48th Mersenne prime found
mersenne.org
mersenne.org
One thing that was annoying however was the prime finding software was put on every lab computer possible. It was suppose to pause when a user got on a machine and resume when they got off. This seemed to never be the case though because they would all run terribly slow and when you checked the process list the prime software would be pegging the CPU. After reporting the problem several times I simply added a line in my bash file to kill it when I logged on.
(http://www.securityfocus.com/news/300)
> A computer network administrator faces multiple felony charges and years in a Georgia prison for allegedly installing Distributed.net clients without permission. Prosecutors say its justice, others aren't so sure
> A college computer technician who offered his school's unused computer processing power for an encryption research project will be tried next month in Georgia for computer theft and trespassing charges that carry a potential total of 120 years in jail.
> The closely-watched case if one of the first in which state prosecutors have lodged felony charges for allegedly downloading third-party software without permission.
What a lot of people missed was the significantly raised electricity bills from having 500 PCs running this software all day.
And a gorgeously authentic 2001 page (http://freemcowen.com/)
Facing a huge prison sentence for "hacking"... sounds eerily familiar. >sigh<
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He faced a theoretical 120 years in jail. Even though that was unlikely he settled because, from the EFF statement:
> "David never should have been prosecuted in the first place, but we're glad that the state decided to stop," said Senior Staff Attorney Lee Tien of the Electronic Frontier Foundation (EFF). "This is a very good result for David. He very likely could have won if the case had gone to trial, but trials cost money and you never know what will happen."
And this is what he got for settling:
> Under the terms of the deal, announced today, McOwen will receive one year of probation for each criminal count, to run concurrently, make restitution of $2100, and perform 80 hours of community service unrelated to computers or technology. McOwen will have no felony or misdemeanor record under Georgia's First Offender Act.
His research was into finding a faster/easier way to do prime number factorization in an attempt to speed up cryptography of any kind that uses it. Part of that was finding an easier/faster way to compute prime numbers in the first place. It was fascinating stuff ... but those machines were useless for anything but doing those calculations since it was using up all cores/HT's.
Edit: note the OS will "boost" priorities on certain processes or threads sometimes. http://msdn.microsoft.com/en-us/library/windows/desktop/ms68...
(also, not sure about cgroups but ionice did absolutely nothing useful with swap churn when I tested it awhile back)
It would have been discovered sooner if you hadn't done that. :)
The first perfect number, 6, written in binary is 110 The second, 28, in binary is 11100 The third, 496, in binary is 1111100 The fourth, 8128, in binary is 1111111000000
See the pattern? Its a number of ones equal to the mersenne prime that generates the perfect number, followed by one less number of zeroes.
Just an interesting tidbit I discovered completely by accident in college that I always thought was cool. :)
Of course it derives directly from the fact that mersenne primes (and perfect numbers) are based on powers of two, but I still thought it was cool (probably because I discovered it accidentally and independently without trying to)
It is not clear when to stop SETI
The cool thing is that those pretty 3D games are one of the reasons why we have those nifty computational resources such as http://www.nvidia.com/object/tesla-servers.html.
In some cases, they're using renewable energy, and in some cases, they're offsetting heating costs. But the important thing is that the people installing the distributed computing software are not the people looking at the electricity bill. And that kind of breaks the whole economics of it.
It's noise. Nothing more.
Using any of the 'well known' primes would be a bad idea as it is easy to go through the 'well known' primes and test to see if they were used as a basis for the encryption.
- Fifteen THOUSAND!
- Uuuh...
http://www.isthe.com/chongo/tech/math/digit/m57885161/prime-...
Here are some links: http://www.mersenneforum.org/showpost.php?p=325878&postc... http://www.mersenneforum.org/showthread.php?p=325951#post325... http://www.mersenneforum.org/showpost.php?p=325995&postc... http://www.mersenneforum.org/showpost.php?p=326020&postc...
Edit: since Dubslow's reply, here's the comparison for the GTX 580: http://www.hwcompare.com/9133/geforce-gtx-560-ti-vs-geforce-... It's also about $400.
For some codes each core gives 60% of an Intel core for many others it is 40%.
The Bulldozers and the Interlogos go down in my mind as the chip that destroyed the AMD. It late, was hard to use, and underperformed.
Is 2^(2^(2^(2^(2^(...(2)...)-1)-1)-1)-1)-1 prime for all levels of recursion?
Also Prime95 doesn't use GMP, its code is all hand-coded assembly, optimized specifically for the LL test and x86 architecture, written by one very dedicated George Woltman.
will yield a text file of 17,937,675 bytes, containing all the digits of the number, plus some overhead for newlines and continuation.
Even with computers I started wondering how they even go about testing these. I know there are multiple algorithms etc for verification. I meant in the sense of how to keep everything in memory and doing computations on it (I assume that numbers these large aren't trivial to work with).
The history of mersenne primes was a an interesting read though. http://primes.utm.edu/mersenne/index.html
http://en.wikipedia.org/wiki/Lucas-Lehmer_test_for_Mersenne_...
But then I realized that they're not searching for them in sequence. I guess it's a very sparse table of primes once you get up there in the magnitudes.
The problem with this approach is that the product of the first n primes grows exponentially as the number of primes increases.
The argument can be made that, because there are an infinity of primes, then either (a) Mersenne primes are also infinite, or (b) a very strange effect prevents Mersenne primes above a certain size, while allowing an infinity of ordinary primes. Occam's razor suggests it's (a).
Edit: Less snarkily, the integers are mysterious and not at all well understood and chock-full of effects like the one you mentioned. It's fallacious to simply argue that because there are infinitely many primes, there must also be infinitely many primes of a given type.
In general, it does. The count of odd numbers in a set of integers. The count of integer square roots derived from a set of integers. And so forth. None of these can be used to argue that Mersenne primes have a fixed non-terminating relationship with their generating function as number size increases, but the reverse assertion cannot be categorically denied either, which is why work in this problem continues.
> It's fallacious to simply argue that because there are infinitely many primes, there must also be infinitely many primes of a given type.
Yes, therefore it's a good thing I didn't do that.
The tl;dr: a continuation of the Mersenne prime series is more likely than its abrupt end, so Occam's razor (only ever an assumption) is applicable.
Proof 1: assumptions (i), (ii) imply that there are infinitely many Mersenne primes.
Proof 2: assumptions (i), (ii), (iii) imply that there are infinitely many Mersenne primes.
Both make the same "predictions", which in math it means they prove the "same" theorem. Then we choose Proof 1, because its assumptions are simpler. That's all.
Occam's razor doesn't apply when we are choosing between different theories that lead to different predictions.
Of course one can always conjecture that there are infinitely many Mersenne primes based on "intuition", and then go on to prove other results which rely on that assumption. People do that for P=?NP, for instance. But there's no point in invoking Occam's razor for that.
Of course it does. If there are two or more possible outcomes, and one of them has a higher likelihood or represents a simpler solution, it's favored by the thinking behind Occam's razor. This can't be used to prove anything and it's only conjecture, but it's useful for sorting out questions that involve imperfect information.
The argument can be made that, because there are an infinity of primes, then either (a) even primes are also infinite, or (b) a very strange effect prevents even primes above a certain size, while allowing an infinity of odd primes. Occam's razor suggests it's (a).
Or, as another poster said: math doesn't work that way.
I don't find the GP's argument credible, but this really isn't a contradiction of it.
I can't resist commenting that, because 2 is the only even prime, this makes it the oddest even number. :)
2. In this case it hasn't been proved that it can't be proved.
Missed opportunity. Award should be $3,571.113
The largest known prime number, 2^(57,885,161)-1, was discovered on January 25th 2013. It has 17,425,170 digits. The new prime number is a member of a special class of extremely rare prime numbers known as Mersenne primes... http://tldr.io/tldrs/51111f3dde23f15658000031/48th-known-mer...