Prime Numbers

Prime numbers are numbers which can only be divided by themselves and by one. The first few prime numbers are: 2,3,5,7,11,13,17 and 19. They are sometimes called the building blocks of maths because all the other integers (whole numbers) can be made from the prime numbers.

In GCSE maths you learn how to break a number down into its prime factors, for example 60=2x2x3x5. This can then be used to find the highest common factor and the lowest common multiple of any two numbers.

Prime numbers have important applications in real life. The encryption used when you make a purchase using a credit or debit card uses the prime factors of very large numbers.

The Goldbach conjecture states that any even number greater than 2 can be written as the sum of two prime numbers, e.g. 4=2+2, 10=7+3 (or 5+5). It is called a conjecture because it has not been proved yet, although it has been shown to be true for every even number up to four billion billion! Only when it has been proved to be true for every case is it called a theorem.

One of the problems with prime numbers is that they do not follow any pattern. Sometimes they are close together and sometimes there are big gaps between them. A mathematician called Riemann studied the distribution of prime numbers and proposed what is now known as the Riemann hypothesis. This is one of the most famous unsolved problems in maths and there is a million dollar prize if you can be the first person to prove it.