Code Breaking [posted by Troy]
I was recently asked why we care about prime numbers. Prime numbers are numbers that is greater than one and can only be evenly divided by 1 and itself. They are 2, 3, 5, 7, 11, 13, 17, 19, 23... But why do we care? Well, the main reason today has to do with code breaking.From Britannica: "In the 20th century, with the help of computers, prime numbers with more than two million digits were discovered. Like efforts to generate ever more digits of p, such number theory research was thought to have no possible application—that is, until cryptographers discovered how large primes could be used to make nearly unbreakable codes. See cryptology: Two-key cryptography." From the BBC: Take a public key based on a huge number which is the result of two prime numbers multiplied together (a prime number being one which can be divided only by itself or by one). You use this number to encode your message but you do not need to know the two original prime numbers. Only the person decoding the message needs to know, because the text was encoded using an equation and both numbers are needed to reverse that equation. The system is safe because it is a curious feature of mathematics that when two prime numbers are multiplied, it is very difficult to factor, that is to work out, the two original numbers. Mathematicians have been trying to find a way to do this quickly for hundreds of years and have failed so far. Since even computers take time to wade their way through all prime numbers to find the correct ones, it has been estimated that, if the number is big enough, the world could end before they succeed. A guess would have a better chance.
8:38:59 AM  permanent link Google It!
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