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.

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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 Penné, 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!

 

 

 

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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.

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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!

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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


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

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I swear some people have way too much time on their hands. LOL. Its so darn amazing to me because numbers go on and on infinitely. I really wonder why they need to know prime numbers so large. How does it help and what does it do for them? I just don't understand why someone would want to know that. My other question is who is paying these people to figure this out? LOL

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I wish I could figure that number out. I would rather work a normal job than do that. I cant think that hard. Id have a mental break down. I have had those in the past... so for me it would not be a good idea.

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wat are prime numbers used for anyway? i remember hearing they were sed by the government to encrpypt data or something so whenever a new one was found they paid th e person heaps of money for it. how are they special i mean? i just dont get what they really are... i did them in primary school but they were never used in anything. hmmm... well anyway, i want one of those prime number posters. they're pretty dandy.

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I think ill go get me a programmers and make a program that checks. I'll be liek 30 befor I get 100,000 but ehh retirement.

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ooh my math teacher had a poster about that.

it's interesting because it's the largest prime number KNOWN, and an even larger prime number can be discovered because numbers go on forever

it can't fit on my calculator xP

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