Chudnovsky algorithm

The Chudnovsky algorithm is a fast method for calculating the digits of π. It was published by the Chudnovsky brothers in 1988, and was used in the world record calculations of 2.7 trillion digits of π in December 2009, 10 trillion digits in October 2011,, 22.4 trillion digits of π in November 2016, and 31.4 trillion digits in September 2018–January 2019. The Chudnovsky algorithm is a fast method for calculating the digits of π. It was published by the Chudnovsky brothers in 1988, and was used in the world record calculations of 2.7 trillion digits of π in December 2009, 10 trillion digits in October 2011,, 22.4 trillion digits of π in November 2016, and 31.4 trillion digits in September 2018–January 2019. The algorithm is based on the negated Heegner number d = − 163 {displaystyle d=-163} , the j-function j ( 1 + − 163 2 ) = − 640320 3 {displaystyle scriptstyle jleft({frac {1+{sqrt {-163}}}{2}} ight)=-640320^{3}} , and on the following rapidly convergent generalized hypergeometric series: A detailed proof of this formula can be found here: