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I was reading about how people calculate millions, billions, and even trillions of digits of constants like $\pi$. All of these calculations use some implementation of a multiple precision arithmetic library such as GMP (GNU Multiple Precision). I was wondering if there were any other applications of these multiple precision arithmetic libraries involving calculations on numbers with greater than a million or so digits.

I know, especially in cryptography, that calculations with a few hundred to a few thousand digits are used, but I was wondering about computations with more digits then this?

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I was just "browsing the internet" reading articles including this one here, http://plouffe.fr/simon/articles/1409.0091v1.pdf, as well as https://www.numberworld.org, and some this page here: https://www.craig-wood.com/nick/articles/pi-chudnovsky/.

The BBP formula can calculate the nth digit of pi in linear time. However, it can not be used to calculate the first n digits.

Brandon Feder
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  • If you told us what you were reading, you would more likely get a useful response. The digits of $\pi$ (in base $16$ at least) can be calculated independently: see https://en.wikipedia.org/wiki/Bailey-Borwein-Plouffe_formula. – Rob Arthan Oct 16 '21 at 21:15
  • I updated my post about what I was reading. – Brandon Feder Oct 17 '21 at 20:02

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