Chudnovsky's Algorithm

The Chudnovsky algorithm is one of the fastest known methods for calculating to millions or even trillions of digits. Developed by brothers David and Gregory Chudnovsky in 1988, it is based on a rapidly converging infinite series derived from Ramanujan-type formulas and complex analysis.

This algorithm has powered many of the world record computations of π, including modern distributed computations that have calculated over 100 trillion digits.

The formula

The Chudnovsky algorithm expresses 1/pi as a summation:

This is a hypergeometric series, and it converges extremely quickly. Each term in the series adds around 14 digits of precision to π.

Each term in the summation includes:

• Factorials , and
• A linear term