Largest Known Prime Number A very long number...

[jsasomerville 0]

It was discovered by the Great Internet Mersenne Prime Search (GIMPS), a distributed network of volunteers using their spare computer power to find the largest Mersenne primes. This system actually discovered the eight largest prime numbers known.

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It warms my heart good to see that people are using their spare computing power to do something completely useless... I wish they would spare their processing power to assist more pressing matters including tedious work needed to understand the physics of the universe or deciphering genetic code fragments. Oh well... maybe I don't understand the potential worth of knowing incredibly large prime numbers...

[jsasomerville 0]

Whoops... I forgot to argue kasm's reasons.

 

- They were first studied because many of the properties of numbers are directly tied to their factorizations. 

 

- They  are used for a variety of encryption methods used to keep transactions safe and in CD and DVD protection.

 

- The search for Mersenne primes has proved useful in development of new algorithms, testing computer hardware, and interesting young students in math. I think the INTEL, Celeron  and AMD are itersted in testing their processor.

 

- NASA scientists even decided that they are a good sign of intelligence and have included a short list of primes on the plaques sent out with the voyager spacecraft. 

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1) It's true what you are saying about numbers, but that still doesn't give a good reason to calculate such enormous numbers.

 

2) Encryption methods today, such as MD5 (using a lengthy password) and other one-way encryptions, would take countless years to complete, even with thousands and thousands of computers working on it. By the time the encryption is cracked, the information would be worth close to nothing.

 

3) In terms of testing processors, searching for prime numbers is a cool tool to measure speed. However, there are only a handful that are worth testing... for now. Once we have processors that can handle doing such computations, we should then approach the problem of finding the next few prime numbers. However, it's a waste of precious time to calculate them now when they are not needed.

 

4) I can't argue with that logic. They are also sending images depicting the anatomy of a male and a female. They should just dress them up in clothes with the symbol of the Target stores on them. Don't forget to include a small note saying "If you can read this, please take us over!"

[Editor 0]

you say its useless however its actually pretty neat i like the fact that technology has come so far as to know that. and no really if you put a 1 at the end it doesnt matter because 11 times 11 is 121 so therefore putting a 1 on the end doesnt really do too much. anywayz im in calc and thats something that i'd like to bring up to my teacher is just that fact that technology has come so far as to realize this...as for a computer making a mistake....for them to prove that something like that is true and to get the actual number they would have to have a really high powered computer and very advanced and im sure that it would have been tested many times over. so if someone has actually proved it and it was in an article...granted you cant trust everything now a days...but still if it was somwhere that u know is credible it was tested a lot of times to make sure that it is true. i still think that its really cool though thank you for the info!

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Wow, i could completely agree with you. And its an unique of finding prime numbers beyond anyone could amangin.

[liauce 0]

it is still very surprising that computers are so limited in calculating something that seems so easy to define. Anyway what no. are we at now, and how fast is our progress? lol the progress of mankind in numbers

[kasm 0]

it is still very surprising that computers are so limited in calculating something that seems so easy to define. Anyway what no. are we at now, and how fast is our progress? lol the progress of mankind in numbers

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it is still very surprising that computers are so limited in calculating something that seems so easy to define. Anyway what no. are we at now, and how fast is our progress? lol the progress of mankind in numbers

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Yes man define , suggest algoriths for solution , traslate this algorithms into programs and the computer execute it.

 

 

We are thinking to execute i.e find the solution or in our example the prime numbers of 10 million figures. Last year we couldnt dream about that before Pentium 4 3000 or more. Next year we can think about the prime of 100 million figure after more strong computer will be created.

 

Exactly as Nasa needs more speady craft toward planets in our solar system and in futureto planet of other system, we still need more powerful computers to solve other computing needs.

 

I ask people [not including you ] who don't contribute and not interested , I asked them to do favour to us and do not post just for posting and they have to initiate their interesting themes. Leave 7000 grazy and intelligent people to do their grazy works. This thread is not a poll to answer the question of to do or not to do.

[Jimmy 0]

Actually, its not completely useless. The defence governments would pay you a huggge amount of money on top of that $100,000 (although it would still be very handy on its own) if you just happened to find the next one. -better get to work- prime numbers are used to encode their top-secret goodies for some reason like they are not divisible by other numbers to make them safe or something or rather. If a new prime number got into the wrong hands it would end up with someone getting very angry, and the risk of their information being leaked. GIMPS now have a decent use...

[shadowdemon 0]

wow, i still cant believe this thread is going on. IT was started in september of last year. THis is impressive for a post. IVe never seen a thread anywhere go on for this long.As for the prime numbers, THey are used for government purposes. THere used as encryptions to hide things from other countries or hackers since most information from the government is stored on a computer. WHat i dont understand is how a number with like 10k numbersd can be used as a security reason

[Kioku 0]

Well that wouldn't be a prime number haha. but nice try
A prime number has to be divisible only my 1 and itself

I bet my Mac could come up with that number in no time flat muahhaah

I seriously doubt that. The $100,000 reward does sound dimunitive in contrast to the over all cost that a computer with the capacity. It would take quite a load of processing power to come up with that many digits, especially since with each added 0, it would require more power than over the tenfold and as previously stated might take millions of dollars to build a computer that could handle such a work load without simply giving out. Even after the millions, the computer might give out anyway, therefor nullifying the chance of any profit and actually make the profit therein negative. Personally, I wouldn't go for it. If somebody would want to pursue this task for hobbyist reasons and had some extra money and time to spend for working on this, I'd say go for this.
Prime numbers are interesting, though. Most likely, since their factor family can only consist of their own self and the number one. I personally think it could be used for security reasons, since that long of a number isn't going to be pulled out of anyone's hat any time soon. Quite a genius thing to use for encryption, in all actuality.

[tdktank59 0]

holy *BLEEP* thats a big **bottom** number lol...ima start my own program on my spare computer lol... lets get this thing going...

[True2Earn 0]

Actually, the largest known prime number is 2^230402457-1 containing 9,152,052 digits, found on December 15, 2005. For information concerning prime numbers and the research into in can be found at http://primes.utm.edu/. All numbers that are submitted as a prime number must accompany proofs. You cannot just say 1 with 10 million zeroes + 1 is a prime. The number submitted will also be verified before being announced. An example of the output of a primality proving program (in this case, Proth) is as follows:

1557*2^231779 + 1 is prime! (a = 5) [69776 digits]1557*2^231779 + 1 is prime! (verification : a = 7) [69776 digits]
1557*2^231779 + 1 doesn't divide any Fm.
1557*2^231779 + 1 doesn't divide any GF(3, m).
1557*2^231779 + 1 doesn't divide any GF(5, m).
1557*2^231779 + 1 doesn't divide any GF(6, m).
1557*2^231779 + 1 doesn't divide any GF(10, m).
1557*2^231779 + 1 doesn't divide any GF(12, m).
1557*2^231779 - 1 factor : 5
1557*2^231780 + 3 factor : 3
1557*2^231780 + 1 factor : 41
1557*2^231778 + 1 factor : 7

This is one I discovered but due to UTM server problems another person discovered it and got it submitted 7 days before I was able. So now, it's back to the drawingboard...

Notice from BuffaloHELP:

Quote tags are used when listing or placing codes. Unless you can claim it that it's yours, please use the correct BBcode.

Yes, the above is directly me from my own private research into prime numbers (one of my hobbies).

Edited May 16, 2006 by True2Earn (see edit history)

[PmH 0]

It's fascinating, really. The realm of technology fused in with the infinite world of math, what I don't understand is what type of program they run that, and how fast that program can go through a certain set of numbers, because eventually won't it just take longer and longer to find the next prime number as they get fewer and far between?And as for $100k for a million digit prime number, I wonder how many have been found already. It seems like a pretty tough task, without the proper technology... which, I, unfortunately am not equipt with .Oh well, guess I have to get a job outside of prime numbering.

[True2Earn 0]

There are many different programs available to do prime research. The ones that I, personally, use are:Paul Jobling's NewPGen - This program performs sieving of a particular range of numbers to factor out candidates quicker.LLR - Written by Jean Penn?, the non-network capable Lucas Lehmer Riesel is the traditional application used to test and prove the primality of numbers of the form k*2^n-1.Proth - Proth_sieve is a sieve program for Proth and Riesel numbers (k*2^n?1) developed by Mikael Klasson and Paul Jobling.George Woltman's PRP - Probabilistic prime testing program. This will take the output of NewPGen to check for probable primes before sending to Proth.Chris Nash's PrimeForm - PrimeForm is a program that performs the "Fermat little theorem" in order to test whether a number is a probable prime. While probable primality does not in itself prove primality, it is a valuable tool and a very quick test to establish if a number is composite. If probable primality is established, it may be possible to prove primality by further testing. In particular, PrimeForm can apply the classical "N-1" and "N+1" tests in the cases where N-1 or N+1 has many small factors. This allows PrimeForm to be used in the proof and discovery of a wide variety of forms.Yes, it can take a very long time to test a number for primality, sometimes years before a discovery. Suppose I was testing for a primes number that has 10,000 digits. Now let's assume it took 10 hrs to discover one. That sets up our baseline for comparison. Now, let's look for a prime with 100,000 digits. One of this size will take 10^3 times longer so 10 hrs * 10^3 = 10,000 hrs (about 1 year 2 months) before finding a prime number.As for the largest known prime number? On December 15, 2005, Dr. Curtis Cooper and Dr. Steven Boone, professors at Central Missouri State University, discovered the 43rd Mersenne Prime, 2^30,402,457-1. The new prime is 9,152,052 digits long. This means the Electronic Frontier Foundation $100,000 award for the discovery of the first 10 million digit prime is still up for grabs! The new prime was independently verified in 5 days by Tony Reix of Bull S.A. in Grenoble, France using 16 Itanium2 1.5 GHz CPUs of a Bull NovaScale 6160 HPC at Bull Grenoble Research Center, running the Glucas program by Guillermo Ballester Valor of Granada, Spain. It takes a lot of computing power!

[T100 0]

What is the point of finding the largest prime number? I always wonder. I know that mathematicians have an idiosyncratic love for prime numbers because they are from one of the field least explored by mathematicians. And they test prime number in the form like 2^2^n +1 because and by the method of exclusion, come up with the largest prime. It is only a brute force technique and there is absolutely nothing scientific about it. But it is interesting though.

[dark_drgn 0]

As for the largest known prime number? On December 15, 2005, Dr. Curtis Cooper and Dr. Steven Boone, professors at Central Missouri State University, discovered the 43rd Mersenne Prime, 2^30,402,457-1. The new prime is 9,152,052 digits long. This means the Electronic Frontier Foundation $100,000 award for the discovery of the first 10 million digit prime is still up for grabs! The new prime was independently verified in 5 days by Tony Reix of Bull S.A. in Grenoble, France using 16 Itanium2 1.5 GHz CPUs of a Bull NovaScale 6160 HPC at Bull Grenoble Research Center, running the Glucas program by Guillermo Ballester Valor of Granada, Spain. It takes a lot of computing power!

That should be in quotes, you ripped that off a website

Amazing what we do nowadays. Why do we need to know these prime numbers in the first place? It's as useless as finding Pi to the 9 millionth decimal place!

[matto 0]

PS.If you can find a prime number which has 10 million or more digits then you can have $100,000 from The Electronic Frontier Foundation. So if you'd like a good life, get a career in prime numbers

Google should try taking a stab at it with their uber network. Probably less than an hour of downtime, and they'd get 100,000 out of it.

But then again, would the loss of adsense revenue for that one hour be worth it? o_O

Amazing what we do nowadays. Why do we need to know these prime numbers in the first place? It's as useless as finding Pi to the 9 millionth decimal place!

I agree with you in the sense that finding any irrational number, or kind of number, that is bigger than can be easily spoken about or used is most likely pointless and unnecessary. However, so is a lot of stuff we do daily. I think the main reason anyone would take the time to figure such a thing out would be entertainment. They find it fun (for some reason or another) to figure stuff like that out. It's just as pointless as watching The Simpsons, or playing peek-a-boo as a child, but that doesn't make it "un-fun".In fact, I've done something very similar to this, and I'm completely aware of its unimportance and stupidity, but I find it entertaining to take part in. I memorized something like 55 digits of pi in like 3 hours, while playing computer games wasting my time. My reason behind it? There are two reasons I can think of: a) I enjoyed memorizing it and utilizing my brain, making me think, on a day when all my friends were on vacation and i had nothing to do (winter break =p) and if I did not take time to memorize it, I would have just spent the 3 hours playing computer games doing absolutely NOTHING.

So, sometimes these pointless things can actually be similar to "brain excersizes," I suppose =D
Edited April 29, 2006 by matto (see edit history)