# My idea about finding the largest prime number [closed]

I have an idea about finding the largest prime number that I'd like to share with you guys and hear your feedback.

The idea is to use many computers to find the largest possible prime number, by using the power of web.

We know what the largest prime number already found is, so we will make a website that will start counting from that number.

Each visitor who is willing to participate will be assigned a number, with client side scripting we will try to find out if that number is prime or not, as long as the visitor stays on that website his computer will be used to find out if the number assigned to him is prime or not.

If he leaves the website for any reason, his browser will remember the calculations that have already been done and we will continue with that in his next visit. If he doesn't come back in a certain period of time, then we will remember the results of the last calculation and assign the number to someone else.

New visitors will be given a new number that has not been tested before.

If the number is found not to be prime we flag that in a database, and move to the next one.

To optimize the algorithms we will start a forum in which mathematicians and computer scientists will try to improve the code and the whole system on regular basis.

My question now is, is there something fundamentally wrong with this method? am I missing something huge? Is it worth trying?

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mersenne.org – pedja May 5 '12 at 3:37
Oh no lol it's ok I'll come up with another great idea – user893730 May 5 '12 at 3:39
Just being a little pedantic, you're not looking for the "largest possible prime number", you're looking for the largest known prime number. Since there are an infinite number of primes, clearly there isn't a maximal element. – chris May 5 '12 at 3:46
I don't see any mathematical question above. It seems to be concerned more with computer science matters. One could replace "primality testing" by any non-mathematical problem amenable to distributed computation without altering the question. If you have specific questions about mathematical aspects of distributed primality testing then you should explicitly state them. Otherwise your question risks being closed as off-topic. – Gone May 5 '12 at 4:21
Ever since I had enough reps to downvote, I never did until I saw this question. As Michael Hardy pointed out, there is no such a thing called the largest prime number. – scaaahu May 5 '12 at 4:54

## closed as off topic by Gone, user17762, mixedmath♦, J. M., Benjamin Lim May 5 '12 at 5:28

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In about 300 BC, Euclid showed that there is no largest possible prime number. He reasoned as follows: Take any finite set of primes. Multiply them, getting $P$. Add $1$ to $P$, getting $P+1$. Now $P$ and $P+1$ cannot have any prime factors in common. For example, if $P$ is a multiple of $7$, then the next multiple of $7$ won't show up until you get to $P+7$, so $P+1$ won't be a multiple of $7$, nor of any of the other primes you multiplied to get $P$. So find a prime factor of $P+1$, and you'll get a new prime that was not in the finite set you started with. (Maybe $P+1$ is itself prime, and that's the new prime, or maybe it's not and some smaller number is the new prime.)
 Note that is quite historically inaccurate to imply that Euclid's proof involves "factoring $P+1$ into primes". Perhaps you should review the texts cited in your Intelligencer article. – Gone May 5 '12 at 5:23 Note that if $p+1$ is not prime then this does not imply that factoring it yields more than one new prime, since possibly $p+1 = q^n$ a prime power, which yields only one new prime $q$. What's worse, in other rings $p+1$ might not yield any new primes since it might be a unit, e.g. in $\rm\:\mathbb Z[1/q]\subset \mathbb Q.\:$ But one can avoid this obstruction in rings with few units, generalizing Euclids proof widely. – Gone May 5 '12 at 5:47 @BillDubuque : OK, I've added one additional word to my answer, which should deal with your objection. – Michael Hardy May 5 '12 at 16:51 @BillDubuque : I don't understand your first comment. Euclid wrote that either $P$ is prime itself, in which case it is a prime that differs from those in the original finite set, or else it is not prime and it has at least one prime factor, and that must differ from those in the original finite set, and that either way, you get at least one prime not in the original set. – Michael Hardy May 5 '12 at 16:56 @Micheal But that's not what you wrote above. Euclid could not have said anything like "factor P+1 into primes" because he did not have the language to speak about arbitrary length products, but only products of length at most 3. – Gone May 5 '12 at 17:10