The Surprising Accuracy of Benford’s Law in Mathematics

@article{Cai2020TheSA,
  title={The Surprising Accuracy of Benford’s Law in Mathematics},
  author={Zhaodong Cai and Matthew Faust and A. J. Hildebrand and Junxian Li and Yali Zhang},
  journal={The American Mathematical Monthly},
  year={2020},
  volume={127},
  pages={217 - 237}
}
Abstract Benford’s law is an empirical “law” governing the frequency of leading digits in numerical data sets. Surprisingly, for mathematical sequences the predictions derived from it can be uncannily accurate. For example, among the first billion powers of 2, exactly 301029995 begin with digit 1, while the Benford prediction for this count is . Similar “perfect hits” can be observed in other instances, such as the digit 1 and 2 counts for the first billion powers of 3. We prove results that… 

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