.... But why that big, why does we know that the solution will be that number or smaller?

Is it a guess from Grahams part or is there a reasoning to go that far? I never seen that explained. Only that G1 is 3 4*arrow 3 and that is the number of arrows between the 3's in G2 and so forth until G64 why not just stop at G1 or why not continue to G1.000.000?