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There are **47** NRICH Mathematical resources connected to **Prime numbers**, you may find related items under Properties of numbers.

Game
Primary curriculum
Secondary curriculum
### Dicey Array

Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Statement Snap

You'll need to know your number properties to win a game of Statement Snap...

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sieve of Eratosthenes

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Much Can We Spend?

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Age 11 to 14

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Factors and Multiples Game

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

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Factors and Multiples Puzzle

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Stars

Can you work out what step size to take to ensure you visit all the dots on the circle?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fac-finding

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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two Primes Make One Square

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Factor Lines

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

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### One to Eight

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Why 24?

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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Em'power'ed

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?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Round and Round the Circle

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Swimming Pool Tiles

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

Age 7 to 11

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Factors and Multiples Game for Two

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

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Prime Sequences

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Flow Chart

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Coins

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### There's Always One Isn't There

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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Numbers as Shapes

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

Age 5 to 7

Challenge Level

Article
Primary curriculum
Secondary curriculum
### An Introduction to Proof by Contradiction

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

Age 14 to 18

Problem
Primary curriculum
Secondary curriculum
### Different by One

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Can it Be?

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

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Public Key Cryptography

An introduction to coding and decoding messages and the maths behind how to secretly share information.

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### A Conversation Piece

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Just Repeat

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Code Breaker

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Penta Primes

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tom's Number

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Powerful Factorial

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!?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Great Granddad

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Factoring a Million

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Factoring Factorials

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Strange Numbers

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 its first or its last digit. Find all strange numbers.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Never Prime

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Thirty Six Exactly

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Gaxinta

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Biggy

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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Some Cubes

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's Left?

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Prompt Cards

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

Age 7 to 11

Challenge Level