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Date: 7/9/2005

How can we generate a prime number?

Prime numbers have intrigued mathematicians for centuries. It is an important sub-branch of mathematics called "number theory". Despite the efforts of the best mathematical minds over the centuries, there is no general "formula" for generating prime numbers. There are some approximations, and there are theorems predicting the number of prime numbers less than a particular upper bound. As of 2003 the largest known prime number is:

The 39th Mersenne prime

m39 = 213,466,917-1

is the largest known prime number (as of the time of this writing, May 23, 2003). In the decimal system it requires 4,053,946 digits to be written fully. Most of this page is taken up by those digits. You can appreciate the size of this number, and perhaps have a psychedelic experience, by scrolling this page across your screen. If you find that the last digit is even then this file was accidentally truncated in the process of downloading it! You can find it written out on the web site: By the way Mersenne primes are prime numbers of the form: Mp = (2^n) - 1. This formula generates prime numbers but also misses some. To investigate prime numbers further, you can start with the sites: There are many interesting relations involving prime numbers which have been examined by computer and are apparently true, but for which no mathematical proof is known. These are known as "conjectures". What is so interesting about primes is that they do not involve complicated numbers -- just the "counting numbers" 1, 2, 3, ... yet they hold many mysteries.

Vince Calder

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