# Prime Numbers

The first twelve prime numbers
are –

2, 3, 5,
7, 11, 13,
17, 19, 23,
29, 31, 37

A number is called prime if its only factors are one and itself.

Many numbers can be made by multiplying smaller numbers together. For example –

3 × 7 = 21

– 3 and 7 are called factors of 21. But some numbers cannot be made in this
way and these are called prime numbers. For example, 23 is a prime number because
it cannot be made by multiplying together smaller numbers. Numbers like 21 which
are not prime are sometimes called composite numbers.

All prime numbers, apart from 2, are odd numbers.

The Mersenne primes are a special type of prime number. The first five are –

3, 7, 31, 127, 8191

– and they can be expressed as a power of two minus one –

2^{2} - 1 = 3

2^{3} - 1 = 7

2^{5} - 1 = 31

2^{7} - 1 = 127

2^{13} - 1 = 8,191

...

For a mathematician, the
equivalent of breaking the 100 metres world record is to find the highest known
prime number. Every year or so, someone discovers a higher one and it gets reported
in the newspapers. These record-breaking numbers are always Mersenne primes.
At the time of writing the highest known prime is
2^{13,466,917}- 1. To write it out you would use 4,053,946 digits and probably get through
quite a few pencils. The record was broken in November 2001 by Michael Cameron
using Prime 95 software by George Woltman.

Whenever someone discovers
a new Mersenne prime they also automatically discover a new perfect
number. (2^{13,466,917}- 1) × 2^{13,466,916}
is the world's largest known perfect number at the time of writing.

It has been proved that the number of primes is limitless and so records for the highest known prime can go on being broken for ever.

Here is Chris Caldwell's page about the largest known primes.

Based on the book *Numbers: Facts, Figures & Fiction*.