There are **42** NRICH Mathematical resources connected to **Prime numbers**, you may find related items under Properties of Numbers.

A game in which players take it in turns to choose a number. Can you block your opponent?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Lyndon chose this as one of his favourite problems. It is accessible but needs some careful analysis of what is included and what is not. A systematic approach is really helpful.

Can you make square numbers by adding two prime numbers together?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5 What can you say about other solutions to this problem?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

This activity creates an opportunity to explore all kinds of number-related patterns.

Factors and Multiples game for an adult and child. How can you make sure you win this game?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

An introduction to proof by contradiction, a powerful method of mathematical proof.

Can you make lines of Cuisenaire rods that differ by 1?

When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?

An introduction to the ideas of public key cryptography using small numbers to explain the process. In practice the numbers used are too large to factorise in a reasonable time.

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

Find the highest power of 11 that will divide into 1000! exactly.

All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either. . . .

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

The sum of the cubes of two numbers is 7163. What are these numbers?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

These two group activities use mathematical reasoning - one is numerical, one geometric.