mathcymru

What are prime numbers?

Prime numbers are usually thought of as numbers that into which no other number can be exactly divided. This is not 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.

2 is the only even prime number, all the rest are odd.
No prime number other than 5 can end in a 5.
After the single digit primes (2,3,5,7) all other prime numbers always end in either a 1, 3, 7 or 9.
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). However, nobody has ever proved or disproved this!

As you move 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 26972593-1, which has over 2 million digits! It was calculated in 1999 using computers and will probably be replaced when even more powerful computers take up the challenge of finding an ever increasing prime number!

Try some of these puzzles which involve prime numbers.
(Source: The Number Detective by John Millington, Tarquin Publications and Mathematical Snacks by John Millington, Tarquin Publications). More information can be found at www.tarquin-books.demon.co.uk

A Special Prime

What prime number is this?

It has two digits and when these digits are written the other way around, this number is also a prime.

If the two digits are added together then the sum is also a prime number.

It has 2 digits and when these are reversed the resulting number is also prime – from this statement 11, 13, 31, 17, 71. 37, 73, 79, 97 are all possibilities.

However, the sum of the digits is also a prime number – but as all of these numbers give an even number when the two digits are added together, the answer must be the number that gives the only even number prime (which is 2). Therefore the answer has to be 11!

What Prime?

What two-digit prime number is this?

There is a difference of 4 between the numbers of the two digits.

Subtracting 1 from this prime number will give a square number (a square number is the answer produced when any number is multiplied by itself).

There is a difference of 4 between the 2 digits of this prime number – 37, 59 and 73 are all possibilities.

Subtracting 1 from this number will give a square number – so 36, 58 and 72 are obtained and from this list 36 is the only square number (6x6). Therefore, the answer to ‘What Prime’ is 37.

Mystery Number

What four-digit number is this?

It is the perfect square of a prime number (a perfect square is the answer produced when a whole number is multiplied by itself).

It reads the same upside down!

The answer is 6889