Hint
The cube root of the given number is a good starting point.
Answer
71, 73, 79.
Reasoning
The cube root of 409,457 is around 74.
The closest consecutive prime numbers to 74 are: 61, 67, 71, 73, 79, 83, 89, 97.
Using a calculator, it is quickly seen that the answer can only be found using 71, 73 and 79.
?
Puzzle 2
The BrainBashers football world tour is well underway and Alex is planning the journey to each country.
Unfortunately, the BrainBashers atlas software is playing up again and has worked out the mileage incorrectly, as shown below.
China 3,500
Finland 6,000
Chile 3,700
Jamaica 3,800
Wales 6,000
According to the software, how many miles is it to Germany?