There are techniques which allow you to, for instance, calculate the 'n'th digit of Pi in base 10 (or binary, or hex, etc.) These are generally more computation

There are techniques which allow you to, for instance, calculate the 'n'th digit of Pi in base 10 (or binary, or hex, etc.) These are generally more computationally/memory expensive than the techniques used to calculate as many digits of Pi as possible. So, you run your big calculation to get all XXX trillion digits on one machine, and run a completely different calculation to check, say, 1000 of those digits. If all match it's a pretty convincing argument that the calculation is correct.