Worth pointing out that busy beavers have the potential to be alot more than just 'interesting'. If you knew what the busy beaver numbers were for a given numbe

Worth pointing out that busy beavers have the potential to be alot more than just 'interesting'. If you knew what the busy beaver numbers were for a given number of states, it could be used to solve various unsolved mathematical problems. For example, Goldbach's conjecture states that every integer greater than 2 is the sum of 2 primes. So far it has been resistant to being proved. But if you could convert it to a computer program with say, 500 states, and you knew the busy beaver number for 500, you could check it by running the program that number of cycles. If you did and the program didn't halt, then it would NEVER halt, and Goldbach's conjecture would be proven true. Of course, BB(500) would certainly be an unfathomably huge number, so there would be practical problems running a computer program that number of cycles. But if you had sufficient computing power, knowing the busy beaver numbers would be an amazing mathematical tool.