Tks, very rivetting.

1/2"]]>

Tks, very rivetting.

1/2"]]>

Someone here asked if finding new Mersenne primes is useful.

Few is known about how Mersenne primes are distributed. Finding new ones helps to check if the theory matches the reality.

Also, the GIMPS project not only searches new Mersenne primes ; it also searches factors of Mersenne composites. One can either find small factors of big near-10 millions digits Mersenne composites, or one can search for big factors of small Mersenne composites, like 2^1061-1. One can even use prime95 to search for a factor of F14=2^2^14+1, the first Fermat number no factor is known.

People also hope to become famous, one of the few ones who have found such a huge prime number.

Big Mersenne primes can be used to generate random numbers. I'm not sure 9Millions digit Mersenne primes can be used ... See: http://www-personal.engin.umich.edu/~wagnerr/MersenneTwister.html

Tony ]]>

--David

(what's YOUR Erdos#?)

> Of course, the binary representation is a bit, well, boring...

Decimalist! Anti-binaryte!

/noise

]]>jkohen,

"I just cancelled the evaluation of that expression after 150 minutes."

What did you do to evaluate it? 2**x = 1

]]>That was kind of my point.

]]>]]>

Okay, so it took 7000 computers 10 months. How many computers does Google own? How about the NSA?

We suspect the NSA is ahead of the rest of the world in, among other things, prime factoring. Estimating the resources available to the NSA and evaluating how long it takes for the NSA to factor primes is an important activity. Remember, the knowledge and resource the NSA has eventually become become readily available, given time. When script kiddies with 7000 node botnets start being able to factor financial institution keys, that's a huge problem.

]]>people say it's a waste of time. hey, we're all gonna die, and it's **our** time! not curious about prime numbers? not curious about anything? don't go into space! don't try to make stem cells! confine yourselves to more mundane terrestrial aspirations, here's one of mine: making the perfect margarita. ]]>

Wow. I find it quite exhilirating, and a touch scary, when I am stuck in the middle of a huge Mountain range.

How sure are you that the "large" prime numbers (it is all relative) will always be important? If resolving prime factors becomes easy, will you like mountains again?

]]>the number 666 is in 7721 Lines, the cross sum of that is 6 again. We are doomed! :-)

then again, my birthdate is in there 5 times, so it cannot all be bad. And I am sure that it predicts the next lottory numbers, you just have to know where to look... ]]>

I stand corrected. The wikipedia page lists some projects that actually *do* look practical. Hmmm... which one isn't gonna overheat my AMD processor... ?

]]>In the mean time, I think I'll go back to searching for space/time ship plans in those 30 million bits of prime.

Oh, and wouldn't 43.txt have been more efficiently distributed as pure binary plus a simple program to render it as decimal digits?

]]>Heard about "basic research", guys?

History indicates that using a certain percentage of funding for advancing knowledge which is not deemed immediately useful produces, in the average, useful knowledge which would probably be difficult to otherwise obtain.

E.g., much of elliptic curve theory wasn't developed for cryptography...

]]>Advancements in techniques for convolution, developed for GIMPS, have improved FFT algorithms, which are of tremendous practical application.

Another interesting benefit of GIMPS is that after a result is found through massive computation, its correctness can be definitely established with much smaller effort. This makes GIMPS a useful way to test distributed computation systems (and the hardware on which they run). In comparison, testing the validity of results in, say, protein folding, can require a complete research project in its own right.

Comparing GIMPS to Folding@home; well, for one thing, GIMPS is consuming far less computrons than the protein folding project. GIMPS does about 18 TFLOPS, while Folding@home does about 190. And Folding@home is now only one of dozens of medically related distributed computing projects, and then there are others like SETI@home (100 TFLOPS). See, for example:

http://en.wikipedia.org/wiki/List_of_distributed_computing_projects

GIMPS is certainly less frivolous than the Electric Sheep project, which generates random fractal movies!

All of these efforts involve donated computer time, so if someone chooses to support GIMPS rather than Folding@home, that's his business. And of course, the vast majority of computer owners are not supporting Folding@home or GIMPS or anything else, their PCs are either using their idle cycles to do nothing but generate carbon dioxide, or else are in a botnet distributing spam.

]]>I just cancelled the evaluation of that expression after 150 minutes. Either Python's "bignum"s are a tad too slow, or it isn't actually more convenient to evaluate the expression instead of just downloading the file.

I know that's not what you suggested, but it would take a 14400 bps modem about this much time to download the whole file without compression. I'm not even sure how much longer the evaluation would have taken.

Talking about compression...

@Evan

Don't understimate the power of compression. Longnum here is a file generated by concatenating 10000 pseudo-random digits and a new line. The compressed files were generated using the maximum compression settings for each compressor.

10001 longnum

5238 longnum.zip

5118 longnum.gz

4536 longnum.7z

4359 longnum.bz2

A non-compressed binary representation will also deliver a significant size reduction, given that only ~3.32 bits are required to store each digit. How about 3798102 bytes instead of 9 MB?

Anyway, you all fortunately realized that I was kidding. I was just mocking myself publicly because I had been careless to start downloading the file before even thinking how big it would be, and I had no need for the data itself.

]]>Can I climb 1/70,000th of the mountain? ;^)

]]>How big were you expecting a 9-million digit number to be?

Anyway, you don't need to download the file, just evaluate (2**30,402,457)-1 :-)

Evaluating it is much easier than proving it's primt.

]]>:-)

]]>It wouldn't hurt to warn the casual reader that the linked file's size is 9 MB+ big :-)]]>

What you do with your massively parralleled computers is up to your funding sources and/or grantwriters.

]]>Sure. But you can definitely have a culture of: "This is secure, it would take a single PC 4,500 years to crunch it."

I guess my point is that unless people see results like this, they don't necessarily consider implications.

Sure, assembling a 7,000 computer node to attack something for 10 months isn't trivial, but it provides a reality vector.

But you and Davi are right, it's essentially an intellectual mountain climbing event.

]]>Mostly to the point:

> This prime, found in just 10 months, would have taken 4,500 years on a single PC.

If we're going to rely on cryptographic techniques to keep data secure, we should know how easy it is to brute-force attack those techniques.

]]>Quite apart from anything else, for most crypto, the machines involved have to be able to generate their own (secret) primes, so a pregenerated prime that takes 7,000 computers 10 months to generate is of no use whatsoever.

]]>"A 20-year-old hacker pleaded guilty Monday to surreptitiously seizing control of hundreds of thousands of Internet-connected computers, using the zombie network to serve pop-up ads and renting it to people who mounted attacks on Web sites and sent out spam." - From Yahoo news

]]>