the lifetime of the universe for a reasonably sized program string. By 10^15 years [wikipedia.org] , it is expected that even the stars will die, providing no more energy to run the computation.

## Re:A good definition (1)

## flooey (695860) | more than 7 years ago | (#16105488)

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 there are a set of them that don't fit any known categorization).

## Re:Not of a special form? (1)

## Ed_Pinkley (881113) | more than 7 years ago | (#16104318)

Ed

## Might be arbitrary enough (1)

## benhocking (724439) | more than 7 years ago | (#16104690)

## FTA (1)

## hansamurai (907719) | more than 7 years ago | (#16103476)

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? (1)

## UbuntuDupe (970646) | more than 7 years ago | (#16103499)

## Re:You know what would be funny? (3, Funny)

## x2A (858210) | more than 7 years ago | (#16103668)

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

## kestasjk (933987) | more than 7 years ago | (#16103994)

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.

## Re:You know what would be funny? (0)

## Anonymous Coward | more than 7 years ago | (#16104081)

Actually 1000-1 = 111, not 11.

In other words, it would be 32,582,657 1s.

## Re:You know what would be funny? (3, Funny)

## r00k123 (588214) | more than 7 years ago | (#16104171)

## Re:You know what would be funny? (1, Funny)

## thelost (808451) | more than 7 years ago | (#16104189)

## Know what... (1)

## electrosoccertux (874415) | more than 7 years ago | (#16104472)

## Come on there (1)

## FoamingToad (904595) | more than 7 years ago | (#16104518)

## Prime Base (0)

## Anonymous Coward | more than 7 years ago | (#16108712)

## Re:Know what... (1)

## Chris_Jefferson (581445) | more than 7 years ago | (#16104599)

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.

## Re:You know what would be funny? (1)

## Cragen (697038) | more than 7 years ago | (#16105116)

## Re:You know what would be funny? (0)

## Anonymous Coward | more than 7 years ago | (#16106030)

A vanishingly small percentage

## Re:You know what would be funny? (1)

## Meostro (788797) | more than 7 years ago | (#16106155)

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] :

So Mersenne primes are very rare numbers. The only reason these primes are so insanely large is that we have efficient* methods of primality testing for numbers of certain special forms. It would be

incrediblydifficult to conclusively prove primality for 2^32,582,657 - 473** instead, since it's not of the same special form.* - Efficient is a relative term - this number took hundreds of CPU hours to test for primality. From the same page, it took 6 days on a system "using 16 Itanium2 1.5 GHz CPUs" to confirm the results. For arbitrary 9 million digit numbers however, it would probably take centuries to test primality conclusively, even using current state-of-the-art methods and massive supercomputers.

** - This could be divisible by 3 for all I know, it's very unlikely that it is prime.

## Or... (1)

## mustafap (452510) | more than 7 years ago | (#16104148)

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

## Re:You know what would be funny? (1)

## Billosaur (927319) | more than 7 years ago | (#16103775)

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... (1)

## NotQuiteInsane (981960) | more than 7 years ago | (#16103525)

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 though - the whole "use your spare CPU cycles to (potentially) find cures for various nasty things" concept is pretty neat, and no-one can say that saving lives isn't worth spending a few clock cycles on.

SETI@Home I'm still not sure about. Yes it would be nice to find 'intelligent' creatures on other planets, but what are we going to do if we find them? Chances are they're going to be at least a few light-years away, so the round-trip times for radio signals are going to be pretty severe...

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

## boyfaceddog (788041) | more than 7 years ago | (#16103591)

## Re:It's nice to see, but... (2, Informative)

## Ruzty (46204) | more than 7 years ago | (#16105050)

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

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

## NotQuiteInsane (981960) | more than 7 years ago | (#16105714)

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

## Re:It's nice to see, but... (0)

## Anonymous Coward | more than 7 years ago | (#16105894)

## Help (-1)

## DaFrog (703113) | more than 7 years ago | (#16103529)

## Re:Help (0)

## Anonymous Coward | more than 7 years ago | (#16103619)

## Re:Help (1)

## quaker5567 (841639) | more than 7 years ago | (#16103620)

## Re:Help (0)

## Anonymous Coward | more than 7 years ago | (#16104293)

## Re:Help (1)

## Iwanowitch (993961) | more than 7 years ago | (#16103623)

## Re:Help (1)

## knightmad (931578) | more than 7 years ago | (#16103630)

## Re:Help (0)

## Anonymous Coward | more than 7 years ago | (#16103637)

## Re:Help (1)

## TadMSTR (996071) | more than 7 years ago | (#16103649)

## Re:Help (1)

## Will2k_is_here (675262) | more than 7 years ago | (#16103653)

## Re:Help (1)

## Will2k_is_here (675262) | more than 7 years ago | (#16103671)

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

## Re:Help (1)

## Veetox (931340) | more than 7 years ago | (#16103888)

## Re:Help (1)

## Will2k_is_here (675262) | more than 7 years ago | (#16104113)

I say bonus karma points to this guy:

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

## Re:Help (1)

## Veetox (931340) | more than 7 years ago | (#16106328)

## Re:Help (1)

## tygerstripes (832644) | more than 7 years ago | (#16103656)

## Re:Help (0, Redundant)

## Beached (52204) | more than 7 years ago | (#16103661)

## Re:Help (15, 63, ...) (0)

## Anonymous Coward | more than 7 years ago | (#16103663)

2^4 - 1 = 16 - 1 = 15 = 3*5

2^6 - 1 = 64 - 1 = 63 = 3*3*7

## Re:Help (0)

## Anonymous Coward | more than 7 years ago | (#16103664)

## Re:Help (0, Redundant)

## knewter (62953) | more than 7 years ago | (#16103702)

2^4=16

16-1=15

15=3x5

## Re:Help (0, Redundant)

## Halo- (175936) | more than 7 years ago | (#16103790)

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..

## Re:Help (0)

## Anonymous Coward | more than 7 years ago | (#16104184)

7*9 = 63

## Re:Help (1)

## MMC Monster (602931) | more than 7 years ago | (#16104229)

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

## Re:Help (2, Insightful)

## FhnuZoag (875558) | more than 7 years ago | (#16104689)

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

## Re:Help (1)

## jizziknight (976750) | more than 7 years ago | (#16104772)

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.

## Re:Help (1)

## Wooloomooloo (902011) | more than 7 years ago | (#16104246)

## *ahem* (1)

## DiamondGeezer (872237) | more than 7 years ago | (#16107587)

## Re:Help (2, Informative)

## publius1234 (615205) | more than 7 years ago | (#16103804)

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

## Re:Help (1)

## wild_berry (448019) | more than 7 years ago | (#16104391)

## Re:Help (0, Redundant)

## FhnuZoag (875558) | more than 7 years ago | (#16103843)

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

## Re:Help (2, Informative)

## fatphil (181876) | more than 7 years ago | (#16103985)

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

## Re:Help (1)

## Kennego (963972) | more than 7 years ago | (#16104194)

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.

## How to you compute? (0)

## Anonymous Coward | more than 7 years ago | (#16103595)

## Re:How to you compute? (0)

## Anonymous Coward | more than 7 years ago | (#16103692)

## Expand it yourself (3, Informative)

## Coppit (2441) | more than 7 years ago | (#16103875)

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:Expand it yourself (1)

## B5_geek (638928) | more than 7 years ago | (#16104397)

## Re:Expand it yourself (0)

## Anonymous Coward | more than 7 years ago | (#16105510)

For real fun add the 'time' command to benchmark your PC'sDon't leave us hanging. Benchmark our PC's

what?## Re:Expand it yourself (1)

## Pharmboy (216950) | more than 7 years ago | (#16104840)

## Re:Expand it yourself (1)

## dylan_- (1661) | more than 7 years ago | (#16104917)

## Re:Expand it yourself (1)

## Pharmboy (216950) | more than 7 years ago | (#16104975)

## Re:Expand it yourself (1)

## Pharmboy (216950) | more than 7 years ago | (#16106295)

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

## Re:Expand it yourself (1)

## crownrai (713377) | more than 7 years ago | (#16107289)

You're not checking even numbers are you?

## Re:Expand it yourself (1)

## Pharmboy (216950) | more than 7 years ago | (#16108341)

## Re:Expand it yourself (0)

## Anonymous Coward | more than 7 years ago | (#16108629)

## Re:Expand it yourself (1)

## FooAtWFU (699187) | more than 7 years ago | (#16105590)

## Re:Expand it yourself (1)

## doti (966971) | more than 7 years ago | (#16106232)

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... (4, Funny)

## Mister Impressive (875697) | more than 7 years ago | (#16104025)

trueprime...OPTIMUS PRIME!## The Actual Number (3, Informative)

## neonprimetime (528653) | more than 7 years ago | (#16104038)

## clicks text link... (2, Funny)

## imrec (461877) | more than 7 years ago | (#16104040)

*head explodes*

## Awww (1)

## The MAZZTer (911996) | more than 7 years ago | (#16104114)

## Huh? (1)

## gravis777 (123605) | more than 7 years ago | (#16108505)

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 it seems to me that sometimes people just get worked up about stuff that we don't really need. I mean, really, yeah, its cool that we found a prime number this large, but whats the point?