This is true but somewhat misleading. The nth busy beaver numbers are known for n <= 4. It's within the bounds of possibility that we will some day learn the nt

This is true but somewhat misleading. The nth busy beaver numbers are known for n <= 4. It's within the bounds of possibility that we will some day learn the nth busy beaver numbers for n <= 10. (What we can say is that the parent's loop will never terminate for any known definition of "ever" that pertains to the physical universe.)