I think an algorithmic breakthrough, at least complete resdesign will be required once you pass a certain limit - specifically when the size of the number 2^n and intermediate calculation > available memory say a 1,000 Gb (= ram plus swap).

When will we reach it? Will we factor, sieve and prp faster than Moore's law? If not we will hit a limit.

2^18T is truly large number., something 3,000,000 bigger than where we are now. A new algorithm will be required unless we are here a long time.

Dave/louie/mathguy/someone else - what n will the new client be able to calculate up to?