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."

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.

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 [msu.edu], took time out for a "short victory dance" upon learning his computer had discovered the 40th known Mersenne prime [utm.edu] as part of The Great Internet Mersenne Prime Search [mersenne.org]. The number itself is 2**20996011-1 and when expressed in base 10, has 6,320,430 digits [wolfram.com] (zipped copy [wolfram.com]). 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 [eff.org] for the discover of the first prime of at least 10 million (decimal) digits. GIMPS clients are available for various operating systems [mersenne.org] as well as information on how GIMPS would distribute the prize [mersenne.org]. A press release on the achievement [mersenne.org] is available as well as [newscientist.com] several [wolfram.com] articles [utm.edu]. Of course, this also means there's a new largest known even perfect number [utm.edu] in town.

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.

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.

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