The quest to find the longest-running simple computer program has identified a new champion. It’s physically impossible to write out the numbers involved using standard mathematical notation. Introduction Imagine that someone gives you a list of five numbers: 1, 6, 21, 107 and — wait for it — 47,176,870. Can you guess what comes next? If you’re stumped, you’re not alone. These are the first five busy beaver numbers. They form a sequence that’s intimately tied to one of the most notoriously diffi...