The Quest to Find the Longest-Running Simple Computer Program

The Busy Beaver Challenge, a notoriously difficult question in theoretical computer science, is now producing answers so large they're impossible to write out using standard mathematical notation. 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? These are the first five busy beaver numbers. They form a sequence that's intimately tied to one of the most notoriously difficult questions in theoretical computer science. Determining the values of busy beaver numbers is a daunting challenge that has attracted a cult following among both professional and amateur mathematicians for over 60 years. Researchers identified the first four busy beaver numbers in the 1960s and 1970s.