Brain Teasers and Puzzles

A box for your workings out:

Hint: The cube root of the given number is a good starting point.

Answer: 71, 73, 79.

The cube root of 409,457 is around 74.

The closest prime numbers to 74 are 61, 67, 71, 73, 79, 83, 89, 97.

It is quickly seen that the answer can only be found using 71, 73 and 79.