Modeling the Biases in Last Digit Distributions of Consecutive Primes

  • Daniel LichtblauEmail author
Conference paper
Part of the Fields Institute Communications book series (FIC, volume 82)


Recent work by Lemke Oliver and Soundararajan, as well as earlier results by Ko, have brought to light an unexpected asymmetry in the distribution of last digits of consecutive primes. For example, in the first 108 pairs of consecutive primes, around 4.6 million end with {1,1} respectively, whereas more than 7.4 million end with {1,3}. This disparity is not explained by the fact that opportunities for the next prime come sooner for n+2 than for n+1. This leaves open the question: what accounts for this sizable bias? We provide justification based on a mix of elementary theory and computation. The model we develop moreover accurately predicts crossovers in relative frequencies of certain pairs-of-pairs.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Wolfram ResearchChampaignUSA

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