Student Discovers Largest Known Prime Number

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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
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  • ATNO/TW
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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.
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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.
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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.
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:lol:
  • Alan2
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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:
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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.
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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.
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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.
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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:
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I'd like to say that eventually they would become proportionally equal, but I doubt that will be the case :-P
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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.
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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
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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
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Thinking about this kinda stuff gives me a headache :roll:
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Marcus wrote:
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


the answer to your question re:formula for prime nos. is in the post above yours.

their is no formula for finding primes:they have only the approximation of how many primes there are upto any given no. (in the formula given)

as i stated the consequence of solving the Riemann hypothesis
will make it much easier to find prime nos. (but remember it is the Holy Grail of maths & may not be solved for a century according to experts in the field)

however i was slightly incorrect in stating that the hypothesis will allow you to find these huge primes exactly.
what it will actually do is allow you to narrow the search field - i.e. it will tell you how many primes exist in a certain no. range exactly - if for instance you are looking in the no. range 1^100 to 1^101,the solved riemann hypothesis will tell you how many primes there are in that range,thus aiding your search.
however it is possible that the solved hypothesis may actually allow predictions of primes,but you will have to ask a qualified mathematician about this(this is a hobby)

as for your question about the computer size required to know about every atom in the universe,logic will tell us that unfortunately, the size of the computer memory required has to be equal to the size of the universe that you wish to record (at the very least),so the maximum size of the universe recordable is 1/2 the universe,which will require a computer memory comprising of the other 1/2 of the universe.
the explanation for this is that for every atom you wish to record,the lowest level of feasible recording for it on a hard-drive would have to be another atom - & a 1:1 ratio is the ultimate correlation you can achieve (more likely you may need something in 1:2 or 1:3 ratios - i.e. 1/3 of the universe to record would require a hard-drive of 2/3 of the universe)

i hope this helps


& to think i only chanced upon this site trying to find out if someone could tell me what kind of money i could make from a sports "calculator" site (as you can see i try to keep my maths thorough) - no one seems to be able to help me with that

ballpark figure?

P.S. seeing the picture of the lovely musik is reward enough to come back to this site!

P.P.S. & of course geekete would never need to take a backseat to any woman!
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What about using mp3 compression for the computer atom problem? and what about the idea of the sum being greater than its parts like the computer being metaphorically 2 + 2 = 7 for instance regarding the computer atom problem?

Now on the R. Theorem.

is it possible to do a reverse brute force computations to find prime numbers by multiplying small but growing numbers against themselves and other larger numbers to produce a list of what prime numbers cant be and then take the stuff missing?

is there a pattern here? obviously the number of prime numbers shrinks as the numbers get larger, is there a curve? can one use the curve to predict in general where the next prime number is going to be?

has anyone attempted to graph prime numbers for predictive purposes? Then use those predictions to look in number ranges for prime number?
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Marcus wrote:
What about using mp3 compression for the computer atom problem? and what about the idea of the sum being greater than its parts like the computer being metaphorically 2 + 2 = 7 for instance regarding the computer atom problem?

Now on the R. Theorem.

is it possible to do a reverse brute force computations to find prime numbers by multiplying small but growing numbers against themselves and other larger numbers to produce a list of what prime numbers cant be and then take the stuff missing?

is there a pattern here? obviously the number of prime numbers shrinks as the numbers get larger, is there a curve? can one use the curve to predict in general where the next prime number is going to be?

has anyone attempted to graph prime numbers for predictive purposes? Then use those predictions to look in number ranges for prime number?



Wake up!


Have you read anything posted?


Mathematicians (the longest haired,most bespectacled,most friend-lacking guys) have been looking for this for 200y!

All of them end up at one stage or another at the prime number question, & no matter how much ganga they smoke or how doogie howserish the age they get their PhD,it always end up as trying to solve the hypothesis.

don't keep asking what ifs?

it's all been asked a million times before


now if you can answer some of those questions,the matematical community will gladly support your quest for the

Fields medal
  • Marcus
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Ok :lol: like sorry and stuff.

Last question

what if C.A.T actually spelled D.O.G

:twisted: :P :D

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