Resources tagged with: Prime numbers
There are 47 NRICH Mathematical resources connected to Prime numbers, you may find related items under Properties of numbers.
Broad Topics > Properties of numbers > Prime numbers
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?
Statement Snap
You'll need to know your number properties to win a game of Statement Snap...
Sieve of Eratosthenes
Follow this recipe for sieving numbers and see what interesting patterns emerge.
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?
Factors and Multiples Game
A game in which players take it in turns to choose a number. Can you block your opponent?
Factors and Multiples Puzzle
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Stars
Can you work out what step size to take to ensure you visit all the dots on the circle?
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.
Two Primes Make One Square
Can you make square numbers by adding two prime numbers together?
Factor Lines
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
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.
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?
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.
Swimming Pool Tiles
This activity creates an opportunity to explore all kinds of number-related patterns.
Factors and Multiples Game for Two
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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?
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.
Coins
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
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.
Numbers as Shapes
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
An Introduction to Proof by Contradiction
An introduction to proof by contradiction, a powerful method of mathematical proof.
Different by One
Can you make lines of Cuisenaire rods that differ by 1?
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?
Public Key Cryptography
An introduction to coding and decoding messages and the maths behind how to secretly share information.
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?
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?
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?
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?
Tom's Number
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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!?
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?
Factoring a Million
In how many ways can the number 1 000 000 be expressed as the product of three positive integers?
Factoring Factorials
Find the highest power of 11 that will divide into 1000! exactly.
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.
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.
Thirty Six Exactly
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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?
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.
Some Cubes
The sum of the cubes of two numbers is 7163. What are these numbers?
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?
Prompt Cards
These two group activities use mathematical reasoning - one is numerical, one geometric.