
48th Mersenne prime found - ColinWright
http://www.mersenne.org/various/57885161.htm
======
Simucal
I went to this university and took several of Professor Cooper's classes. He
was a great guy and he seemed really passionate about his Mersenne project.

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.

~~~
yock
What OS was this? Processes like these (Folding, Seti, etc) should be "niced"
on *nix-like OSes to have the lowest possible priority. Not sure what this
looks like on Windows, but I imagine it's possible.

~~~
acdha
nice doesn't help with I/O pressure or memory contention, particularly if it
used enough memory to contribute to swap activity. Even something like
pressure on the system L2/L3 caches can be a big deal, particularly on older
systems where those were less generous.

~~~
eeperson
Thats where ionice or, even better, cgroups[1] come in :)

[1] <http://en.wikipedia.org/wiki/Cgroup>

~~~
acdha
Agreed, although I would note that at least on Linux and FreeBSD those haven't
been a realistic option for a terribly long period of time – if the user
didn't go to school recently, it's likely that they weren't an option.

(also, not sure about cgroups but ionice did absolutely nothing useful with
swap churn when I tested it awhile back)

------
pzxc
In my freshman year of college, I discovered something neat about perfect
numbers and Mersenne primes (verified by my math professor):

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)

~~~
jnotarstefano
This is in fact the consequence of a fact first proven by Euler: every even
perfect number is of the form (2^(p-1)) * (2^p - 1) where 2^p - 1 is a prime.
That is, it's p ones shifted left by p-1 zeroes.

------
NelsonMinar
Good for GIMPS, 2⁵⁷⁸⁸⁵¹⁶¹ - 1 has a nice ring to it! GIMPS is one of the
largest distributed computations in the world and have been tooling away
finding primes since 1996. SETI@Home gets most of the credit for popularizing
this kind of distributed computing, but GIMPS has been at it for even longer
and has delivered consistent results.

~~~
falsestprophet
To be fair, SETI@Home has delivered most consistent results.

~~~
yread
you mean "nothing" ?

~~~
cryptoz
What? Don't be silly. If they delivered no results or "nothing" at all, the
project would have been shut down years ago. SETI has consisently reported
that they have searched through a very large amount of signal and found only
natural noise. That data is extremely valuable and is absolutely not
"nothing".

~~~
shaurz
The aliens are using subspace communication, no wonder we haven't found
anything yet.

~~~
rorrr
Or encrypted communications, indistinguishable from noise.

~~~
timbre
An unintended consequence of the "https everywhere" practice.

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stevenleeg
So what's the application of finding these sorts of primes? (I don't mean to
sound like a dick or anything, I'm genuinely curious what this kind of
knowledge can help us with).

~~~
jerf
Honestly, this is pretty much a "because we can" thing, other sibling replies
to the contrary. It is cool and fun, and the resources dedicated to this are a
pittance compared to, oh, say, the amount of computational resources applied
to playing pretty 3D games.

~~~
cmsmith
I think that the resources required deserve to be considered. If these
computers are running 24 hours per day, and they require an extra 100 watts to
look for primes (over their idle power consumption), then each computer is
using the equivalent of 10 kg of coal per month.

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.

~~~
jerf
Yes, but large numbers tend to just blow people's minds. Compare it to, say,
power lossage due to people leaving their light bulbs on too long, or using
incandescent bulbs instead of something more efficient.

It's noise. Nothing more.

------
sikhnerd
GIMPS "why" page is an interesting read as well:
<http://primes.utm.edu/notes/faq/why.html>

~~~
crazcarl
I was wondering what the significance of these findings were. I was
disappointed that it is mostly "fame and fortune".

------
sanxiyn
If we meet aliens, we should exchange Mersenne primes.

~~~
yesbabyyes
To them, that would be like someone wants to exchange integers with us.

 _\- Fifteen THOUSAND!_

 _\- Uuuh..._

~~~
gokhan
You assume that they will be advanced enough to come to us. What if we find
them in Europa or Titan?

~~~
yesbabyyes
Then we will probably not ask them to exchange Mersenne primes with us either.
:-)

------
rsiqueira
In 2004, Liechtenstein issued a postage stamp with the 39th Mersenne prime
number (2^13466917-1), this is the picture from a mathematical stamps
collection: [http://stamps.postbit.com/photos/math-stamps-
collection/liec...](http://stamps.postbit.com/photos/math-stamps-
collection/liechtenstein-math-stamp-2004-prime-number-mersenne.html)

------
ashleyblackmore
If for whatever reason you want to download the number, there are a couple of
links here:

[http://www.isthe.com/chongo/tech/math/digit/m57885161/prime-...](http://www.isthe.com/chongo/tech/math/digit/m57885161/prime-c.html#middle)

------
sp332
This part confuses me: "a 32-core server in 6 days" and "i7 CPU in 4.5 days"
to do the same verification? Is the MLucas code really that much slower than
GIMPS, or did the verification only use one core on the 32-core machine or
what?

~~~
Dubslow
It's a myriad of answers. The Mlucas run used a larger FFT than was necessary,
partly due to multithreading reasons. The Mlucas code also only uses SSE2
instructions, where the overclocked i7-2600K using GIMPS' Prime95 program is
fully AVX capable. I would also expect that the i7 runs at a higher frequency,
with a higher IPC, than the server. The "main" CUDALucas run took around 90
hours on a GTX 580. We didn't even hear about the 560 Ti run by Gilchrist,
that was on the side.

Here are some links:
[http://www.mersenneforum.org/showpost.php?p=325878&postc...](http://www.mersenneforum.org/showpost.php?p=325878&postcount=12)
[http://www.mersenneforum.org/showthread.php?p=325951#post325...](http://www.mersenneforum.org/showthread.php?p=325951#post325951)
[http://www.mersenneforum.org/showpost.php?p=325995&postc...](http://www.mersenneforum.org/showpost.php?p=325995&postcount=38)
[http://www.mersenneforum.org/showpost.php?p=326020&postc...](http://www.mersenneforum.org/showpost.php?p=326020&postcount=51)

~~~
Dubslow
One last clarification: the reason to use Mlucas, and not Prime95 since it's
so much faster, is for independent-code verification of the prime. (CUDALucas
also counts in that regard, but the more independent triple and quadruple
checks, the merrier!)

------
Yhippa
Is 2^57,885,161-1 Numberwang?

~~~
ChrisClark
Sorry, it was 3.

~~~
barbs
Let's rotate the board!

------
mikecane
Wolfram Alpha needs to update:
[http://www.wolframalpha.com/input/?i=what+is+the+largest+mer...](http://www.wolframalpha.com/input/?i=what+is+the+largest+mersenne+prime+number%3F)

~~~
jrajav
Well it's not up to date, but it's not wrong either. It says "Largest known
... as of July 2012"

------
ctdonath
I've long wondered:

Is 2^(2^(2^(2^(2^(...(2)...)-1)-1)-1)-1)-1 prime for all levels of recursion?

~~~
pndmnm
Those are the Catalan-Mersenne numbers, and it is unknown whether c_5 is
prime: <http://oeis.org/A007013>

~~~
ctdonath
May be. Each value in the series is, in binary, all 1s with the quantity of
digits equal to the previous value in the series. Someone took a stab at this
theory: <http://www.mail-archive.com/mersenne@base.com/msg06260.html>

------
littledot5566
When dealing with numbers of such magnitude, how are they stored in memory?

~~~
kedean
I'm not sure how GIMPS does it, but if you're interested in how it CAN be done
you could look into the GMP library for C.

~~~
Dubslow
It's definitely just a standard lots-of-bits. Every bit of information is
needed, lose one and the whole test will be wrong. For current wavefront
exponents, like 2^60,000,000-1, save files are around 8 MB, or ~60M bits --
exactly what you'd expect.

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.

------
gesman
Finally! Now i can sleep well....

------
xy22y
If you care what the number actually is, and you have gnu bc, : echo
'(2^57885161)-1' | bc > prime.txt

will yield a text file of 17,937,675 bytes, containing all the digits of the
number, plus some overhead for newlines and continuation.

~~~
iso8859-1
if you use a real Unix, you can use dc: »dc -e '2 57885161 ^ 1 - p'«

------
hfsktr
Just imagine if we didn't have computers how many fewer primes would have been
found.

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>

~~~
scythe
The number's representation in binary can fit in RAM comfortably -- it's
"only" 3 million bits or so. From there, the goal is to perform the Lucas-
Lehmer test in as few operations as possible:

[http://en.wikipedia.org/wiki/Lucas-
Lehmer_test_for_Mersenne_...](http://en.wikipedia.org/wiki/Lucas-
Lehmer_test_for_Mersenne_numbers)

------
undershirt
I first wondered they wouldn't just multiply all the prime numbers up to this
new prime and then subtract one from it to get an even bigger prime number.

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.

~~~
robterrell
Or, you could test that theory with some smaller primes and realize it
wouldn't work.

~~~
undershirt
oops.

~~~
cantos
It will not necessarily be a larger prime. But it will always be divisible by
a larger prime. See <http://en.wikipedia.org/wiki/Euclids_theorem> (Though not
necessarily the next largest prime).

The problem with this approach is that the product of the first n primes grows
exponentially as the number of primes increases.

------
speeder
The absurd amount of time that takes just to verify the thing, shows how much
we have yet to improve our computing power to be able to do more and more
precise and groundbreaking science.

~~~
aartur
But... numbers are an infinite, artificial construction, there always will be
a number exceeding current computing powers by any wanted factor.

~~~
gejjaxxita
Mersenne primes may not be infinite ;)

~~~
lutusp
> Mersenne primes may not be infinite ;)

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).

~~~
Someone
> Mersenne primes may not be infinite ;)

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.

~~~
jessaustin
It's up to you whether this is strange or not, but the effect you're looking
for is _the definition of even numbers_.

I don't find the GP's argument credible, but this really isn't a contradiction
of it.

------
pkamb
> _The discovery is eligible for a $3,000 GIMPS research discovery award._

Missed opportunity. Award should be $3,571.113

------
shaurz
They give the date to the nearest second but neglect to mention the year...

------
czzarr
tl;dr version:

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...](http://tldr.io/tldrs/51111f3dde23f15658000031/48th-known-mersenne-
prime-discovered)

------
jpwagner
this is not scalable :P

