## New Mersenne prime (probably)!

The Great Internet Mersenne Prime Search has just announced that they have (probably) discovered a new Mersenne prime. They haven’t released any details yet so speculation abounds. Will this be the prime to win the \$100,000 prize awarded by the Electronic Frontier Foundation to the first discoverer of a ten million-digit prime? We’ll see in about a week, once an independent computer check confirms the result.

So, what’s the big deal? A Mersenne number is a number of the form $2^n - 1$; for example, $2^2 - 1 = 3$, $2^3 - 1 = 7$, and $2^{10} - 1 = 1023$ are all Mersenne numbers. Mersenne numbers which are also prime (that is, which have no divisors other than themselves and one) are called (not surprisingly) Mersenne primes. For example, 3 and 7 are Mersenne primes, but 1023 is not ($1023 = 3 \cdot 11 \cdot 31$). The thing about Mersenne numbers is that there are ways to write computer programs to check whether they are prime which are a LOT faster than simply trying all possible divisors. For a while now, the largest known prime numbers have been Mersenne primes.

The Great Internet Mersenne Prime Search is a distributed computing effort — sort of like SETI @Home if you’ve ever heard of that — which tries to find new Mersenne primes. Anyone at all can sign up to help; all you have to do is go to their webpage (linked above), download some software, and then whenever you are not using your computer it will work on checking really big Mersenne numbers to see if they are prime. Give it a try! It won’t run while you’re actually using your computer, so you won’t notice any slowdown. And you have a small chance of being famous (well, sort of) or even receiving a cash prize if your computer happens to be the one to discover a new prime.

So, how big are these numbers we’re talking about? Well, the largest currently known prime number (not counting the one that was just announced, which we don’t know yet) is $2^{30,402,457} - 1$, which has a whopping 9,152,052 digits! You can download it here, but keep in mind that since each digit takes 1 byte to store, the file is 9MB in size!