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
I think the thing I love most about this is that is, like so much involving prime numbers and factorization, an extremely powerful brand of catnip for amateur crank mathematicians such as myself. You can _kind of see_ the patterns there! There are the barest hints of a _lot_ of subtle structure. The secret must be within our grasp!
I mean, does this not look _just like_ the 3x+1 problem, turned on its head? Almost? Maybe?
And yet.... and yet....
@gemelen I quote from that movie all the time. "As soon as you discard scientific rigour, you're no longer a mathematician. You're a numerologist."
mhoye
gemelen