I love Numberphile, and I love this kind of Numberphile specifically: here, starting from small numbers using ideas and operations that are extremely easy to understand and (at some scale) iterate by hand, is a wild unsolved problem absolutely beyond the reach of our current mathematical or computational capacities:

https://m.youtube.com/watch?v=OtYKDzXwDEE&pp=ugUEEgJlbg%3D%3D