# Chudnovsky algorithm

The Chudnovsky algorithm is a fast method for calculating the digits of π. It was published by the Chudnovsky brothers in 1989,[1] and was used in the world record calculations of 2.7 trillion digits of π in December 2009,[2] 5 trillion digits of π in August 2010,[3] and 10 trillion digits of π in October 2011.[4][5]

The algorithm is based on the following rapidly convergent generalized hypergeometric series:[2]

$\frac{1}{\pi} = 12 \sum^\infty_{k=0} \frac{(-1)^k (6k)! (163\cdot 3344418k + 13591409)}{(3k)!(k!)^3 640320^{3k + 3/2}}.\!$

Note that,

$e^{\pi \sqrt{163}} \approx 640320^3+743.99999999999925\dots$

This identity is similar to some of Ramanujan's formulas involving π,[2] and is an example of a Ramanujan–Sato series.