for anyone who enjoyed this, i will recommend Carl D. Offner's paper--Computing the Digits in π. In the nature of Readup honesty, i will admit that i haven't finished reading it but i recommend it anyways, at least the first section titled "Why do we care?"

i will offer a computer engineering addition to this article which is a quote by Baily referenced in ditto paper:

"In recent years, the computation of the expansion of π has assumed the role as a standard test of computer integrity. If even one error occurs in the computation, then the result will almost certainly be completely in error after an initial correct section. On the other hand, if the result of the computation of π to even 100,000 decimal places is correct, then the computer has performed billions of operations without error. For this reason, programs that compute the decimal expansion of π are frequently used by both manufacturers and purchasers of new computer equipment to certify system reliability."