I discovered only recently about Google’s challenge to find the first ten-digit prime number in the consecutive digits of e. For fun, I solved the challenge (and the follow-up challenge), but the interesting part is a cool algorithm that I came across to compute the digits of e, one by one.
The algorithm lets you compute the digits sequentially without any pre-commitment to the total number of digits you’ll eventually take. The technique behind the algorithm can be used to compute other things, and so it’s worth a look.
If you’re interested, please take a look at my HuSi diary entry on the subject, Google challenge task and computing the digits of e, where I explain the method in detail. I’ll also refer you to Jeremy Gibbons’s paper An Unbounded Spigot Algorithm for the Digits of Pi, which is the inspiration for the method.