Cryptography is fun in and of itself. However, there are powerful theoretical issues at play throughout – as evidenced by the ever-increasing number of publications in this area.

With this in mind, we pick two of the many theoretical questions to address. Certainly we can only touch on basic questions, but the reader will be gratified to see how much variety there is even in this!

• How do we find all these big primes, anyway?

• How can we be sure it's not so easy to break the codes – such as by factoring big numbers?