If I did the arithmetic correctly if one uses the 71 km/MPs number agreed upon, one can work out that the universe at 13.7 billion light years is expanding away from us so fast that any EM emissions emitted at that distance would be red shifted to DC from our viewpoint.

It just so happens that the age of the universe is agreed to be 13.7 billion years. Is this an interesting coincidence or is it that these numbers are derived from one another in some non-obvious way. (According to the material I read, the two numbers seemed to be derived independently.)

If this is correct, Wouldn't all the high frequency light emitted from a sphere just shy of 13.7 B light years from us be red shifted to something like the Cosmic Background radiation?