45th Known Mersenne Prime Found?

An anonymous reader writes "The Great Internet Mersenne Prime Search (GIMPS) has apparently discovered a new world-record prime number. A GIMPS client computer reported the number on August 23rd, and verification is currently under way. The verification could take up to two weeks to complete. The last Mersenne prime discovered was over 9.8 million digits long, strongly suggesting that the new value may break the 10 million digit barrier — qualifying for the EFF's $100,000 prize!"

Re:Forgive my ignorance

[fractic]

The beauty is that it doesn't HAVE to be useful.

Because

[Bragador]

You shouldn't think like that. Just think about your question, seriously. Whatever we do is pointless and useless and everything will be destroyed eventually through the heat death of the universe.

That being said, all that is important is that you have fun doing whatever you do. Believe it or not, some people really dig maths. Also, it's one more thing the species knows.

Re:Forgive my ignorance

[AndroSyn]

I guess some of us have different standards on beauty...

Re:Forgive my ignorance

[srjh]

"Physics is like sex. Sure, it may give some practical results, but that's not why we do it." - Richard Feynman

I'm guessing it's the same logic at work here.

Re:Forgive my ignorance

[kestasjk]

Because it's 2^n-1 it'd be 1111111....1111111 (the prime number is entirely made of 1s in base 2). So there's way less than 31MB of information in the number

Re:What would really be neat...

[Anonymous Coward]

That is kinda less interesting because it depends on the system used to represent the number (binary, decimal, etc.) rather than an intrinsic property of the number

Re:Forgive my ignorance

[Firehed]

I think the real question is why it is worth $100k. I'd sure be interested to know, especially seeing that my system can probably attempt to find prime numbers pretty damn quick if it's a threaded app.

Re:I dont understand why this is important

[kesuki]

doing it by hand would be like building the pyramids, by yourself.

it's not a weekend project, just writing down all the numbers from 1, to the number composed of at least 9 million but possibly ten or eleven million digits long... much less then dividing that number by every number from 1 to the number of the same length to make sure it is only evenly divisible by itself, and 1.

i repeat myself it's like trying to build they pyramids by yourself. or even better, trying to build a four lane highway by yourself. I remember hearing about a guy from Duluth Minnesota, who had been trying to build a highway the most direct route between Fargo, ND and Duluth, MN, and he actually started on the Duluth side, i know he didn't get far, but Duluth Minnesota is one of those 'rare' towns that was booming about 100 years ago, but then started shrinking (i forget when) and has never really completely recovered.

the guy started on his quest to get the highway built believing a direct route to Fargo would increase trade and tourism and what not (it would save on average an hours drive each way)

but i think he finally died, having completed somewhere between 12-40 miles of highway.

today's PCs are like having millions of number crunching slaves with never ending papyrus scrolls, there are things computers can do that a human being would never complete if they lived a million years. and even with those millions of number crunching slaves some things take a long time to compute.

the point being, the reason why people do these things with computers is because computers are the only thing that can do them, and to be the first to do something vastly unimaginable by normal standards. kinda like, 'why did we shoot a robot lander to mars?' instead of say, making beer free for everyone in the united states for a day.

Re:Forgive my ignorance

[MadnessASAP]

You stopepd reading a comic because it made fun of you? I'd hate to live in that sad boring dreary life of yours, Monday, Wendsday and Friday that comic makes fun of me and I love it for it.

If you can't laugh at yourself then you have no right to laugh at anyone else.

Re:I dont understand why this is important

[MadnessASAP]

Becuase it is there and becuase we can. why bother to do anything at all? In a hundred years nobody will care or remember you for anything you have done at all during your lifetime, perhaps you should just go crawl back into bed and stay there for the rest of your life? You will have the exact same impact on the rest of the universe that you would have otherwise. While your doing that the rest of us will 'waste' out time discovering the universe around us, it may not server any purpose but we choose to do it and we feel better for it.

Mod parent up

[ari_j]

I didn't see your response, so I wrote my own instead of moderating yours like I should have. If anything, laughing at yourself should be easiest of all since you are more likely to get the joke given an intimate knowledge of its subject matter. =)

Re:What would really be neat...

[MatrixBandit]

Actually no; prime numbers in decimal are still prime numbers when converted into into a different numbering system. The "prime" rule transcends representation. So actually what we are talking about IS an intrinsic property of the number and does NOT depend of the system used to represent it. You can think of it as being a naturally occurring phenomenon of whole numbers. Just as pi is a naturally occurring ratio between circle circumference and diameter, regardless of how it is expressed numerically.

Re:What would really be neat...

[kvezach]

How about, make records of large primes of the form a^b +/- 1, as judged by sqrt(a) * b, where both a and b are prime. That's base-neutral. Some Mersenne primes fit the form, at least.

Re:Forgive my ignorance

[something_wicked_thi]

After reading that strip, I went to the wikipedia article on Deconstructionism, read it, and then still had no idea what Deconstructionism was. I'm pretty sure it doesn't actually mean anything.

Re:What would really be neat...

[ghoti]

1^2-1 = 0, not one! Besides, 1 is not a prime number, by definition.

Re:What would really be neat...

[dkf]

Every prime number has a prime number of digits in some base.

Can you prove that?

Every prime, p, consists of p digits in unary [wikipedia.org].

Re:Forgive my ignorance

[BotnetZombie]

See, this is what happens when psychologists try to be funny. There's always someone who finds it insightful.

ntt instead of fft?

[slew]

Perhaps you could use a number-theoretic fft (using modular arithmetic instead of fp arithmetic) on a gpu to avoid the errors accumulation. Although old gpus only processed single precision fp, new gpus can process 24-bit integer multiplication at full speed as well (at least for nvidia's cuda). You probably gain a little bit of accuracy using NTTs vs single precision FP FFTs (where you probabaly need a few guard bits to avoid subtraction errors) which is likely an exponental speedup with these types of algorithms.

Of course the double precision arithmetic is only somewhat slower than single precision on GPUs, but consumes twice the register space (so on actual algorithms, it runs quite a bit slower because of this). Right now, GPU ffts are quite a bit faster than CPU ffts, but not yet 10x (unless you have a very large GPU and a fairly ordinary CPU) if you copy the data back to the CPU every time after an fft, but if you leave the data in the GPU and code the rest of the digit-convolution algorithm on the GPU, I'll bet it isn't that far off of 10x on average.