Slashdot Mirror
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
Counterexample: 15.
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
Wrong, 2^(4-1) = 8, which is not 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.
Seriously? Not every 2^n - 1 number is a prime.
2^8-1 is 255, which is divisible by three.
Someone posted recently that slashdot editors intentionally add mistakes to summaries in order to get the replies going. Now I think they were right, but I still can't help myself.
257,885,160 is not a prime number, 2^57,885,161-1 is. Also, who says "less one" to mean "minus one"?
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.
any number 2^n-1 is prime
2^4-1 is prime?
n = 4
2^n - 1 = 15
15 is not prime.
Might wanna read that article one more time.
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.
I dare you to write the whole number, including every digit. It shouldn't take up more than a few megabytes.
... 2^4-1 = 15 = 3*5 ...
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.
You misunderstand what a Mersenne prime is.
2^n - 1 isn't necessarily prime (e.g., if n = 5, then 2^5 - 1 = 15).
If n is prime AND 2^n - 1 is prime, then 2^n -1 is a Mersenne prime.
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?
Democracy Now! - your daily, uncensored, corporate-free
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.
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.
Any binary number that consists of a prime number of 1's is going to be prime. There's no way of factoring them by subdividing them evenly. You would need two numbers, one of which is like a set of fenceposts and another which is the actual bit of fence: 11111111 = 01010101 x 11
So by that logic 15 = 2^4 - 1 is prime?
If 2^n - 1 is prime then it is also Mersenne prime. It doesn't mean that anything of the form 2^n - 1 is prime.
Notation is one of the most hotly debated things in mathematics because you cannot write proofs that one system of notation is better than another!
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
This post is painfully incorrect. Please reread carefully, and if you still don't understand why it's wrong, please ask. I'd rather not even try to formulate a response because it is hurting me.
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.
Considering any number 2^n-1 is prime, this isn't too impressive, except for maybe that they bothered to expand it into a full number.
Oh look! I've discovered a new, larger prime! 2^57,885,162-1 What do I win?
(2^8)-1 = 255 is a prime number?
Then again I am kind of nitpicking. According to the first paragraph of the Wikipedia article a Mersenne prime is Mp = 2^p-1 where p = prime. While a Mersenne number is mn = 2^n-1.
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.
Not even then. For example, if p=11, 2^11-1 = 2048-1 = 2047. But 2047 = 23*89. As p gets larger, less and less 2^p-1 are in fact prime.
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
Sir, I applaud your dedication to the age-old skill of actual trolling. Though this is indeed a short-form troll, rather than a long-form one that spans multiple threads, you have quite impressively gone for the sounds-intelligent-but-is-fatally-flawed style of troll, complete with a misleading citation for your obviously wrong information. Well done! It is rare that we see that sort nowadays, what with the sad prevalence of trolls simply going for the low-hanging fruit of easily-ignored racial slurs, misogynistic comments, and assertions regarding the sexual proclivity of our mothers.
But, you're still a troll and knew you were wrong when you posted that, so kindly piss off.
http://bit.ly/VW0mFj -- GOOD DAY SIR
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
AFAIK humans like to disagree on the most basic things (lets call it bikesheding) and from my limited exposure to math papers i can only assume that every mathematician has his own definition of any mathematical concept, which they happily define the first 2/3 of said paper in the most mindnumbing wway possible.
No.
A Mersenne prime is a special type of prime that is both prime and and can be written as 2^n-1.
Not all primes are Mersenne primes, and not all values of 2^n-1 are prime.
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
I don't think so, 2^11-1 = 2047 which is 23 * 89.
so 2^p-1 is not prime for prime p=11
QED
besides, it would be quite easy otherwise to find a new bigger prime, as if this were true, I could give you
a bigger prime in mere seconds:
2 ^ (2^57885161 - 1) - 1 ,oh wait
2 ^ (2 ^ (2^57885161 - 1) - 1 ) - 1, oh wait ...
"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'
wouldn't this be somewhat ideal to compute using GPUs, and substantially faster than CPUs?
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
I said GOOD DAY!
I just cannot believe that the early mathematicians only tested their statement for
Mv2, Mv5, Mv7 and then decided, ok, we checked enough, no need to check the next one Mv11
It's not that it's sooo hard to factor 2047...
Definitely not true:
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...
Those numbers contain two 1s, but they don't consist of two 1s. The first one consists of two 1s and a 0, while the second one consists of two 1s and two 0s. There is exactly one number (per base) which consists of two 1s, namely 11.
Of course his claim isn't true anyway, as 2^11-1 shows.
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
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.
Counterexample: 2^11 -1 = 2047 = 23*89. 11 is a prime.
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.
.....[hands back everlasting gobstopper].....
Yeah, it's better to get the math completely wrong.
Someone mod this fag troll for not understanding the wiki article.
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
Any person using FTFY or editing my postings agrees to a US$50.00 charge
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
Considering any number 2^n-1 is prime, this isn't too impressive, except for maybe that they bothered to expand it into a full number.
Oh look! I've discovered a new, larger prime! 2^57,885,162-1 What do I win?
brilliant troll, sir!
A bit brazen, but effective.
Did they use this web page?
http://alpha61.com/primenumbershittingbear/
That would kill the bear!
the preceding comment is my own and in no way reflects the opinion of the Joint Chiefs of Staff
the gp is right n has to be prime, for 2^n-1 to be prime, but nothing ever said 2^n-1 is always prime if n is prime.
If that were the case, there would be no point in the calculation. You could just take the largest prime number, write that many 1's, and then use it as an exponent of 2, subtract 1, and get another new largest prime number. This is only interesting because most prime numbers don't work as exponents in a Mersenne prime.
dom
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.
you win unending ridicule from computer people. it's not hard to win that.
but still, nice job with the arrogance despite being wrong. it's even funnier because if you read the link you posted, it explains how you are wrong.
2^n-1 are indeed Mersenne numbers all, but all Mersenne numbers are not prime.
sorry, thanks for the laugh
if i recall if n is a composite number then 2^n-1 can't be prime.
so n has to be prime for 2^n-1 to be prime. but 2^n-1 isn't always prime if n is prime. example n=11
Further reading: Set theory.
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..
Mathematics may not deal in disputed definitions, but Wikipedia certainly does.
[citation needed]
I am officially gone from
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.
Mathematics does not deal in disputed definitions!
If only that were true. Get a bunch of mathematicians together and ask them if the "natural numbers" include zero or not. Analysts tend to say no; discrete mathematicians tend to say yes. The poor number theorists--who should be the ones who own the definition---usually can't decide. In one of the best known number theory textbooks, they define the naturals one way on page 1, and use them the other way on page 2!
Other examples: A "ring", depending on who you ask, may or may not be associative, may or may not have a multiplicative identity, and may or may not be commutative. An (algebraic) "variety" may or may not be defined to be irreducible. A "compact" space may or may not be required to be Hausdorff.
Most advanced mathematics textbooks begin with a page or two of conventions in notation and terminology so that the reader will know where the author stands with regard to definitions that are not universal accepted.
You are confusing Fermat's conjecture, which is different (and wrong), with M-primes.
Fugue for Aaron Swartz
This is not even slightly interesting unless you can print out a list of all the primes up to and including this number.
(Yes, I know that's a much harder problem than taking pot shots at the "largest known" prime number.)
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).
I bet you also tell athletes to stop running so that we can use air more efficiently.
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.
Democracy Now! - your daily, uncensored, corporate-free
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).
No one ever made such a conjecture. Indeed, Mersenne's original conjecture was backed up by a lot more calculation, took centuries to check completely, and had 5 errors.
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.
Perhaps we could focus on a real world problem...
echo '2^57885161-1' | time bc | tee bigprime.txt | md5sum
What did you get ? (assumes BC_LINE_LENGTH=70 )
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.
17,425,170 *decimal* digits
I'd imagine the benefit per kilowatt-hour is far greater than the average TV set.
The next prime is somewhere between 2^57,885,161+1 and (2^57,885,161-1)! + 1. That prime is not necessarily in the form 2^x - 1.
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?
time (echo '2^57885161-1' | bc | tee bigprime.txt | md5sum)
f14d82090509a1cb1915c8aac26c6916 -
0.10s user 0.07s system 0% cpu 54:49.90 total
You appear to be mistaking a necessary condition for a sufficient one.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."