Resources tagged with: Prime numbers

Filter by: Content type:
Age range:
Challenge level:

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

Broad Topics > Properties of Numbers > Prime numbers

Various Venns

Age 7 to 11 Challenge Level:

Use the interactivities to complete these Venn diagrams.

Factors and Multiples Game

Age 7 to 16 Challenge Level:

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

Factors and Multiples Puzzle

Age 11 to 14 Challenge Level:

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

Stars

Age 11 to 14 Challenge Level:

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?

Fac-finding

Age 14 to 16 Challenge Level:

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.

Two Primes Make One Square

Age 7 to 11 Challenge Level:

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

Factor Lines

Age 7 to 14 Challenge Level:

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

One to Eight

Age 11 to 14 Challenge Level:

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.

Why 24?

Age 14 to 16 Challenge Level:

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.

Em'power'ed

Age 16 to 18 Challenge Level:

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?

Round and Round the Circle

Age 7 to 11 Challenge Level:

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.

Swimming Pool Tiles

Age 7 to 11 Challenge Level:

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

Factors and Multiples Game for Two

Age 7 to 14 Challenge Level:

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

Sieve of Eratosthenes

Age 11 to 14 Challenge Level:

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

Prime Counter

Age 16 to 18 Challenge Level:

A short challenge concerning prime numbers.

Prime Sequences

Age 16 to 18 Challenge Level:

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

Flow Chart

Age 11 to 14 Challenge Level:

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

Coins

Age 11 to 14 Challenge Level:

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

Rarity

Age 16 to 18 Challenge Level:

Show that it is rare for a ratio of ratios to be rational.

There's Always One Isn't There

Age 14 to 16 Challenge Level:

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.

Numbers as Shapes

Age 5 to 7 Challenge Level:

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

An Introduction to Proof by Contradiction

Age 14 to 18

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

Different by One

Age 14 to 16 Challenge Level:

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

Can it Be?

Age 16 to 18 Challenge Level:

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

Public Key Cryptography

Age 16 to 18

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.

Factorial Fun

Age 16 to 18 Challenge Level:

How many divisors does factorial n (n!) have?

A Conversation Piece

Age 7 to 11 Challenge Level:

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?

Just Repeat

Age 11 to 14 Challenge Level:

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?

Code Breaker

Age 7 to 11 Challenge Level:

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?

Penta Primes

Age 7 to 11 Challenge Level:

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

Tom's Number

Age 7 to 11 Challenge Level:

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

Powerful Factorial

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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?

Factoring a Million

Age 14 to 16 Challenge Level:

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

Factoring Factorials

Age 11 to 14 Challenge Level:

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

Strange Numbers

Age 11 to 14 Challenge Level:

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. . . .

Thirty Six Exactly

Age 11 to 14 Challenge Level:

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

Gaxinta

Age 11 to 14 Challenge Level:

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?

A Biggy

Age 14 to 16 Challenge Level:

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.

Some Cubes

Age 16 to 18 Challenge Level:

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

What's Left?

Age 5 to 7 Challenge Level:

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

Prompt Cards

Age 7 to 11 Challenge Level:

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