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."

Comments

Fraud

[addaon]

The last digit is a four!

Wait, no, it just got slashdotted before it fully loaded...

Re:Fraud

[Anonymous Coward]

Actually, it's a 7.

2^1-1 mod 10 = 1
2^2-1 mod 10 = 3
2^3-1 mod 10 = 7
2^4-1 mod 10 = 5
2^5-1 mod 10 = 1
2^6-1 mod 10 = 3
2^7-1 mod 10 = 7
2^8-1 mod 10 = 5
etc.

20996011 mod 4 = 3 so it's a 7.

Here's something stupid to do.

[satanami69]

I found my /. ID (209636) shows up 5 times.

I wonder who has the most occurrences.

Re:Here's something stupid to do.

[infornogr]

Statistically, whoever has the forum ID with the lower number of digits. Somehow I think the nine people that would have to duke it out to answer your question won't respond to this post, however.

Re:Here's something stupid to do.

[Muad'Dave]

You guys are unblocking the file before searching, right? You'll miss instances of your that wrap around eol. Use:

dd if=prime6.txt of=p6.txt cbs=75 conv=block

I bet it's not that big

[Anonymous Coward]

Everyone claims their prime is over 6 million digits in length when in reality most are only about 5.5 million digits.

Finally!

[Rick the Red]

Now I can generate a secure PGP key pair!

Wow!

[HoldmyCauls]

It's actually 1916 pages in lynx under a 1024x768 framebuffer!!!

Hah, you really thought I actually counted for a second there!

40th?

[Tom7]

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.

Time to update all pages

[Anonymous Coward]

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.

Awesome!

[falsification]

This is great news. Once we have the 42nd, we will know the secret of the universe.

math == piracy

[Anonymous Coward]

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!

Well, that's the way it goes...

[Charbal]

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.

If I post the number here...

[Twintop]

...do you think we could /. the /. server?

6 Megabytes, eh?

[jvmatthe]

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. :^)

Re:6 Megabytes, eh?

[k98sven]

Yes, 2.5 megabytes is what it'd take to store it in binary form.

If we want it in human-readable form, convert to base-10:
2^20996011 = 10^(20996011*log(2))
20996011*log(2) is about 6,320,000, decimals.
1 decimal = 1 char = one byte = 6 Mb.

interesting

[nocomment]

But can it play DVD's?

New name for this?

[dacarr]

If one googol is 10^100, would this number be about 6 smeagol?

Re:6 million digits can be stored in under 6 megab

[notyou2]

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.

mugabytes

[epine]

How did 21.0 mebibits turn into six megabytes? I think he meant mugabytes.

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Subatomic Particles

[Kosher Beef Jerky]

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?