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SALT LAKE CITY — The Internet does a lot of things for us, from streaming movies to catching up with loved ones. However, few are aware that it helps us find the very building blocks of numbers themselves.
Wednesday it was announced that mathematicians in Missouri have discovered the largest known prime number yet, 257,885,161-1, a number so large that it has over 17 million digits. Storing this single number in an ordinary text file would take nearly 30 megabytes of storage.
Curtis Cooper and his team at the University of Central Missouri found the number using [GIMPS, the Great Internet Mersenne Primes Search](<http://www.mersenne.org/ target=_blank>), which uses computers worldwide to crunch numbers and spit out primes, though years often pass before a new number is found.
The question is: Why does it matter? What's the big deal about primes? That's an immensely huge number, but why should anyone care?
Primes
Prime numbers are both incredibly simple and slippery as a Teflon-coated frog. All of us probably remember learning the basics. They are simple, because they are easy to define — any number that can only be divided by itself and the number 1 is a prime. Slippery, because they are rare, unevenly distributed among numbers and there is no fool-proof method for actually finding them.
But there's more to it than that. Prime numbers are absolutely central to mathematics. You might say they are the elementary particles of the mathematical world. All matter is made up of protons, electrons and other particles. All numbers are made up of primes.
As a matter of fact, the Fundamental Theorem of Arithmetic is all about primes. Pick a number, any number — there is one, and only one, set of prime numbers that produce that number when they are multiplied together. For instance, 1200. 3x2x2x2x2x5x5 = 1200. 3, 2, and 5 are all primes, and no other group of prime numbers will get you 1200 if you multiply them. Just like Hydrogen is made up of one proton and one electron, 1200 is made up of one 3, four 2s and two 5s, and that's just it.
So in searching for them, there's a sense that you are searching for what makes every other number among the infinite numbers that it is possible to make.
Still not convinced? You depend on primes every day.
Even if you don't care about the fundamental atoms of mathematics, you still use primes — probably every day — without knowing it. How? With encryption. Every time you buy something securely off the internet or send a credit card number or a PayPal invoice, you depend on primes.
Taking a large number and breaking it into primes is incredibly difficult, and takes time and massive computing power. So cryptologists will use a large number made up of only one or two "atoms," that is, prime numbers, and make it the key to decoding your information. If you know the prime factors, it's easy to decode; if you don't, it's nearly impossible to break the encryption.
Glory
For mathematicians, there is also a certain amount of glory involved. Finding primes these days is hard. Really hard. Small primes are easy, like 3, 5, 7, 11, 13 and so on. But the bigger they get, the more slippery they are. Thousands of computers working across the globe around the clock produce a new large prime number only once every few years.
"Every time I find one it is incredible," Cooper told the Associated Press. "I kind of consider it like climbing Mount Everest or finding a really rare diamond or landing somebody on the moon. It's an accomplishment. It's a scientific feat."
The greatest mathematical minds of all time have all done work on prime numbers, from Euclid, thousands of years a go, to Leonard Euler, to Copper. It's part and parcel of mathematics.
