What is a prime number?

Take 12 building blocks and try to arrange them in a rectangle. You can make 1 row of 12, 2 rows of 6 or 3 rows of 4. Lots of options. Now try 7 blocks. The only rectangle is 1 row of 7. Numbers like 7, which can only make a single line, are prime.

In maths language, a prime has exactly two factors: 1 and the number itself. A whole number bigger than 1 that is not prime, like 12, is called composite.

Two numbers cause arguments:

• 1 is not prime. It has only one factor, so it doesn't meet the rule.
• 2 is prime, and it is the only even prime. Every other even number divides by 2.

The primes up to 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47. That is 15 of them.

To test whether a number is prime, try dividing it by the primes 2, 3, 5, 7… in turn. You can stop once the prime you are trying, multiplied by itself, is bigger than your number. For 91: 2 no, 3 no, 5 no, 7 yes (7 × 13). So 91 is not prime, although it looks like one.

Primes are the building blocks of all whole numbers. Every composite number can be split into primes multiplied together, in only one way (apart from order). For 84: 84 = 2 × 42 = 2 × 2 × 21 = 2 × 2 × 3 × 7. A factor tree is a neat way to draw this.

Over 2,000 years ago, the Greek mathematician Euclid proved that the primes never run out. There is no biggest prime.