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40th Mersenne Prime Found
FenwayFrank writes "A release from New Scientist announces that the Great Internet Mersenne Prime Search found another one: 2^20996011 - 1 is prime. Weighing in at 6,320,430 digits (6 megabytes of prime number...), it becomes the world's largest. Slashdot readers may remember then announcement of the 39th Mersenne Prime, a mere 3.5 million digits."
The last digit is a four!
Wait, no, it just got slashdotted before it fully loaded...
I've had this sig for three days.
I found my /. ID (209636) shows up 5 times.
I wonder who has the most occurrences.
I really hate Dan Patrick.
Everyone claims their prime is over 6 million digits in length when in reality most are only about 5.5 million digits.
Now I can generate a secure PGP key pair!
If all this should have a reason, we would be the last to know.
It's actually 1916 pages in lynx under a 1024x768 framebuffer!!!
Hah, you really thought I actually counted for a second there!
Emacs: for people who just never know when to
This is not necessarily the 40th Mersenne Prime, just the 40th that we've found. We still need to prove many ones in between to be composite before we can mark its place as 40th.
The first Mersenne primes are 3, 7, 31, 127, etc. There are only 39 known Mersenne primes.
Well, now it is 40 known Mersenne Primes, and also 6 discovered by the GIMPS: they need to change the front page to reflect this, and also some banners ("the largest 5 Mersenne primes").
I think it's worth noting that GIMPS not only discovers new Mersenne primes, but also is the discoverer of the biggest six known ones.
This is great news. Once we have the 42nd, we will know the secret of the universe.
by a strange coincidence, the 40th prime is also an MP3-encoded audio file of an unreleased Missy Elliot track.
the RIAA is lobbying to have mathematics outlawed due to the $400 billion lost yearly to these illegal primes.
remember kids, learning math makes you a pirate! stick to watching TV and eating delicious Oreo(R) cookies!
Of course, it didn't occur to me to take a look at the Science section before submitting my own copy of this story (which, since it has several other useful links in it, follows):
Michael Shafer, a graduate student at Michigan State University, took time out for a "short victory dance" upon learning his computer had discovered the 40th known Mersenne prime as part of The Great Internet Mersenne Prime Search. The number itself is 2**20996011-1 and when expressed in base 10, has 6,320,430 digits (zipped copy). However, this is not necessarily the 40th Mersenne prime; there could be another between the previous largest known prime (M39=2**13466917-1, also discovered by GIMPS) and this one. Also worth noting is the still-standing USD$100,000 EFF prize for the discover of the first prime of at least 10 million (decimal) digits. GIMPS clients are available for various operating systems as well as information on how GIMPS would distribute the prize. A press release on the achievement is available as well as several articles. Of course, this also means there's a new largest known even perfect number in town.
Prudence forbids me to explain myself further. - Isaac Barre, 1765
*ahem* :)
with one exception
The power of Christ compiles you.
A Random Blog
okay... corrected version:
Any expression
2^n
where n is a positive integer will be even,
and subtracting 1 will make it odd.
The power of Christ compiles you.
A Random Blog
Just when I thought no one could ever guess my password. Now I have to change it again.
-- I have monkeys in my pants.
...do you think we could /. the /. server?
Quick? Has anyone checked yet to see if it factorizes the X-box public key?
(joke)
If the number is 2^20996011 then it will take 2099602 bits to store it, or 2624501 bytes along with 4 extra bits. Let's just call it 2624502 bytes. Now, 2624502 divided by 1024*1024 (number of bytes I'd say are in a megabyte) is about 2.5. Which is all to say that somewhere around 2.5 megabytes would be required to store this number, not 6 megabytes as the post here claims.
:^)
This is all perfectly true, modulo an arithmetic error on my part.
Curmudgeon Gamer: Not happy
But can it play DVD's?
/* oops I accidentally made a comment, sorry */
I presume the *text* of the number is ~6 meg, since each digit as a character is a byte (assuming it's ASCII).
-Ster
This should be in "Your Rights Online" since it contains my personal information:
Age, DL#, SSN, and even my IP! (19216801)
Obviously it's a thinly veiled ploy to steal my identity! I'ma gonna have to sue the student who found this. Be sure to check if you're in there! Luckily they don't have my credit card numbers, but I bet the next big prime is going to have all that and more.
Be afraid. Be very, very afraid.
-Adam
While we're doing decompression, I offer the following 12-byte version:
2^20996011-1
Seriously, though, where did you get the factor of 300 difference? You think it takes less than a 37th of a bit to represent each digit?
If one googol is 10^100, would this number be about 6 smeagol?
This sig no verb.
It takes 6 megabytes to store 6 million digits if you encode them in ASCII... but this is highly inefficient.
It would be far more efficient to store them in binary coded decimal (BCD, google for it if you don't know what that is), which requires only 4 bits per decimal digit without sacrificing accessibility of the decimal data. In that case it would only take 3 megabytes.
DiscDividers tabbed plastic CD dividers: divider cards f
You think it takes less than a 37th of a bit to represent each digit?
Pretty simple - binary math - each place of a binary number is a power of two. Since this number is 2^20996011 - 1, it can be represented in binary form as 20996010 1's, thus 21 KB. It's also why you can count to 2^10 - 1 on your fingers if you use each finger as a binary digit. If you try counting in ASCII base 10 digits on your fingers you can only count to 9, or 2^3 + 1.
And since when are there around 1000 bits in a byte? 20996010 bits is approximately 2.5 MiB.
21 million bits is not 21 KB, which is 168 thousand bits. It's 20996011 (not 20996010) bits = 2624502 bytes = 2563 kilobytes = 2.503 megabytes.
why not store them the most efficient way of all (for a binary machine, that is)...in binary! one decimal digit takes log base 2 of 10 ~ 3.32 binary digits, or 1,806,141 binary digits to store 6 million decimal digit number
P.S.: of course, looking at the exponent of this prime, we see exactly how many binary digit it takes to encode it.
heh, since COBOL and RPG allowed it as one possible internal representation. On a not completely unrelated note, gotta love those old Gene Amdahl designed mainframes with their decimal divide instruction.
To all the other children of the parent, I think the logic that gave him his answer was something like the following:
(2^20996011-1) => 2^(20996011-1)
= 2^(20996010)
So of course, his logic is flawed, but the answer he came up with is correct based on his logic.
(2^20996010)mod 2 = 0
Therefore 2^20996010 is not prime
Maybe this kid should go back to elementary school and be re-taught the proper Order of Operations.
Because that involves an actual conversion between bases, which means that re-extracting (to print the digits out in base 10 again, for example) takes a non-trivial amount of time.
On the other hand, the number was probably originally calculated using base-2 arithmetic (I'm assuming), so storing in binary might be more natural anyhow.
DiscDividers tabbed plastic CD dividers: divider cards f
IMAM ( I am a mathematician, well ok I got a Maths degree from Trinity Cambridge ( and I di..dn't like Quicksilver (though I did love Cryptonomicon (and I can write Lisp )))).
But should I run the Seti screen saver, the Climate predication model or this one?
My current vote is the CP model but somehow it feels less sexy
(lastStatement.getSounds()==Statements.SOUNDS_GEEK Y ? statement.replace(lastStatement.text(),lastStateme nt.geekFactor()-1),lastStatement.text())
Ant deploy
I guess it's time to go home
bzip2 that's it! ;D
\m/
That's because ^ is the XOR operator, not the power operator.
So effectively you are doing 2 XOR 3 - 1 = 1 - 1 = 0
How did 21.0 mebibits turn into six megabytes? I think he meant mugabytes.
Offtopic, Inflammatory, Inappropriate, Illegal, or Offensive comments might be moderated, and messages that are too short might be downrated.
The obvious mathematical breakthrough would be development of an easy way to factor this number.
-
- - You can't take something off the Internet! That's like trying to take pee out of a swimming pool.
Use Base 2^20996011 - 1 and write it as just 10. Seems like that'd be the most efficient way to write it. -- C.
2^20996011-1
Any sufficiently simple magic can be passed off as mere advanced technology.
I think you'll find that factoring the product of two huge primes becomes slightly easier when the attacker knows one of the primes!
Mathematica can figure the number quite nicely. Only took about 10 minutes on a P4 with 256MB RAM.
Dunno...can python handle this? bc? (heh)
...Time is the best teacher, unfortunately it kills all of its students.
I was informed today that there are, in the universe, approximately 10^450 subatomic particles in the world. A prime number of 6 million digits (6* 10^100000) cannot be possibly demonstrated in any real object. I proceeded to calculate: Apparently the highest resolution for a monitor so far is 3840x2400 (Can anyone find higher?) and it would therefore take about 108506945 monitors of this resolution just to display 1 quadrillion pixels... (10^12). Any thoughts?
Another prime number? That's great! Not long now until we've found them all!
qntm.org
With this new Mersenne prime one can also form a new largest perfect number. Euclid proved that if 2^k-1 is prime, then 2^(k-1)*(2^k-1) is a perfect number. Anyone care to put this together?