Can $\pi$ generate itself? A Monte Carlo analysis of 314 trillion digits

Abstract

At the end of 2025, a record computation of $\pi$ reached 314 trillion decimal digits, providing the largest numerical dataset ever generated for this constant. We exploit this unprecedented dataset to investigate whether the digits of $\pi$ themselves can serve as a source of pseudorandom numbers for estimating $\pi$ through the simplest Monte Carlo method. Our results go beyond the normality hypothesis by providing empirical evidence of a high degree of statistical randomness in the available digits, although not of digit independence, which cannot hold for a deterministic sequence. By optimizing the mapping of the digit sequence into Monte Carlo samples, we obtain the highest precision allowed by the dataset. As predicted, the method successfully reproduces the first sequence of decimal digits, demonstrating that the largest available dataset of $\pi$ digits can be used to recover $ \pi \approx 3.141593 $ through Monte Carlo simulation.