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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.
One of EFFs goals is personal privacy. Encryption is based on prime numbers, the larger the prime, the more secure it is. Having an insanely large prime would take nearly forever to crack the encrypted message. http://www.cpaadvisor.us/sub/8_encryption.htm
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
http://primes.utm.edu/mersenne/
(6*6) -1 = 35
It pays to be obvious, especially if you have a reputation for being subtle.
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.
Nope.
17*89 = 1513
34^2+1 = 1157
You are 50% correct, however, as you probably meant to type 13*89, which would work.
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).
There is a link in TFA to the number. It gives an abbreviated version first, but links to the full number as well:
http://prime.isthe.com/chongo/tech/math/prime/m42643801/prime-c.html
Sure, but when you consider how often primes must be generated in this sort of algorithm, optimizations are very useful. (That's why most algorithms actually in use use parabolas in place of primes, generating random primes is too computationally intensive.) But research is always worthwhile to see if new approaches can be found (and often the research leads us down paths that most people would say "What can you do with that? Why the fascination with..."
If we knew it wouldn't be called research, it would be called engineering.
No, I wasn't kidding at all when I said "very secure". I really mean it. It's just that Kalirion (and you AC), and I are thinking of, and referring to, two very different systems of PK encryption, which have very different properties, and would be affected very differently by the choice of prime numbers.
In the case of Diffie-Hellman, only *one* prime number is used, and it is not a secret at all. It is transmitted in the clear, over an insecure channel, to the other party, in order to be used to establish the mutually shared secret key. This is by design, and in no way weakens the security of the encryption system. Please, don't take my word for it, just read the link in my first post.
In contrast, in the RSA system, which you and Kalirion are both referring to, *two* prime numbers are used, and these two primes must both be kept secret. Obviously, in this case, choosing one of the two secret primes from among the "famous" prime numbers, would certainly weaken the overall security of the encryption, by reducing the search space for a brute-force attack. However, given the huge set of primes from wich the other one could be chosen, I don't know whether choosing just one "famous" prime number for your secret pair would make the resulting secret key easy, or even computationally feasible to find, given our current state of technology.