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New Largest Known Prime Number: 2^57,885,161-1
An anonymous reader writes with news from Mersenne.org, home of the Great Internet Mersenne Prime Search: "On January 25th at 23:30:26 UTC, the largest known prime number, 257,885,161-1, was discovered on GIMPS volunteer Curtis Cooper's computer. The new prime number, 2 multiplied by itself 57,885,161 times, less one, has 17,425,170 digits. With 360,000 CPUs peaking at 150 trillion calculations per second, GIMPS — now in its 17th year — is the longest continuously-running global 'grassroots supercomputing' project in Internet history."
Actually it would be 2 multiplied by itself 57,885,160 times, minus 1.
Post responses of cool names.
Some people die at 25 and aren't buried until 75. -Benjamin Franklin
... if they didn't limit the search to just Mersenne primes.
now we need to go OSS in diesel cars
2^4-1 = 16-1 = 15.
5 * 3 = 15.
Go read it again.
You might want to read that link again. Not any number 2^n-1 is prime. Just that a prime in the form of 2^n-1 is called a Mersenne prime.
n=4: 2^4-1 = 15, which isn't prime.
You get nothing! You lose, GOOD DAY SIR!
Tubal-Cain smokes the white owl.
You didn't read your link did you? There is no equation for prime numbers right now. There are some 'hacks' that work up to high prime numbers but no existing formula.
Some people die at 25 and aren't buried until 75. -Benjamin Franklin
Not all Mersenne numbers are prime. Consider 2^4-1.
now we need to go OSS in diesel cars
Sigh, you need to go back and read the link you posted:
"Though it was believed by early mathematicians that Mp is prime for all primes p, Mp is very rarely prime."
There must be a lot of prime numbers in your world
2^n-1 is always prime?
n=4
(2**4)-1 = 15
My turnips listen for the soft cry of your love
So.... is there an equivalent to rc5stats for GIMPS, so we can compare, uh, our harnessed computing prowess?
No, I'm not going to google it. I want your opinion on whether it's any good or not.
No. Any number 2^n-1 is not prime. It is only prime when n is also prime.
Mp=2^p - 1 is prime where p is prime
Not for n = 4 2^4 -1 = 16 - 1 = 15 = 3 * 5 ==> not prime!
I see a problem though: According to wikipedia, "Some definitions of Mersenne numbers require that the exponent n be prime."
Some? Huh? Mathematics does not deal in disputed definitions! I've never heard before that Mersenne numbers need a prime exponent.
Considering any number 2^n-1 is prime
Why don't you try that with n=4...
Live today, because you never know what tomorrow brings
Um, no. read that wiki article again.
Hmm, the humour and sarcasm seem to have been be lost on you.
Considering any number 2^n-1 is prime [wikipedia.org], this isn't too impressive, except for maybe that they bothered to expand it into a full number.
Nope: 2^6 - 1 = 63. Correct me if I'm wrong, but 63 isn't prime.
No, 2^n-1 is not prime for all n (example n = 4). A Mersenne prime is a Merseene number that is also prime.
Wrong - you mean all Mersenne Primes take the form 2^n-1, not that all numbers of the form 2^n-1 are prime. 11, for example, is prime but cannot be rationally expressed in the form 2^n-1.
If you could find new primes that easily then internet banking wouldn't be secure (well...as secure as it currently is, which is "enough for the insurance companies").
Please consider this account deleted, I just can't be bothered with the spam anymore.
2^4-1 = 15
Maybe you meant 2^n-1 where n is prime. Still no good 2^1-1 = 2047 = 23 * 89
Unless you meant this as a bad joke, you are mistaken.
I know that that is called a Mersenne prime. Why do they always look for primes of that form? Are these numbers more likely to be prime? Why don't they start looking for primes of the form 2^n+1?
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I thought the Slashdot summary goofed on this, but the scientists did as well.
It's the largest known Mersenne prime. For instance, 1000000! - 1 is also known to be prime, and it is much larger than this number.
Sorry, 2^11-1 = 2047
Uh, did you actually read the article you linked to?
Not all 2^n-1 numbers (Mersenne numbers) are prime. For instance, if n is not prime, then 2^n-1 is not prime (so no, 2^57,885,162-1 is not prime). But even if n is prime, 2^n-1 is not prime - take n=23, where 2^n-1 (8388607) is divisible by 47 and 178481. In fact, only 48 Mersenne primes are currently known, as listed in the article you linked.
... except when it isn't ... like 2^11-1.
now we need to go OSS in diesel cars
It's really just a matter of semantics. If n is composite, then 2^n - 1 cannot be prime.
I think, rather, that Hanlon's razor applies here: Never attribute to malice that which is adequately explained by stupidity.
Tubal-Cain smokes the white owl.
Now if that were true wouldn't we be able to say the largest known prime is:
2^((2^57,885,161)-1) ? That can't be true or they would have found it already.
Hmm, the humour and sarcasm seem to have been be lost on you.
Mathematics does deal with a lot of "disputed" definitions. Mathematics deal even with a lot of "disputed" logic and "disputed" interpretations. Read about the axiom of choice, set Theory in general, Constructivism (mathematics) and Finitism and you will understand that things get quite more complicated than you thought.
They're all right here: http://mersennewiki.org/index.php/List_of_known_Mersenne_primes
Since the only known perfect numbers are derived from Mersenne Primes, this means there are also now 48 known perfect numbers. Interestingly, this property of Mersenne Primes was discovered by Euclid about 2000 years before Mersenne was born (time machine, anyone?). Finding a non-Mersenne perfect number would be a huge accomplishment.
Have you read my blog lately?
This
Um.... let's try n=4. 2^4-1 = 15, so not a prime. You might want to read that wikipedia article a little closer.
Though it was believed by early mathematicians that Mp is prime for all primes p, Mp is very rarely prime. In fact, of the 1,622,441 prime numbers p up to 25,964,951,[5] Mp is prime for only 42 of them. The smallest counterexample is the Mersenne number
Mv11 = 2^11 1 = 2047 = 23 × 89.
Hmm, the humour and sarcasm seem to have been be lost on you.
I wonder if 2^(2^57,885,161-1)-1 is also prime.
Hey, has anyone told you that your post is wrong yet?
"Our two-party system is like a bowl of shit looking at itself in a mirror." - Lewis Black
Mathematics may not deal in disputed definitions, but Wikipedia certainly does.
111 1111 1111 == 2047 == 23 * 89
Funny how many assertions here that number disproves
Epic fail 57885162 = 2×3×9647527 and a Mersenne prime is only a Mersenne prime if p is prime, which it clearly isn't.
2 ** 57885167 - 1 might or might not be a prime, but at least you can't rule it out automagically because 57885167 is in fact a prime.
"Science flies us to the moon. Religion flies us into buildings." - Victor Stenger
If you could find new primes that easily then internet banking wouldn't be secure (well...as secure as it currently is, which is "enough for the insurance companies").
No, it relies on factoring being much more difficult than multiplication. That is, if I have two large primes p and q I can trivially calculate p*q = n, but you can not easily find p and q from n. Being able to generate primes quickly doesn't give you anything.
Live today, because you never know what tomorrow brings
"There are 10 kinds of people in the world. Those who understand binary, and those that don't."
This new number is 2^57,885,161 - 1, so naturally it has 57,885,161 digits, all of them 1. A simpler example: 2^5 - 1 is a Mersenne prime. Written in binary it's 100000 - 1 = 11111.
Oh! You meant that it has 17,425,170 decimal digits. Booooooooring!
Doesn't a mersenne prime require that the exponent also be prime? As 2^n-1, where n is composite is *never* prime, as far as I am aware.
File under 'M' for 'Manic ranting'
That has 2 1s, which is prime (2 is prime), but 6 definitely is NOT prime...
Likewise,
That has 2 1s, which is prime, but 9 definitely is NOT prime...
If a man isn't willing to take some risk for his opinions, either his opinions are no good or he's no good
Can you print it out and send me a hardcover copy? that'd be soooo cool ...well, at least until the next prime number is found.
Better idea: Tattoo
"Science flies us to the moon. Religion flies us into buildings." - Victor Stenger
I said GOOD DAY!
Using CPUs is generally a simpler approach when building a distributed system like this. Yes, per individual computer GPUs can be more efficient, but you also need to look at the number of assisting nodes you're going to get, and this number may (I'm guessing) be higher if you let any old CPU join the party rather than fewer high-end GPUs.
Please consider this account deleted, I just can't be bothered with the spam anymore.
In fact, of the 1,622,441 prime numbers p up to 25,964,951,[5] Mp is prime for only 42 of them.
I can't believe you wrote that without giving credit to Ford and Arthur!
https://app.box.com/WitthoftResume Code: https://github.com/cellocgw
Optimus Prime is bigger.
Facts take all of the premium out of arm waving - T. Reynolds
...and 2^6 -1 (63=3*3*7), and 2^8 -1 (255=5*51), and 2^9 -1 (511=7*73), and 2^10 -1 (1023=3*11*31), and 2^11 -1 (2047=23*89), and 2^12 -1 (4095=3*3*5*7*13), and 2^14 -1 (16383=3*43*127), and so on. Note that even when the power is a prime (as in 2^11 -1), the resulting number need not be prime.
Now I have to find a new combination to my luggage. Again.
Well, there's spam egg sausage and spam, that's not got much spam in it.
I'm just trying to weigh the energy consumption versus potential benefit. The GIMPS homepage does a terrible job of explaining why (I'm not suggesting that there is no reason to do this) and a linked FAQ is hardly better ( http://primes.utm.edu/notes/faq/why.html ). Can anyone provide a better answer or instruct those running the GIMPS homepage to do so?
Well, this is not an epic fail, but there is something epic about it anyway :) :)
Looks to me like someone just said 'I think things tend to naturally go up' and you had to explain general relativity in full detail to prove him wrong when dropping a stone was enough
PS: this is supposed to be humorous, not meant to offend you in any way
Yes. And both are used for GIMPS.
See the Mersenne Forum's GPU Computing sub-forum for details.
There are, however, many more CPUs than GPUs out there, so most of the work is still done by CPUs. Two different GPUs using different software (CUDALucas) were used to confirm that 2^57,885,161-1 was prime, in addition to two other CPUs (one using different software than the GIMPS standard Prime95/mprime).
what exactly is its real significance here..can anyone explain as to the applications of the same. A license plate number ?
I come to Slashdot only to read sigs. One you are reading is mine.
error: Violation of Order of Operations Rules
actually its 15 not 8 due to it being (2^4)-1
http://en.wikipedia.org/wiki/Order_of_operations
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I've got a problem with that WW meme.
In the movie, that was NOT WW's final judgement. It was a final test of Charlie's character. Charlie contested WW's brusque send-off and ended up owning a chocolate factory.
What kind of lesson is this teaching our kids?!
the preceding comment is my own and in no way reflects the opinion of the Joint Chiefs of Staff
That would kill the bear!
the preceding comment is my own and in no way reflects the opinion of the Joint Chiefs of Staff
Hey, don't believe everything you read on the Internet! I'm going to check this puppy out!
OK... 2^57885161 - 1 is not even.
2^57885161 - 1 is not divisible by 3.
2^57885161 - 1 is not divisible by 5.
Hmm... this might take a while.
Mersenne Prime is both a Mersenne Number (2^N-1) and a Prime number (no even divisions besides itself and 1). So 15 is a Mersenne Number but not a Mersenne Prime.
57,885,161 bits requires nearly 7 megabytes to represent this number in binary form. Wow!
I went to eat some animal crackers and the box said, "Do not eat if seal is broken." I opened the box and sure enough..
If the exponent is not prime, then the number will not be prime.
I don't do HTML, I'll use the symbol ^ for exponent (I don't do C either). Let's suppose c = a*b, then 2^c - 1 is divisible by both 2^a - 1 and 2^b - 1. (That's true with x instead of 2, the difference being 2^1 - 1 is 1 which is not prime.) Whether the definition requires primality or not, mathematics dictates that the exponent must be prime.
Yeah, it's better to get the math completely wrong.
Well, it's difficult to get the math partially wrong!
Ezekiel 23:20
Will prime number be a good bitcoin replacement? Bitcoin has a hard limit, which is not really how money works. Prime number seems to be ever increasing and hard to farm too.
You are confusing Fermat's conjecture, which is different (and wrong), with M-primes.
Fugue for Aaron Swartz
Banks are plenty secure when they can get federal bailouts.
Well in my world there are an infinite number of primes but not an uncountable infinite number of primes. Though even there 2^n-1 isn't always prime even when n is also a prime.
Time to offend someone
I wonder what the energy use of this project has been? 17 years? How many megawatthours? And what would be the 'carbon footprint' ?
Is 0 a natural number?
2 + 2 = 5
2^5-1=32-1=31, which is prime. Try 2^{11}-1 (using brackets because the exponent has more than one character).
If you could find new primes that easily then internet banking wouldn't be secure
LOLWUT?' ...++++ .++++
$ openssl genrsa
Generating RSA private key, 512 bit long modulus
e is 65537 (0x10001)
-----BEGIN RSA PRIVATE KEY-----[...]
Took a second, maybe, and generated two "new" primes. Each and every time you run it. I find it interesting that anyone would think otherwise. You haven't generated any RSA private keys recently, I think...
A successful API design takes a mixture of software design and pedagogy.
What kind of luddite asks for something like this in the first place?
God invented whiskey so the Irish would not rule the world.
As other people have said, generating primes is actually quite easy. It is a direct consequence of two facts: checking if a number is prime can be done in polynomial time (see AKS primality test), and the distribution of primes is dense (that is, if you pick a random number, in a large enough range it has a non-negligible probability of being prime; see prime number theorem). That means you can quickly generate primes by picking a random number in your designated range and checking if it is prime, repeating until you get one.
2^100+1 is not divisible by 3.
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its an aesthetic discipline not an objectively useful one.
alot of it turns out to be useful, sometimes hundreds or thousands of years after its first 'discovery'.
Quaternions would be a perfect example, imaginary numbers another.
so right now we have no idea what the usefulness of finding high primes is.
but in 200 years it might allow us to calculate the control points necessary to create an anti-matter damper for protonium neon flux casings in hyperdimensional warp transferrence beam generators.
now lets imagine the energy consumed to create and power all of those factories in various quasi-modern countries (where building codes are substandard) and lets imagine all the enrgy consumed to ship it over seas on gigantic boats some of which sink then lets imagine all the energy to unload the boats then lets imagine the big trucks that move that stuff out over the country and then lets imagine all of the shopping outlets that the stuff goes into and lets imagine all the light, heat, water, etc, and all the power it takes to run those things and lets imagine what 'use' a shopping mall actually has. actually, none, which is why in the soviet era they probably didn't have "hot topic". the soviet era, however, was also massively inefficient and produced the worst environmental disasters in modern history many of them still secret, (other than whats happening in China, another communist country...)
so lets just stop bitching at everyone about what they use energy for and how 'wasteful' it is, unless you want to personally stop watching TV, stop eating meat, stop driving a car and having a job and just become homeless and live off of dumpster diving because that truly would be the most 'energy efficient' lifestyle (other than say being a hunter gatherer in the amazon forest - but alot of them have ipods and want to charge it. . . more 'waste' i guess).
Since many security systems are based on large prime numbers (e.g. SSL), I've always wondered if having a huge list of primes would weaken those system? Seems like it would have to unless I'm missing something.
You are correct, except that the parent was talking about the definition of Mersenne numbers, not Mersenne primes.
It's actually pretty easy to do in calculus!
Some argue yes. However, one might simply write ℕ = {x ∈ ℤ : x ≥ 0}, which says that a natural number is defined to be a number in the set of integers greater than or equal to 0. From that point forward, one could continue using the term "natural number" unambiguously throughout a paper. Oh, and in case people can't see that, it's basically N = {x in Z : x >= 0}, where N is a notation used for natural numbers and Z is used for integers.
I have been a captive in America my entire life. Everybody and everything uses customary units instead of metric.
2^57,885,163-1 Huh. Isn't *every* odd power of two minus 1 a prime number, in which case it makes it much less impressive to find a (2^(2N))-1 ?
Help! I am a self-aware entity trapped in an abstract function!
Thank you for that post. I thought it was wrong, as I haven't been taught any number theory for the last 10 years, but reading the WP article on AKS primality test instead taught me something new. Thank you.
He reminds me of those crackpots who whizz through the Theory of Special Relativity, do a "divide by zero" somewhere and proudnly announce that they've shown Einstein was a clown.
To have a right to do a thing is not at all the same as to be right in doing it
2^6 - 1 = 63. Correct me if I'm wrong, but 63 isn't prime.
It might as well be if you've only done your times tables up to 6, which apparently a lot of people here have.
To have a right to do a thing is not at all the same as to be right in doing it
Searching for Mersenne primes keeps my study warm in the winter.
No left turn unstoned.
It would be more accurate in the story to mention that Dr. Cooper is running the Mersenne Prime Search program across all of the systems in the computer labs at the University of Central Missouri, in Warrensburg, MO.
Mitchell and Webb anyone?
Also:
2^6-1 = 64-1 = 63 = 7*9
2^8-1 = 256-1 = 255 = 15*17
2^10-1 = 1024-1 = 1023 = 31*33
2^12-1 = 4096-1 = 4095 = 63*65
Basically all even powers of 2 minus 1 are not primes, as 2^(2k)-1 = (2^k-1)*(2^k+1). It's much easier to see in binary:
1000000-1 = 111111 = 111 * 1001
100000000-1 = 11111111 = 1111 * 10001
10000000000-1 = 1111111111 = 11111 * 100001
1000000000000-1 = 111111111111 = 111111 * 1000001
Why is 0! defined as 1?
You appear to be mistaking a necessary condition for a sufficient one.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."