These are the first five busy beaver numbers. 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. Busy beaver hunters have now discovered that this stupefyingly big number must be even bigger. Turing proved this seminal result by inventing a formal mathematical model of computation in which programs are represented by hypothetical devices now called Turing machines.