What is the first prime number greater than 3?

Square it and subtract 1. What do you get?

What is the next prime number?

Square it and subract 1. What is your answer this time? Do the same for the next prime number and note down the result. Look at the three numbers you have ended up with.

What do you notice about these numbers? Have you any ideas why this is? Email any suggestions you have, even if you can't explain them fully. Many thanks to John Harrison for suggesting this problem.