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Did they check it on Intel or AMD CPU?

Both.

https://www.mersenne.org/prime...

The results were checked with several different pieces of software on multiple platforms.

How "big" is 22,338,618 digits? Text file containing the prime is 22.8 MiB in size. http://www.mersenne.org/primes...

3. [...]no moving parts. SSD for boot,

As far as I can tell this is speculation on your part. Past a certain weight people are not going to throw the box around. As a heater it's also quite possible that it will be fastened to a wall or something too. Not that it matters anyway.

3. The article says that the supplier supplies power. Whatever cable they use for that can easily have a fibre built in for data.

That however is totally unrealistic. First they say they'll pay for power, not that they will lay their own electric cable all the way to the customer to bring power. That would be incredibly stupid, wasteful and so expensive they would never get a positive return on investment. So they will at most install a separate electric meter at the customer's premises, and then hook up their machine to a regular power outlet. So then this fiber you want to put in the power cable will have nowhere to plug into. And again, given that most houses/apartments don't have fiber yet it, requiring a fiber connection would limit them to just a fraction of the potential market, or would force them to lay their own fiber which again is incredibly expensive (but at least it would not be redundant if they manage to resell it to regular ISPs). But it's more likely they will simply reuse their customer's Internet connection (remember data caps are mostly a US thing). So really what this tells us is that they will limit themselves to workloads which don't require too much communication. The ideal case would be CPU/GPU intensive computations like Folding@Home, SETI, GIMPS, etc.

I wonder if there is any opportunity for public participation?

seti@home
folding@home
GIMPS

cern@home ????

From what I know, the Great Internet Mersenne Prime Search (GIMPS) uses a Fast Fourier Transform to quickly find the square of a number. This is a required part of the Lucas-Lehmer test (the test that determines if the number is prime).

If this form of FFT can do fast squaring, it will reduce the amount of time taken to find new, large primes.

This is a potentially exciting development in this field.

Dunno about furmark (never heard about it) but there's an equivalent to Prime95 called mprime, also on the mersenne download page. Same torture effect on the CPU AFAICT.

If you don't like the GUI, there's always the Lisp interface. If another OSS project gets named after a disability, I'm sure the gimp devs will incorporate it somehow.

Then they will no doubt be adding support for the Great Internet Mersenne Primes Search

When that worked, that would've reduced the potential culprits to the memory, CPU, and then lastly the mainboard. Memtest would've found no memory issue (which would also indicate that the mainboard is also less likely a problem), so that's when the CPU switch should've happened...

Maybe, maybe not. Memtest has never been good at finding timing issues or partially good memory.

In the case of flaky hardware, your best bet is a stress/torture test of the hardware. Moving lots and lots of data around between the RAM/CPU and checking to see that it doesn't get corrupted along the way. One good tool is Prime95 in torture test mode for 24-48 hours. It'll run your memory/CPU into the ground and expose timing issues, poor cooling, or calculation errors due to the immense amount of work that it forces the CPU/RAM to perform.

Put it this way. Let's say someone on his own initiative runs program on ALL of Exxon Mobils workstations. If the program accomplishes nothing, the guy might wind up getting fired. But... if the program finds a cure for cancer, you can certainly bet that Exxon Mobil would be running ads about how they cured cancer and how great they are, and the guy would at least get a trial promotion for being successful.

Case in point: A record Mersenne prime was found by running a distributed project at the UCLA math department, and now the department has been awarded half of the EFF prize of $100,000.

never heard of prime95?

it's been used for years to check stability in rigs by overclocking and gaming enthusiasts.
They even have various different "levels" of FFT tests to limit the torture tests to within CPU cache levels which tests the CPU...or more than tests the RAM, PSU, etc.

Prime95

CPU:
Prime95 (Step 2): http://www.mersenne.org/freesoft/#newusers ... Blend test for memory+CPU stability, Small FFT for CPU
Lynx: http://www.softpedia.com/get/System/Benchmarks/LinX-benchmark.shtml

Video Card:
3dmark: http://www.futuremark.com/benchmarks/

When testing the video card, listen for high pitch squealing (power issue), over heating, and symptoms like white dots appearing at random. This is not a test tool but will put some stress on the card.

You are an idiot

• Digits of 2^42643801 - 1 with dot separators (instead of commas)
• English name of 2^42643801 - 1 using the American system
• English name of 2^42643801 - 1 using the European system
• English name of 2^42643801 - 1 using the American system with dashes
• English name of 2^42643801 - 1 using the European system with dashes

The dashed form of the English name is available at assist those who might actually want to read all or part of the +324 Megabyte name. :-)

The system used for this is GIMPS, the Great Internet Mersenne Prime Search. The system uses a distributed computing system using unused computing power in personal computers to search for various candidate primes. Computers do one of two things: Either trying to factor candidate Mersenne numbers or running a Lucas-Lehmer test on candidates without any small prime factors (the Lucas-Lehmer test is a special primality test for Mersenne numbers that is very fast). They use modular arithmetic and a variant of the Fast Fourier Transform to handle the multiplications which might otherwise become too difficult. The procedure is naturally a problem that can be made into a parallel processing problem like this since there are so many different candidate numbers to look at.

The summary doesn't mention but it is worth noting that the Lucas-Lehmer test allows one to check the primality of Mersenne numbers (numbers of the form 2^p-1, p prime) much faster than you can test the primality of generic numbers (or almost any other specialized form). Thus, for most of the last hundred years the largest primes known have been Mersenne primes. Currently the largest known prime is a Mersenne prime and the next 4 largest are also Mersenne primes. The GIMPS website - http://mersenne.org/ has a lot more details of both the math and software and explains how you can join in to help the project.

It was found through the GIMPS (The Great Internet Mersenne Prime Search). The site http://www.mersenne.org/prime.htm is currently down.

*snicker* ;)

( but http://www.mersenne.org/ )

If you haven't yet, download Prime95 right now and run it on your Windows systems.

http://www.mersenne.org/freesoft/

I've found that the prime95 stress test will catch errors that memtest won't. You need to run prime95 twice. Once right after booting the system, and a second time after the system has been running for more than a week (and in use for that week). Each run should be at least 1 hour.

This is a bit more mathematics than general science, but I'd suggest GIMPS for a chance to find a huge prime or, if they're more interested in actually finding a prime than searching for an enormous one, I'd suggest No Prime Left Behind (NPLB).

How long does it take your transistor radio to switch on? What about your television? (Unless it is decades old, it is probably two seconds or less.) When you turn on your kitchen tap, how long is it before water starts coming out

General purpose computers with complex operating systems that start dozens of applications during boot are relatively new technology compared with what you list. The PC is what, 20-30 years old depending on your definition of Personal and Computing?

I bought a house that had been in probate for a year. The water lines had been flushed with air. When I got the water running, it took maybe 30-40 seconds for the water to pressurize the line and come out the faucet.

Also, I've used old restored radios from the 1920s that had to warm up the tubes before they worked. 'Boot' times on those were around 2-3 minutes. Beautiful pieces of wood furniture, but horrible impractical compared with an 'almost instant' boot iPod.

To use a car analogy, One hundred and twenty years of innovation can do a lot. When you got into your automobile this morning did you remember to manually advance the engine timing and work the clutch leavers while someone cranked over the engine to get it started? No, you put the key in ignition and turned it.

But it's still nice to see someone taking note that Ubuntu can be dog slow starting up. Just one more reason to keep the system running your favorite distributed app while away.

Some of my servers that don't have much to do contribute to GIMPS

I'm inclined to believe the results you posted, since there's a news post which suggests that by 2006, the computational speed was 20 TFLOPS: http://mersenne.org/ips/stats.html

It is, though, still two orders of magnitude smaller than Folding@Home.

http://v5www.mersenne.org/ is where I got my info; clearly we have a slight disconnect between that and http://mersenne.org/primenet/. Thanks for the heads-up.

http://v5www.mersenne.org/ is where I got my info; clearly we have a slight disconnect between that and http://mersenne.org/primenet/. Thanks for the heads-up.

details here: http://mersenne.org/prize.htm

Yes, half of it.

If you were to find a 10,000,000 digit prime today the above rules imply that $3,333 would go to Michael Cameron, discoverer of the 39th known Mersenne prime, $3,333 would go to Michael Shafer, discoverer of the 40th known Mersenne prime, $3,333 would go to Josh Findley, discoverer of the 41st known Mersenne prime, $3,333 would go to Dr. Martin Nowak, discoverer of the 42nd known Mersenne prime, $6,667 would go to Curtis Cooper and Steven Boone the discoverers of the 43rd and 44th known Mersenne prime, $5,000 would go to GIMPS, $25,000 would go to charity, and $50,000 would go to you.

This is great news, I've been crunching Mersenne numbers myself and it's nice to finally see a potential >10M digit one.

Testing a single candidate Mersenne prime takes a month of straight computation on a single 2.4 GHz Pentium 4 (assuming a 10 million digit prime, which would be the minimum to win the prize). This assumes the use of only one core, but you'd need at least 100 cores to make it anything resembling "quick" (~7 hours), if you could even parallelize the procedure that much.

Never mind the fact that only about one in 150,000 exponents will yield a prime, meaning that on average, 150,000 months of computation is required for a single prime to emerge, and furthermore, finding giant Mersenne primes is easier than most other kind of primes. So, I don't think your computer will find these giant primes "pretty damn quick".

Pessimism aside, I think this is a pretty impressive achievement considering that GIMPS doesn't have nearly the power of larger efforts like Folding@Home (GIMPS has around 500 GFLOPS while F@H has around 3372 TFLOPS, or 3372000 GFLOPS).

basically, they distribute the prize to contributors...currently $50,000 would go to you

Prize money in the $100K and up ranges are available for primes that are found above 10 million digits.

Apparently it's very achievable -- CMSU came pretty close to claiming the $100,000 prize in late 2006.

Try figuring out a new prime number, perhaps win some money too mersenne.org if you can figure out the first 10 Million Digit Prime.

Apparently the EFF is offering a $100,000 prize for discovering new prime numbers. As stated on the website. I'd be putting that processing to good use. If you've got a good system, the odds are not much worse than a lottery. And it's free. :)

Clearly, I said exactly that later on. We were talking to an "average Joe," remember? The question was meant to spark thought about the power of distributed computing in an infinite time frame, not to frighten anyone.

Formerly insoluble problems are now soluble through these methods, including generating the large prime numbers for future crypto. I'm talking about monkeys and typewriters here, not completely breaking SHA-256.

This isn't useful to crackers, because you can't arbitrarily break any specific crypto problem with brute force, and so the industry itself is completely secure, because there is no solution that is reliable, discrete, specific and practical. You can't target anyone, and so phishing is easier, and more profitable, for the time being.

But dumb luck? Just going at it for an infinite period of time with unknown resources and seeing what shakes out? Freak occurrences are another matter entirely, and playing a long game with a distributed computing network is one (highly tedious, and by current assumptions and methods, fruitless) way to get at these problems.

Don't underestimate the power of dumb luck and persistence, and don't forget that assumptions can radically change. The former is the way most things get done, and the latter is a fact of a fallible human existence.

Truly, the question was meant to fuel imagination, not highlight a cause for alarm. As I later said, it's unlikely any of this has happened yet. I'll make that more emphatic: the likelihood is infinitesimal. There's no current threat, at least not in our current understanding of mathematics, and with competent folks versed in cryptography (e.g.: NSA) making recommendations about cypher strength.

But in my experience, while you can bank on not being outsmarted, dumb luck and persistence are never to be underestimated. While there is no threat, there is a danger.

I'm not willing to be Grand Moff Tarkin in his "moment of triumph."

--
Toro

Running a CINEbench that lasts 18 seconds is not a decent test of stability. Even hobbyist overclockers ultimately aim to end up with a system that they can use day in, day out for several hours at a time.

We run Prime95 for at least 48-72 hours - while also exercising the disks in the system (and the graphics card if possible). While Prime95 is mainly used for a distributed computing project, it's proven so sensitive to CPU/RAM issues that it ships with a "torture test mode". The calculations that it performs are extremely complex and really exercise the CPU, RAM and cache. I've seen Prime95 uncover issues that went unnoticed by MemTest86, such as mis-matched memory timings that only caused intermittent errors and crashes in the EQ client.

(And I'm not even an over-clocker - I just like to burn-in my systems for a few days before releasing them to end-users.)

When looking at the exponents, we expect only 1.78 Mersenne primes between powers of two, and prior to 2003, a maximum of 3 Mersenne primes were found between powers of two. The last 5 Mersenne prime exponents all fell between 224 and 225 -- and we haven't finished testing all the exponents in that range!

Sometimes you need to use tools other then MemTest86+ to diagnose flaky / transient issues. MemTest86+ doesn't put enough of a load on the CPU to catch things like flaky memory timings. My preference is the Prime95 client, which folks have used for close to 10 years as a torture test. In fact, the Prime95 folks finally added a "torture test" option many years ago. QuickPar is also sensitive to flaky systems and will often catch errors (but isn't as thourough of a test as Prime95 is).

System shutdowns are typically either:

- Thermal initiated (so use SpeedFan and monitor your temps)

- Power related, the PSU can't keep up with the load, drops a voltage and the motherboard / CPU panics.

If your system can run Prime95 for 48 hours straight with zero errors, you've got a good stable system. We typically run Prime95 as our burn-in test while exercising the disks with another program for a few days prior to releasing the machine to the end-user.

GIMPS looks for Mersenne primes. This is clearly an exact integer operation. However, for speed, they use Fast Fourier Transforms to do the big squaring operation with floating point. Obviously, they need an exact result.

The trick is to carefully calculate exactly how much error each operation can generate. It is possible to know exactly how many bits of your result contain valid information. If you need more accuracy, you can split it into multiple operations. As long as the final accumulated error in their result is less than .5, you have the integer answer they need. Note that it's basically impossible to do this without using assembly language, because the order of operations and subexpression elimination definitely matter.

Another interesting problem occurs with floating point results. You cannot expect the complete answer to be exactly identical on all machines. Even on the same machine, compiler settings affect the answer: x87 differs significantly from SSE. If you are doing something that needs bitwise identical results on all machines, you need to either implement it with integer math, or do what GIMPS does and do error tracking.

Melissa

FFTs are also useful for squaring large numbers with a modulo. That's what http://www.mersenne.org/ uses them for.

Melissa

What about Prime95?

I banged at the 2.0GHz duo core with Prime95 and could not get even a whisper out of a fan.
This was splitting the task equally, or running with affinity set to one CPU or the other.

Disappointedly, on paper it benches 1:1 to a Sempr0n 3000+ at 1.8GHz with 128K L2 cache.

The PRIME95 speedtestsshows the AMD/Intel similarity if you consider the
T2500 is halfway between the results already posted for the T2400 and T2600 on non-Apple.

You should see my admin key: it is a 10^12 digit mersenne prime.

Hey! You should tell the GIMPS guys! They've only gotten up to ones that are 10^10 digits big! ;)

And possibly win money in the process.

Although, i'm kinda tired of spending an extra $20 on electricity each month... anyone want to buy a quad PIII Xeon for cheap?

I would start here instead... Read the part about Lucas-Lehmer testing...

If you think this is your grand chance to win money easily using GIMPS, think again.

As it states here

If you were to find a 10,000,000 digit prime today the above rules imply that $5,000 would go to Michael Cameron, discoverer of the 39th known Mersenne prime, $5,000 would go to Michael Shafer, discoverer of the 40th known Mersenne prime, $5,000 would go to Josh Findley, discoverer of the 41st known Mersenne prime, $5,000 would go to Dr. Martin Nowak, discoverer of the 42nd known Mersenne prime, $0 would go to discoverers of algorithmic breakthroughs, $5,000 would go to GIMPS primarily to fund future awards, $25,000 would go to charity, and $50,000 would go to you.

Now the bad news. Testing a single 10,000,000 digit number takes two months on a 2 GHz Pentium 4 computer. Your chance of success is roughly 1 in 250,000.
Someone may find a 10,000,000 digit prime before GIMPS does.

2 ~ 25964951-1

keep looking

Does anyone know of something like the GIMPS to factor these RSA numbers? It seems like if 80 Opterons can do it in 5 months, a massive distributed network of computers donating idle time could do this in a much shorter amount of time, such as churning out a new factorization every few weeks. I have a feeling the larger RSA numbers quickly become much more complicated to factor. Does anyone know the complexity class of factorization?

They could use them to help find Mersenne Primes. Just a thought.

I don't know, maybe Memtest86 would have shown errors if I ran it for a longer time but Prime95 certainly showed them more quickly. I recommend trying both Memtest86 and Prime95.

Overclockers often use Prime95 to do CPU temperature/stress testing. It is available in many flavors:

• Linux
• FreeBSD
• OS/2
• Windows 95/98/Me/NT/2000/XP
• Windows NT/2000/XP Service
• Windows 3.1

Trust me, it will heat things up!

Prime95. Available for numerous OSs.

Does this mean I've been wasting my CPU cycles?

although 25,964,951 is prime, what's even more amazing is that 2^25,964,951-1 is prime, it's about 7.8 million digits and it's only divisible by one and itself!
you can download it from http://www.mersenne.org/