Student Discovers Largest Known Prime Number

  • Bigwebmaster
  • Site Admin
  • Site Admin
  • User avatar
  • Joined: Dec 20, 2002
  • Posts: 8926
  • Loc: Seattle, WA & Phoenix, AZ
  • Status: Online

Post December 10th, 2003, 4:42 pm

DETROIT — More than 200,000 computers spent years looking for the largest known prime number (search). It turned up on Michigan State University (search) graduate student Michael Shafer's off-the-shelf PC.

"It was just a matter of time," Shafer said.

The number is 6,320,430 digits long and would need 1,400 to 1,500 pages to write out. It is more than 2 million digits larger than the previous largest known prime number.

Shafer, 26, helped find the number as a volunteer on an eight-year-old project called the Great Internet Mersenne Prime Search (search).

Tens of thousands of people volunteered the use of their PCs in a worldwide project that harnessed the power of 211,000 computers, in effect creating a supercomputer capable of performing 9 trillion calculations per second. Participants could run the mathematical analysis program on their computers in the background, as they worked on other tasks.

Shafer ran an ordinary Dell computer in his office for 19 days until Nov. 17, when he glanced at the screen and saw "New Mersenne prime found."

A prime number is a positive number divisible only by itself and one: 2, 3, 5, 7 and so on. Mersenne primes are a special category, expressed as 2 to the "p" power minus 1, where "p" also is a prime number.

In the case of Shafer's discovery, it was 2 to the 20,996,011th power minus 1. The find was independently verified by other participants in the project.

Mersenne primes are rare but are critical to the branch of mathematics called number theory. That said, what is the practical significance of Shafer's number?

You can see the full story here:

http://www.foxnews.com/story/0,2933,105383,00.html
Ozzu Hosting - Want your website on a fast server like Ozzu?
  • Anonymous
  • Bot
  • No Avatar
  • Joined: 25 Feb 2008
  • Posts: ?
  • Loc: Ozzuland
  • Status: Online

Post December 10th, 2003, 4:42 pm

  • ATNO/TW
  • Super Moderator
  • Super Moderator
  • User avatar
  • Joined: May 28, 2003
  • Posts: 23404
  • Loc: Woodbridge VA
  • Status: Offline

Post December 10th, 2003, 8:20 pm

Ummmm....can anyone say "infinity"? I'm sure there's quite a few more beyond that, and I seriously doubt we have enough trees in the world to make the paper to print them all out.
"There's no place like 127.0.0.1 except for ::1."
Alexandria Networks. Leader in IT consulting for associations/non-profits, and small to medium sized businesses around the northern Virginia and Washington D.C. metro area.
  • Nego
  • Expert
  • Expert
  • User avatar
  • Joined: Aug 28, 2003
  • Posts: 697
  • Loc: Chicago
  • Status: Offline

Post December 10th, 2003, 8:42 pm

I agree, I'm something of mathematician.I think prime numbers can go higher than that, I mean just think logically. Obviously if numbers go way higher than that than the largest prime number must be larger.
  • ATNO/TW
  • Super Moderator
  • Super Moderator
  • User avatar
  • Joined: May 28, 2003
  • Posts: 23404
  • Loc: Woodbridge VA
  • Status: Offline

Post December 10th, 2003, 9:34 pm

The info Bigweb provided in his post is related to this. I have one computer running on my home network, and that's all it does (this type of thing). It "folds" proteins and this research appears to be initiated by Stanford:

http://www.stanford.edu/group/pandegroup/folding/

This is called distributive computing and is a huge boost to Universities and others in researching things a single computer just couldn't do.

I am all for this concept. I chose this particular one because my father passed away last year from complications due to Parkinson's disease. To the best of my knowledge, this research can help not only people with Parkinson's Disease, but also Altzheimers and several others.
"There's no place like 127.0.0.1 except for ::1."
Alexandria Networks. Leader in IT consulting for associations/non-profits, and small to medium sized businesses around the northern Virginia and Washington D.C. metro area.
  • musik
  • Legend
  • Super Moderator
  • User avatar
  • Joined: Aug 06, 2003
  • Posts: 6892
  • Loc: up a tree
  • Status: Offline

Post December 10th, 2003, 9:37 pm

:lol:
Opportunity To Do - Changing the lives of children around the world.
Rose.id.au - Doing Life.
  • Alan2
  • Graduate
  • Graduate
  • User avatar
  • Joined: Aug 20, 2003
  • Posts: 112
  • Status: Offline

Post December 11th, 2003, 2:28 pm

copies and pastes...

topic goes off page :P

I do agree that there will be a higher number.

<< I supose I should get it since I run my computer erm. way too much of the time :oops:
  • Bigwebmaster
  • Site Admin
  • Site Admin
  • User avatar
  • Joined: Dec 20, 2002
  • Posts: 8926
  • Loc: Seattle, WA & Phoenix, AZ
  • Status: Online

Post December 11th, 2003, 6:35 pm

I actually first heard about people searching for larger prime numbers in one of my math classes in college. If I recall there is actually a very good reason they are searching for higher prime numbers. If I remember, they are able to use them to make better encrypting algorithms. I may be wrong, but for some reason I remember some kind of discussion on that. I remember discussion on PGP too.
Ozzu Hosting - Want your website on a fast server like Ozzu?
  • UNFLUX
  • Genius
  • Genius
  • User avatar
  • Joined: Dec 20, 2002
  • Posts: 6382
  • Loc: twitter.com/unflux
  • Status: Offline

Post December 11th, 2003, 6:37 pm

that's the same reason I heard, and again today in a report on the
radio about it. My dad used to do cryptology in the Marine Corps, and
he confirmed it as well. he says they've been searching for longer than
reporting for this particular number.
UNFLUX.FOTO
  • Bigwebmaster
  • Site Admin
  • Site Admin
  • User avatar
  • Joined: Dec 20, 2002
  • Posts: 8926
  • Loc: Seattle, WA & Phoenix, AZ
  • Status: Online

Post December 11th, 2003, 6:39 pm

Factoring N would clearly enable RSA to be broken. It has not been proven that there is no polynomial time solution to finding prime factors of large numbers (i.e. it is possible that an algorithm that could factor N quickly enough to break RSA may be discovered in the future). However, despite constant improvements in factoring algorithms none have been found that satisfy the polynomial-time criteria which would make cracking RSA a tractable problem.
It is important to note that it has not been proven that security of RSA relies solely on the mathematical diffculty of finding the prime factors of large numbers. However, many of the other possibilities for finding D given E have been shown to be of equivalent difficulty to factoring N. One possibility is that an algorithm could be devised to find the Eth root mod N more easily than factoring N. Nevertheless, no such algorithm has been discovered so far, and RSA has withstood many attempts to crack it.

Found that on this page:

http://www.momentus.com.br/PGP/doc/howpgp.html

Sounds like the fact that prime numbers are so hard to find, is how PGP works so good.
Ozzu Hosting - Want your website on a fast server like Ozzu?
  • Dragoris
  • Beginner
  • Beginner
  • No Avatar
  • Joined: Dec 09, 2003
  • Posts: 48
  • Loc: Erie, PA
  • Status: Offline

Post December 11th, 2003, 6:47 pm

yeah but get this... If there are an infinate set of #'s, then there Must be an infinate set of primes. BUT the # of primes Has to be smaller than the # of regular #'s yet at the same time they are both infinate. Which # is bigger? :hmm:

-aint math fun? :lol:
  • b_heyer
  • Web Master
  • Web Master
  • User avatar
  • Joined: Jun 15, 2003
  • Posts: 4583
  • Loc: Maryland
  • Status: Offline

Post December 11th, 2003, 6:49 pm

I'd like to say that eventually they would become proportionally equal, but I doubt that will be the case :-P
Pixel Acres V2
  • Bigwebmaster
  • Site Admin
  • Site Admin
  • User avatar
  • Joined: Dec 20, 2002
  • Posts: 8926
  • Loc: Seattle, WA & Phoenix, AZ
  • Status: Online

Post December 11th, 2003, 6:55 pm

The larger the numbers increase, the smaller amount of primes that can be found. In other words the overall distance between prime numbers keeps increasing. However every now and then they will find a 2 huge prime numbers that are within 2 from each other. I forget what kind of prime numbers those are called, but there is a special name for them.
Ozzu Hosting - Want your website on a fast server like Ozzu?
  • eldrick
  • Newbie
  • Newbie
  • No Avatar
  • Joined: Dec 14, 2003
  • Posts: 6
  • Status: Offline

Post December 18th, 2003, 1:11 pm

Euclid discovered the proof of the infinite numbers of prime numbers nearly 3000y ago!

http://www.utm.edu/research/primes/note ... clids.html

it's not difficult to understand,but needs some concentration


also the prime number theorem gives an approximation for the number of prime numbers present any given number,x ( i.e. if our given number is 25,there are 9 primes upto then)

the theorem is given as

no. of primes ~ x/log x

(in natural logarithms,not base 10 logs)

this approximation is regarded as one of the greatest achievements in the history of mathematics


BTW,most mathematicians consider the holy grail,Riemann's hypothesis (which is conjectured drove john nash of "a beautiful mind" fame, mad!!)

i believe that a completed proof of this will allow the exact prediction of prime numbers - however i read that mathematicians don't give much hope of it being achieved within this century!
  • Marcus
  • Beginner
  • Beginner
  • User avatar
  • Joined: Oct 31, 2003
  • Posts: 35
  • Loc: NYC
  • Status: Offline

Post December 19th, 2003, 5:49 am

Is there a formula for finding prime numbers that doesnt require brute force?

This thread causes me to digress and ask the question...

Consider if all the matter/mass (anyone know what that is) in the universe where utilized to create a networked supercomputer whose architecture was on an atomic scale, what would that maximum number that computer could handle? and what would the maximum number of calculations a second that computer could do? And what would be necessary to make that computer conscious of itself, and to know the position of every electron or atom in the universe at any given period in time?

Thanks
  • RyTRiX
  • Graduate
  • Graduate
  • User avatar
  • Joined: Mar 28, 2003
  • Posts: 239
  • Loc: Michigan
  • Status: Offline

Post December 19th, 2003, 10:01 am

Thinking about this kinda stuff gives me a headache :roll:
  • Anonymous
  • Bot
  • No Avatar
  • Joined: 25 Feb 2008
  • Posts: ?
  • Loc: Ozzuland
  • Status: Online

Post December 19th, 2003, 10:01 am

Post Information

  • Total Posts in this topic: 19 posts
  • Users browsing this forum: No registered users and 134 guests
  • You cannot post new topics in this forum
  • You cannot reply to topics in this forum
  • You cannot edit your posts in this forum
  • You cannot delete your posts in this forum
  • You cannot post attachments in this forum
 
 

© 2011 Unmelted, LLC. Ozzu® is a registered trademark of Unmelted, LLC.