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Then why did we need to put in so much effort to get to the 100 billionth or so? When all we could ever need are 40, maybe 50 if you want?
It is not about actual use when they calculate pi to tthese numbers.
It is about finding out if pi is actually irrational or is it recurring on some level.ie: does it start repeating at some point.
nope, just for testing computers. We know pi is transcendental. Which implies it is irrational. This has been mathematically proven.
We don't need to check. We know that it does not repeat.
There’s facts about pi we don’t know, though. We have not proved whether or not pi contains every finite sequence of digits. A breakthrough about this will probably have little to do with brute force computing billions of digits of pi, but maybe there can be a clue there. As far as I know we basically just calculate a bunch of pi to flex. It’s the mathematical equivalent of walking around shirtless to show off your abs.
Nope. Alexander Yee literally just wrote the program for shits and giggles. (Even the mathematical routines aren't generally useful).
Pi can be proven to be irrational with a pen and paper.
For the sheer unadulterated thrill of calculating pi.
In addition to what @Pons_Aelius replied, it is also used as a benchmark/flex for computers, as to who can build a beefy enough machine or good enough card to calculate more digits of pi.
Nobody optimises their computer build by targeting pi computation. LAPACK benchmarks are far more useful, because linear algebra is actually extensively use; nobody calculates transcendental constants beyond IEE754 precision.
Additionally that's not how hardware is designed.
Why do most records exist?