The Music of the Primes
January 24, 2008On this winter vacation I have actually found some time to read which is a pleasure that everyone should take advantage of whenever possible. Unfortunately the types of books I choose are not to most folks liking. The book that had me up until 2 am by the poolside with a beer in hand? None other than “The Music of the Primes - Searching to Solve the Greatest Mystery in Mathematics” by Marcus du Sautoy.
Yeah … my wife has the same opinion that many of you will .. “are you kidding?” She wants to know who would drop almost 10 bucks for a book whose main cover quote is “An amazing book! Du Sautoy provides a stunning journey into the wonderful world of primes.”
Just in case you have forgotten your high school mathematics prime numbers are numbers that are divisible only by themselves and 1. Example - 3 is prime. The list of the first few primes 2, 3, 5, 7, 11, 13, 17, 19, 23, … (the list is infinity long which Euclid proved sometime around 300 BC)
Why would anyone care about primes? Well - you should because all e-commerce security is built upon the difficulty in writing large numbers as the factor of 2 primes. The basic idea is this - we can choose 2 very large prime numbers and multiply them together to produce a very large number but it is very difficult to decompose that number into the product of its primes. A person can use this fact to create a secure code to encrypt data and information so that prying eyes cannot read it. The mechanics of how this is done takes a bit of explaining but the basic idea is that I can give you a public key to encode your information but I am the only one who can decode it because it relies on knowing the prime factors of a large number which only I who created the key would know.
So again .. why should anyone care? Well if mathematicians find a way to easily factor large numbers into prime factors then all modern e-commerce security would disappear overnight and everything could be read by anyone. Rest assured for now though … turns out this seemingly simple thing is actually exceeding difficult.
