Prime 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?

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

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

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

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

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?

How many of the numbers 1 to 20 are not the sum of two primes?

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.

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