Episode three of Another Five Numbers, the BBC radio series presented by Simon Singh.

Think of a number. Any number. Chances are you haven't plumped for 2 to the power of 13,466,917 -1. To get this, you would need to keep multiplying 2 by itself 13,466,917 times, and then subtract 1 from the result. When written down it's 4,053,900 digits long and fills 2 telephone directories. So, as you can imagine, it's not the kind of number you're likely to stumble over often. Unless you're Bill Gates checking your bank statement at the end of the month.