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 used in the world record calculations of 2.7 trillion digits of π in December 2009, and 5 trillion digits of π in August 2010.

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 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