In math you often don't need super precise bounds. I think it just happens that 70m works. If you try harder you can probably find something more accurate. IMO even a bound like 100m is good because it's a finite number.
It _could_ be that some super-expensive calculation is required for each candidate bound, and Zhang guessed 70000000 as a starting point and did the calculation for that number, which succeeded, but he didn't bother repeating it for any smaller numbers because it would cost him too much. But if that was the case, that would be interesting in itself.