I must confess, in general, I dislike numbers. I love math, but numbers just hurt my head. Not all numbers were created equal, however (yes, that is a really bad pun). Certain numbers are more fascinating than others. Take prime numbers, for example. Mathematicians continue to search for larger and larger prime numbers, and we just found another one.
A prime number is any integer that can be divided by only itself and one. Two is the only even prime number. Others include three, thirteen, and twenty-nine. The largest known prime number would fill over 3,000 pages. It's two to the exponent 43,112,609 minus one. Yeah, that's big.
What's the big deal about prime numbers? Surely they have no application in the real world! Those silly mathematicians are too lazy to do work, so they just sit around making up numbers all day! You might have been right, once. Then someone came along and built computers, and prime numbers now have purpose!
All integers (whole numbers) can be broken down into a unique combination of primes. For example, 10 is the product of two prime numbers, 2 and 5. Factorization is the operation of finding a number's prime factors; you probably did this in school. It's relatively easy for small numbers. With large numbers, it becomes harder and takes longer.
I imagine that most of you have bank accounts. If not bank accounts, then Facebook accounts, email accounts, etc. What stops hackers from getting into those accounts? Prime numbers! Prime numbers are an integral part of cryptography and securing computer systems. One way to encrypt data is to take two huge prime numbers and multiply them together, producing a larger number. To decrypt the data, you need to know the prime numbers.
As computers get faster, we need to find larger and larger primes with which to encrypt data. If quantum computing ever becomes viable, it would have great implications for current cryptographic methods, since a quantum computer would be able to factor numbers in a fraction of the time it takes current supercomputers. Bye-bye bank account! Fortunately for cryptographers, quantum computing is in its infancy.
As you can see, prime numbers have real-world applications. Our ability to find larger primes and calculate prime factors has ramifications for the security of your data.
Computing prime numbers is an excellent test of computing resources, too. Incidentally, most of the largest known prime numbers have been found using a distributed computing project called GIMPS, or the Great Internet Mersenne Prime Search (Mersenne primes are a special type of prime, and they are often the easiest to find). You can run GIMPS software on your own computer and help contribute to the search for primes! There's even prize money involved.
Of course, most of you aren't running supercomputers at home, so your computer isn't finding primes all by itself. It runs tests over months on a number, reports back to the mothership, and continues running tests. As the GIMPS website states:
A single test will take approximately 3 years on a Core 2 Duo computer. Your chance of success is roughly 1 in 2,000,000.
So don't hold your breath.