52nd Known Mersenne Prime Found (mersenne.org)
- Reference: 0175295615
- News link: https://science.slashdot.org/story/24/10/21/1525215/52nd-known-mersenne-prime-found
- Source link: https://www.mersenne.org/primes/?press=M136279841
> After [2]more than six years of work since the last discovery, the Great Internet Mersenne Prime Search (GIMPS) has found the 52nd known Mersenne Prime number. This is also the largest prime number known to humans.
>
> The number is 2^136,279,841-1, which is 41,024,320 decimal digits long.
>
> Luke Durant, a researcher from San Jose, CA, found it after contributing a fantastic amount of compute to the GIMPS project.
[1] https://slashdot.org/~chalsall
[2] https://science.slashdot.org/story/18/12/22/2130212/51st-known-mersenne-prime-number-found
Decimal? (Score:3)
"The number is 2^136,279,841-1, which is 41,024,320 decimal digits long."
Wouldn't it be easier to express in binary, as every digit would be 1
Re: (Score:2)
But then it would be 136,279.840 digits long.
Re: (Score:2)
Not 136,279,841 digits long?
Re: (Score:2)
No, because it's one less. 2^n is one followed by n-1 zeros. 2^n-1 is n-1 ones.
Re: (Score:1)
> No, because it's one less. 2^n is one followed by n-1 zeros. 2^n-1 is n-1 ones.
2^1 is one followed by how many zeros?
Re: (Score:2)
Crud, you're right; I screwed it up. It would indeed take 136,279.841 binary digits to write out this Mersenne prime.
Re: (Score:2)
Maybe you should use run-length encoding.
Re: (Score:1)
In base 2^136,279,841 it is just one digit.
Re: (Score:2)
But add just 1 and it doubles the number of digits! Isn't nature grand!
Just 52? (Score:2)
Isn't 2^2-1 a Mersenne prime?
Re:Just 52? (Score:5, Informative)
Yes, that's the first Mersenne prime. Small primes have better chances of working as Mersenne exponents because there aren't many candidates to divide 2^p - 1. The first 48 such exponents are listed in [1]OEIS A000043 [oeis.org]; I'm not sure why no-one has added the 49th and onwards to the B-list.
[1] https://oeis.org/A000043
Re: (Score:3)
Indeed. The first prime exponent that is not prime is 2^11 - 1 = 23 * 89.
The next is 2^23 - 1 = 47 x 178,481.
There are 10 Mersene primes below 100. After that, they get sparse.
Re: (Score:2)
"Indeed. The first prime exponent that is not prime is 2^11 - 1 = 23 * 89."
It should be noted that only prime exponents are of interest. It is not required by the definition of a Mersenne prime that the exponent be prime, but it has been shown that any Mersenne prime will have a prime exponent.
Re: (Score:2)
> it has been shown that any Mersenne prime will have a prime exponent.
This is easy to explain in binary, where for example 2^5 - 1 = 11111_2 and in general 2^N - 1 = N ones. If N is composite such as 6 = 2*3, you can split the binary number 111111 into groups of 2*3 ones as in 11 11 11, which can be written as the product 010101 * 11. So every composite exponent makes the resulting Mersenne number composite.
Re: (Score:2)
Oh, wow. That method is really slick.
I already commented about factoring a "Mersenne composite" that is equivalent, but your method is more intuitive.
My example was 3*5, which would be:
2^15 - 1 = 111111111111111 = 11111 * 10000100001 = 31 * 1057
So, same answer, but more intuitive in binary.
Re: (Score:2)
> it has been shown that any Mersenne prime will have a prime exponent.
This is very easy to prove.
If the exponent is composite, then by definition, it can be written as the product of two integers, n*m.
Then, it can be factored as:
2^(n*m) - 1 = (2^n - 1) * (1 + 2^n + 2^2n + 2^3n + 2^4n + ... + 2^((m - 1)*n))
Which is obviously composite.
QED.
Example: n = 5, m = 3.
2^(5*3) - 1 = (2^5 - 1) * (1 + 2^5 + 2^(2*5))
2^15 - 1 = (31) * (1 + 32 + 1024)
32767 = 31 * 1057
Of course, the inverse is not true. A prime exponent is necessary but not sufficient, with 11 being the first example.
Re: (Score:3)
No. For some reason 1 doesn't count as a prime number.
Re: Just 52? (Score:3)
Eh?
2^2-1=3
Re: (Score:2)
Mea culpa. I read you wrong.
Re: (Score:1)
There are very good reasons to exclude 1 as a prime, and really no good reason to include it. And there are analogues in other definitions, for example:
* 0 is not a simple module
* The empty set is not connected
The number of mathematicians crusading to make 1 a prime number is 0.
Forgot the link (Score:4, Informative)
This is the link: [1]https://www.mersenne.org/ [mersenne.org]
In honor of this, I kicked it off again, but I need to use "Throttle=10" on my laptop, otherwise it will catch fire :) I won't find anything, but it will help with somekind of verification.
With that throttle, and my BOINC settings, I can now have World Community Grid going along side mprime while keeping the Laptop CPU Temp under 35F (55C).
And yes, running mprime is fun for me and with my settings, it uses less electricity than watching a youtube video.
[1] https://www.mersenne.org/
Re: (Score:2)
I also have BOINC running on the two desktops I have at home but neither have GPUs so sadly I cannot participate in this project.
Re: (Score:2)
> I also have BOINC running on the two desktops I have at home but neither have GPUs so sadly I cannot participate in this project.
The official GIMPS software runs on CPUs only. GPU software for finding primes has been around for a long time, but their use with GIMPS remains a little experimental. Generally, the GPU worker doesn't deal with the network for connecting to GIMPS servers, so you need another piece of software for that. Currently GIMPS [1]recommends [mersenne.org] [2]AutoPrimeNet [github.com] (which is based on my earlier [3]Primetools [github.com]).
[1] https://www.mersenne.org/manual_assignment/
[2] https://github.com/tdulcet/AutoPrimeNet
[3] https://github.com/teknohog/primetools
Temps (Score:2)
"while keeping the Laptop CPU Temp under 35F (55C)."
That doesn't seem right, maybe 135F would be closer to 55C
Re: (Score:2)
Correct :) Forgot the 1 :)
Is it truly known to man? (Score:2)
If a computer does the calculation, can we truly be certain that the output is correct?
Re: (Score:2)
If computers did not reliably do their calculations correctly, you could not have posted that.
Re: Is it truly known to man? (Score:2)
Sure, you can verify it via a second calculation, if you like. It'll be much easier to confirm (or deny) than it was to find in the first place.
Re: (Score:2)
Certainly we can trust it more than if a human did this by hand. Which a human likely cannot do given the observed statistical limits of human lifespans. Once we've got this number it can be validated over and over (with a lot of time but not as much as it took to find it), with different algorithms or implementations of algorithms.
Amazing (Score:3)
I don't know what this tangibly accomplishes for math or science - maybe nothing - but there is something insane and remarkable to think that a number that unimaginably large has no divisors other than 1 and itself, and something monumental about the fact that we were able to identify it.
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I'm in the opposite camp where it almost seems unremarkable. I realize the way exponents work and that is a VERY large number, but intuitively computers seem so fast and we have so many of them that the fact we've only been able to check 136,279,841 of them is surprising.
Re: (Score:2)
I'm not sure you can say you understand how exponents work and that intuitively you think it's surprising that it's hard to check this number. Checking large numbers is a problem of exponential complexity increase. That's kind of the problem with exponents, and this level of complexity increase is what we rely on ensuring we have security mechanisms which computers can't easily crack. Just in this case it's applied to calculating primes.
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It's not something I would have expected from a 6-digit uid, but the attitude isn't uncommon. For the last 20+ years we've been telling kids that memory is infinite and that performance issues are best addressed by adding hardware. It's not hard to find a CS grad that doesn't understand, or care about, time complexity.
If he were to try implementing a function that takes a positive integer n and checks to see if 2^n-1 is prime, I expect that he'd rather quickly develop an appreciation for exponential growth
Damnit. (Score:3)
Now I have to change my luggage combination again. Also the passcode to the air shield. Damn you mathematicians!
Re: (Score:2)
Mod parent funny. Big suitcase.
Fun fact (Score:2)
The last five decimal digits of the number are 71551, or TISSI which is Finnish for "titty". This is easy to check e.g. in Python using
> pow(2, 136279841, 10**5) - 1
(FWIW, I'm the author of [1]Primetools [github.com] which connects GPU workers to the GIMPS project. It has later been forked/extended into different projects such as AutoPrimeNet, which is currently [2]recommended [mersenne.org] by GIMPS.)
[1] https://github.com/teknohog/primetools
[2] https://www.mersenne.org/manual_assignment/
The number⦠(Score:2)
The number is 2^136,279,841-1, which is 41,024,320 decimal digits long.
Hey⦠Thatâ(TM)s my luggage combination!
GIMPS (Score:2)
Congratulations! Not a trivial task to do that level of math work while wearing latex hoods, dog collars and leashes.
But why? (Score:2, Interesting)
> Luke Durant, a researcher from San Jose, CA, found it after contributing a fantastic amount of compute to the GIMPS project.
> (From TFA) It is only the 52nd known Mersenne prime ever discovered, each increasingly more difficult to find.
So it's like mining bitcoin, but much less useful. At least you can sell the bitcoin for real money.
Re: (Score:2)
From what I can tell they're only useful for finding perfect numbers, which fascinate some people.
I don't care too much but I don't want to hear the same people complain about poor people taking hot showers because "the planet".
Maybe some day we'll find higher meaning in perfect numbers - I dunno.
Re: But why? (Score:2)
Ah, useful science! If we science would only be measured against what is today deemed useful, and useful would only be measured as what today can be sold for money, mankind would never have had electricity, the wheel, fire, and such.
Re: But why [paywall science]? (Score:2)
I think you're propagating a vacuous Subject, though I rather like your comment.
However what your comment and the story both reminded me of is a recent report about a new breakthrough in recognizing primes. The clickbait intro described it as the first major advance in 25 years--but when I clicked it seemed to be a scientific website that would not show me more unless I subscribed. From the visible bits I couldn't even figure out what to search for to find a public version of the result. (But now it's an ex
Re: (Score:3)
God damn that's a heckuva definition of useful.
Re: (Score:2)
> So it's like mining bitcoin, but much less useful. At least you can sell the bitcoin for real money.
The ability to find value in things other than their utilitarian or monetary worth is one of the things that distinguishes us from lower forms of life.
Re: But why? (Score:2)
If you can explain exactly what the value is in this case, people can decide if they rather have that, or $67,000
Re: (Score:2)
You can get $67,000 by doing something useful in life, like getting a job.
Re: (Score:3)
Slashdot bitches and moans about the power consumption needed to run LLMs that people actually use in their daily lives, but 6 years of computation to find a number solely because it tickles mathematicians' fancies and they don't say peep.
Re: (Score:2)
Because it is there! ( [1]George Mallory [wikipedia.org])
[1] https://it.wikipedia.org/wiki/George_Mallory
Re: (Score:2)
For science! Not everything in life is about money. If you're going to waste electricity, better to do it on science which is more useful to the world than the scam that is bitcoin.