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The version presented below is also known as the Gauss–Euler, Brent–Salamin (or Salamin–Brent) algorithm; [1] it was independently discovered in 1975 by Richard Brent and Eugene Salamin. It was used to compute the first 206,158,430,000 decimal digits of π on September 18 to 20, 1999, and the results were checked with Borwein's algorithm.
Later computers calculated pi to extraordinary numbers of digits (2.7 trillion as of August 2010), [4] and people began memorizing more and more of the output. The world record for the number of digits memorized has exploded since the mid-1990s, and it stood at 100,000 as of October 2006. [ 6 ]
Calculation made in Philadelphia, Pennsylvania, giving the value of pi to 154 digits, 152 of which were correct. First discovered by F. X. von Zach in a library in Oxford, England in the 1780s, and reported to Jean-Étienne Montucla, who published an account of it. [20] 152: 1722: Toshikiyo Kamata: 24 1722: Katahiro Takebe: 41 1739: Yoshisuke ...
For the first term in the Taylor series, all digits must be processed. In the last term of the Taylor series, however, there's only one digit remaining to be processed. In all of the intervening terms, the number of digits to be processed can be approximated by linear interpolation. Thus the total is given by:
The digits of pi extend into infinity, and pi is itself an irrational number, meaning it can’t be truly represented by an integer fraction (the one we often learn in school, 22/7, is not very ...
Haraguchi holds the current unofficial world record for reciting 10,000 digits of pi in 16 hours, starting at 9:00 a.m. (16:28 GMT) on October 3, 2006. He equaled his previous record of 83,500 digits by nightfall and then continued until stopping with digit number 100,000 at 1:28 a.m. on October 4, 2006.
Durant’s remarkable discovery, officially called M136279841, consists of an astounding 41,024,320 digits and marks the first prime breakthrough in almost six years.
It was used in the world record calculations of 2.7 trillion digits of π in December 2009, [3] 10 trillion digits in October 2011, [4] [5] 22.4 trillion digits in November 2016, [6] 31.4 trillion digits in September 2018–January 2019, [7] 50 trillion digits on January 29, 2020, [8] 62.8 trillion digits on August 14, 2021, [9] 100 trillion ...