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12M Digit Prime Number Sets Record, Nets $100,000

Posted by CmdrTaco on from the that's-a-lotta-bits dept.

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."

7 of 232 comments (clear)

  1. Actually the 47th by eldavojohn · · Score: 4, Informative

    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.
    1. Re:Actually the 47th by eldavojohn · · Score: 3, Informative

      Doesn't that make the 48th Mersenne prime 2 to the power of 43,112,610 minus 1? Can I have my $100,000 now please?

      No, because not all Mersenne numbers are prime numbers. Example: 2 ^ 4 - 1 = 15 And 15 is divisible by both 3 and 5. It's highly unlikely for two Mersenne primes to be adjacent to each other as Mersenne numbers but not impossible. If you could verify your assertion, you might just be eligible. I'm guessing it's already been checked by no by GIMPS though.

      --
      My work here is dung.
    2. Re:Actually the 47th by gnasher719 · · Score: 5, Informative

      No, because not all Mersenne numbers are prime numbers. Example: 2 ^ 4 - 1 = 15 And 15 is divisible by both 3 and 5. It's highly unlikely for two Mersenne primes to be adjacent to each other as Mersenne numbers but not impossible. If you could verify your assertion, you might just be eligible. I'm guessing it's already been checked by no by GIMPS though.

      Here's the complete list of all consecutive Mersenne numbers that are both primes: 3 = 2^2-1 and 7 = 2^3-1.

      2^n-1 can only be a prime if n is a prime, because 2^(ab) - 1 is divisible by 2^a - 1 and 2^b - 1. And (2, 3) are the only two consecutive primes.

  2. Re:woo by Nibbler999 · · Score: 5, Informative

    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.)

  3. Re:so? by maxfresh · · Score: 3, Informative

    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

  4. 45th in order of discovery by Noren · · Score: 3, Informative

    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.

  5. Re:Sounds cool, but... by Anonymous Coward · · Score: 4, Informative

    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).