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12M Digit Prime Number Sets Record, Nets $100,000
coondoggie writes "A 12-million-digit prime number, the largest such number ever discovered, has landed a voluntary math research group a $100,000 prize from the Electronic Frontier Foundation (EFF). The number, known as a Mersenne prime, is the 45th known Mersenne prime, written shorthand as 2 to the power of 43,112,609, minus 1 . A Mersenne number is a positive integer that is one less than a power of two, the group stated. The computing project called the Great Internet Mersenne Prime Search (GIMPS) made the discovery on a computer at the University of California, Los Angeles (UCLA) Mathematics Department."
The number known as a Mersenne prime, is the 45th known Mersenne prime, written shorthand as 2 to the power of 43,112,609, minus 1
Wikipedia lists it as the 47th known prime.
My work here is dung.
The biggest prime number I know is 8675309. I'll have to tell Jenny about this new one.
The CB App. What's your 20?
n00b
"A person is smart. People are dumb, panicky dangerous animals and you know it." - K
Great,everyone starts using the new largest known prime number in their private key! That's like SUPER secure!
The money does not come from regular donations.
http://www.eff.org/awards/coop
(Prize money comes from a special donation provided by an individual EFF supporter, earmarked specifically for this project. Prize money does NOT come from EFF membership dues, corporate or foundation grants, or other general EFF funds.)
Yes, in fact, it is very secure.
The fact that the (very large) prime modulus is not secret, but rather public, is part of the design of many PK encryption systems, and therein lies their beauty, simplicity, and charm. If you are interested in learning more about it, here's a description of one very widely used system: http://en.wikipedia.org/wiki/Diffie-Hellman_key_exchange
They just got advertising in every math/scientific magazine on the planet.
Mostly read my professionals that make decent money.
Sounds like a well spent 100K to me.
The Kruger Dunning explains most post on
They could have made the reward $100,003 instead...
Now that everyone knows this number, I have to change my luggage combination again. Thanks for nothing EFF!
Well, there's spam egg sausage and spam, that's not got much spam in it.
The article is correct by order of discovery- it was the 45th Mersenne prime to be discovered (on August 23, 2008.) Two smaller Mersenne primes were discovered later, on September 6, 2008 and April 12, 2009, which are also included in the Wikipedia table.
Think about how easy it is for a computer to multiply together (2^43112609 - 1) and (2^13466917 - 1).
Then think about how long it would take a computer to identify the factors of the resulting number, given that it is composed of two primes with twelve and four million digits, respectively.
Cryptography is all about simple math operations that can be performed one way, but cannot be easily and quickly reversed without knowing a secret (in my example, one of the original primes).
Strictly speaking, large primes are useful but not specific large primes. Indeed, this Mersenne prime is much too large to be useful for practical cryptography.
The main reason that primes are useful for cryptography is that there are functions associated with primes where the functions are easy to calculate but have inverses that are very difficult to calculate unless one has extra information. The classic example of this is the discrete log problem. Essentially, if one is doing modular arithmetic with a given prime (that is arithmetic where you only look at the remainders when divided by that prime. This is essentially like a clock with p numbers on it. On a normal clock is arithmetic mod 12) then it turns out that for any prime p, there is a number k such that k^1, k^2, k^3... k^(p-1) taken mod pruns through all the possible remainders 1,2,3... p-1 (obviously not in order). Such a k is called a primitive root (or a generator) Now, it is very easy given a k and an n to calculate k^n (mod p). However, given the equation k^x=m (mod p) it is very hard to find the right value of x without doing a lot of work (essentially, you have to more or less list out k^1,k^2,k^3... until you get to m). The difficulty in this process is used in a number of public key crypto systems and other systems. For example, the Diffie-Hellman algorithm which was the first modern crypto algorithm discovered uses the difficulty of this process to make it so that two people can without ever having talked to each other before have a conversation and at the end of it have a secret code that no one else can figure out without impractical levels of computation. This is true even if one has access to all the communication that goes on between the two parties. The RSA algorithm which is more practical than DH for a variety of reasons also works off of a similar procedure.
The above is assuming that the discrete log is actually a difficult problem which everyone believes but is not proven. Proving this would imply that P != NP which is one of the Clay Millennium Problems (so million dollar prize and all that fun stuff). Mersenne primes are very interesting but not for any crypto related reason.
The project GIMPS that is mentioned in the title uses a distributed computing system to search for Mersenne primes. They use a modified form of the Lucas-Lehmer test http://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test where they use a Fast Fourier Transform to be able to do the large multiplications efficiently.
We care about Mersenne primes because they correspond to even perfect numbers. If one has a Mersenne prime 2^p -1 then (2^p-1)(2^(p-1)) is an even perfect number. This was proven by the ancient Greeks. Euler then proved much later that every even perfect number is of this form. The oldest two unsolved problems in mathematics are whether there are infinitely many even perfect numbers and whether there are any odd perfect numbers. Thus, every time we discover a new Mersenne prime we get a new even perfect number. And if we can ever get enough insight to resolve whether or not there are infinitely many Mersenne primes then we can resolve one of the oldest unsolved problems in all of mathematics.
"Voluntary" math research group? Is there any other kind?
I'm trying to imagine an "involuntary" math research group, and all I'm getting is scenes from dystopian science fiction ... or possibly a scene from the life of Léon Theremin.
-kgj