Chudnovsky algorithm

The Chudnovsky algorithm is a fast method for calculating the digits of π. It was used by the Chudnovsky brothers to calculate more than one billion digits. It was the algorithm used in world record calculations of 2.7 trillion and 5 trillion digits of π in December 2009 and August 2010 respectively.

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

$\frac{1}{\pi} = 12 \sum^\infty_{k=0} \frac{(-1)^k (6k)! (13591409 + 545140134k)}{(3k)!(k!)^3 640320^{3k + 3/2}}.\!$

This identity is very similar to some of Ramanujan's formulae involving π.

See also

• Numerical approximations of π

References

• Chudnovsky, David V.; Chudnovsky, Gregory V. (1989), "The Computation of Classical Constants", Proceedings of the National Academy of Sciences of the United States of America 86 (21): 8178–8182, doi:10.1073/pnas.86.21.8178, ISSN 0027-8424, JSTOR 34831, PMC 298242, PMID 16594075, http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=298242 .