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Prime Numbers

Prime numbers, have exactly two factors. They are beautiful things; rare and incredibly unpredictable numbers, the only real thing we can see with any degree of pattern is diagonal lines in the Ulam spiral (to read more about this fascinating subject please go here, http://www.numberspiral.com/). Prime numbers are the building blocks of Mathematics, like anything you need to have some base as a starting point and in maths, primes are that. You can create any integer, any integer at all with only prime numbers. The fact alone that it is the building blocks of a subject that I love so much makes it interesting to me.

The most common method of finding 'new' prime numbers is via a method coined by Marin Mersenne (thus my name), there appears to be a reasonably high amount of prime numbers that can be found with 2^n-1. 3, 7, 31, 127 are the first four mersenne primes; there's a large jump up to the next one, 8191. In fact there is only 47 mersenne primes that have ever been found, which is staggeringly low, or so it appears. The method of finding primes in this way is the only real way to randomly stumble across a prime, and thus why it is still used, despite its small return rate. 9 of the top 10 largest prime numbers are mersenne primes, which shows how hard it is to actually discover one of the damn things!

The current largest prime is 2^{43,112,609} − 1, and to put that into context it has: 12,978,189 digits, to write the number out with 75 digits per line and 50 lines per page you would need 3461 pages... That is a mammoth of a number. They're cool but what's the point? I hear you ask. Well, they are incredibly important in computer security; if you times two prime numbers together you get a number with only 4 factors, itself, 1 and two primes. This means it's very hard to break down and thus secure. These numbers are so important, and well interesting that there is a large amount of money dedicated to them. The first prime found with over 10,000,000 was awarded $100,000! The first person to find a prime with over 100,000,000 digits will receive a prize of $150,000. That's erious money. Want to join in but aren't a God of maths? GIMPS is amn online project dedicated to finding programs, it's a small program that runs in the background while you mind your own business and it hunts for mersenne prime numbers. Want to get involved? Go here; http://www.mersenne.org/.
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