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Largest Prime Number Yet Found

if you read the article, you'll see that it was not done on a supercomputer cluster like G5's at VTech. it was on a distributed computing project, much like SETI. these are 200,000+ home-use computers volunteering their idle CPU cycles...

sometime, i like the purity of this kind of pursuit... why does everything need to be practical? (or at least immediately...) "i want to know because i'm curious." is a good enough reason for me once in a while...
 
i imagine they took the number of computers submitting results (~200,000) and the average amount of time it took for the process to be completed at each computer to deduce the total computing power...
 
studying primes contributes to the better understanding of number theory.

number theory has been applied to developing encryption methods...

in this case, this particular number itself probably won't be applicable, but it does give mathematicians more knowledge in the field of number theory...
 
How does this work? Do they write some sort of algorithm that allows them to skip the lion's share of the numbers...Like, if it's not divisible by two, then you don't have to test any of the even numbers, and three, and five, and so on, so that you eliminate the need to check say 75-80% of numbers? Anyway, I think this is cool, and as someone else said, math is cool sometimes for its own sake...Its purity and mystery, beauty even.
 
well, its a little more complicated than just seeing what will divide into a possible new prime.

given a number that is 2 to the 21,000,000th power, you're talking about a huge number. How do you represent that in memory? Storing the number alone is 21 megs! So to do calculations on that requires interesting code :D And you have to check all the prime numbers up to that point, so if there is a prime at 2 to the 4,100,203rd -1 you've got another really large number to throw into the equation.

Great stuff! :D

D
 
Originally posted by themadchemist
How does this work? Do they write some sort of algorithm that allows them to skip the lion's share of the numbers...Like, if it's not divisible by two, then you don't have to test any of the even numbers, and three, and five, and so on, so that you eliminate the need to check say 75-80% of numbers? Anyway, I think this is cool, and as someone else said, math is cool sometimes for its own sake...Its purity and mystery, beauty even.
Click to expand...

i'm not a mathematician - and even most phd mathematicians won't be able to answer the factorization question unless they specialize in it - but you don't (or more like can't) do simple systematic divisions. it's just not possible.

what they do is convert factorization into some other kind of problems - a quick search on google (how to factor a large number?) gave me at least one link mentioning factorization using elliptic curves. i know nothing about elliptic curves, but i do remember it being used in a part of andrew wile's proof of fermat's last theorem...

i believe what mathematicians are finding is that there's very subtle but firm connections at a very deep level between different branches of mathematics - even ones seemingly unrelated like number theory and analytic geometry... and often, "impossible" problems/theorems in one branch is connected to another in a different branch...
 
It's really not that hard to make code to search for prime numbers. Infact I even made little scripts to do that years ago.
I think its not hard either to make it search through distributed computers.. efficiency is lower, but lets say that one computer searches prime numbers from a-b another one from b-c etc.
I don't know how they managed handling and storing such big numbers though.
 
Originally posted by Megaquad
It's really not that hard to make code to search for prime numbers. Infact I even made little scripts to do that years ago.
I think its not hard either to make it search through distributed computers.. efficiency is lower, but lets say that one computer searches prime numbers from a-b another one from b-c etc.
I don't know how they managed handling and storing such big numbers though.
Click to expand...

well, these mathematicians aren't really searching for general primes. the numbers are simply too big to "search." at least for this project, what they are doing is testing if a certain type of numbers (mersenne primes, 2^p -1 where p is another large prime number) are actually primes or not.

again, the number is so large that it takes more than the conventional method of simple division to test it. i don't know the details, but i'm 100% sure that they are not distributing candidate divisors between computers to see if it will divide into that number or not. (how else to explain one person given the "credit" as original news indicate?)

doing simple divisions between distributed computers would be like having distributed computers string together random characters and looking for a work of shakespeare to show up. yeah, it will happen eventually but that eventually is such a long time (many orders of magnitude longer than the life of the universe, perhaps...) that it's considered mathematically impossible. (usually defined as anything with probability less than 1 in 10^50 or 10^100.)
 
It seems slightly pointless to try to find such obscure numbers. But, what the heck, more stuff that I can say to make me look smart. ;) :p :D
 
Originally posted by Freakk123
It seems slightly pointless to try to find such obscure numbers. But, what the heck, more stuff that I can say to make me look smart. ;) :p :D
Click to expand...

Actually, these numbers can be very important to the fields of number theory and even cryptography.
 
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