How I Spent My Christmas Vacation

Electrical engineer Jonathan Pace of Tennessee lent his computer to a project called GIMPS -- the Great Internet Mersenne Prime Search. It's a kind of crowd-sourced project that links multiple computers to increase their processing power. And on Dec, 26, Pace's computer was the one that found the largest known prime number and 50th Mersenne Prime, after six solid days of computing.

Volunteers download a software package to run that searches for the prime numbers, which are numbers that aren't divisible by any number other than themselves and one. They have no pattern and so the only way to check if a number is prime is to start dividing it by all of the numbers smaller than it is. This can work early on, but by the time we get into large numbers it takes longer and longer, requiring calculations done at computer-only speed. Even then, Pace's six-day run shows that the job is not easy.

The number was given the name M77232917 because it is 2 raised to the 77,232,917th power, minus one. It has more than 23 million digits. The computer found it by multiplying 77,232,917 2s and then subtracting 1.

Mersenne Primes take their name from the French monk Marin Mersenne, who in the 17th century offered a theory about certain kinds of prime numbers that today bear his name. M77232917 is just the 50th Mersenne Prime. They're found by multiplying two together x times, where x represents another prime number, and then subtracting 1. So 3 is a Mersenne Prime, because 2 multiplied by itself is 4, minus one is 3.

They also generate what mathematicians call "perfect numbers," which are numbers whose proper divisors add up to the number. The smallest perfect number is 6, because 6 is divisible by 1, 2 and 3, and 1+2+3 = 6. The perfect number from M77232917 has more than 46 million digits. Perfect numbers so far are all even, which is interesting because other than 2 itself, all prime numbers are odd.

These numbers are so huge they exist in complete abstraction -- there is not enough of anything in the universe to require them to actually count it. But immense primes have proven useful in cryptography and internet security, so the search goes on. And for Pace, M77232917 = 3,000, because that's the cash prize he's eligible to share in following the discovery.