π能生成自身？对314万亿位数字的蒙特卡洛分析
Can $π$ generate itself? A Monte Carlo analysis of 314 trillion digits
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中文总结 AI 辅助
研究利用314万亿位π数字数据集，探究其能否作为伪随机数源，经优化映射后通过蒙特卡洛方法成功以最高精度恢复π≈3.141593，证实π数字具高度统计随机性
中文摘要 AI 辅助
2025年末，一项创纪录的π计算达到了314万亿位十进制数字，为这个常数提供了有史以来最大的数值数据集。我们利用这一前所未有的数据集，探究π的数字本身是否可作为伪随机数源，通过最简单的蒙特卡洛方法估计π。我们的结果超越了正态性假设，为现有数字的高度统计随机性提供了经验证据，尽管不存在数字独立性（确定性序列不可能具备该属性）。通过优化数字序列到蒙特卡洛样本的映射，我们获得了该数据集允许的最高精度。正如预测的那样，该方法成功复现了首段十进制数字序列，证明最大可用的π数字数据集可通过蒙特卡洛模拟用于恢复π≈3.141593。
英文摘要
At the end of 2025, a record computation of $π$ 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 $π$ themselves can serve as a source of pseudorandom numbers for estimating $π$ 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 $π$ digits can be used to recover $ π\approx 3.141593 $ through Monte Carlo simulation.
