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The largest prime number

Sunday, October 08, 2006

Prime numbers are usually thought of as numbers that no other number can be exactly divided into. This isn’t quite true as prime numbers always have 2 factors, the number 1 and itself (a factor is a number that can be exactly divided into another number). Because of this rule, the number 1 is not a prime number as it has only one factor (i.e. 1).

The first ten prime numbers are:

2 3 5 7 11 13 17 19 23 29

Prime numbers have fascinated mathematicians for centuries and they also have some unique properties.
1. 2 is the only even prime number (all the rest are odd).
2. No prime number other than 5 can end in a 5
3. After the single digit primes (2,3,5,7) all other prime numbers always end in either a 1, 3, 7 or 9.
4. If a prime number (other than 2 or 3) is increased or decreased by 1, one of these resulting numbers is always divisible by 6. (e.g. 19-1=18, 59+1=60 etc)

It is also believed that every even number except for 2 can be made by adding two prime numbers together e.g. 6=3+3, 8=5+3, 28=13+15, 64=61+3 etc).

As you go into bigger and bigger numbers….1000, 2000, 3000…..the number of prime numbers in each thousand gets smaller and smaller.

But what is the largest prime number so far discovered? The answer is 44th known Mersenne prime, (2^32,582,657)− 1 (Two to the power of thirty two million five hundred and eighty two thousand, six hundred and fifty seven, minus one), which has over 9 million digits! It was calculated in 2004 using computers and will probably be replaced as even more powerful computers take up the challenge of finding an even bigger prime number!

Farther reading: Wikipedia


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