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    Hitting a prime in 2.43 dice rolls (on average)

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    2209.07698.pdf (139.7Kb)
    Links to Files
    https://arxiv.org/abs/2209.07698
    Permanent Link
    https://doi.org/10.48550/arXiv.2209.07698
    http://hdl.handle.net/11603/26187
    Collections
    • UMBC Faculty Collection
    • UMBC Mathematics and Statistics Department
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    Author/Creator
    Alon, Noga
    Malinovsky, Yaakov
    Author/Creator ORCID
    https://orcid.org/0000-0003-2888-674X
    Date
    2022-09-16
    Type of Work
    5 pages
    Text
    journal articles
    preprints
    Rights
    This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
    Abstract
    What is the number of rolls of fair 6-sided dice until the first time the total sum of all rolls is a prime? We compute the expectation and the variance of this random variable up to an additive error of less than 10−4 , showing that the expectation is 2.4284.. and the variance is 6.2427... This is a solution of a puzzle suggested a few years ago by DasGupta in the Bulletin of the IMS, where the published solution is incomplete. The proof is simple, combining a basic dynamic programming algorithm with a quick Matlab computation and basic facts about the distribution of primes.


    Albin O. Kuhn Library & Gallery
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    www.umbc.edu/scholarworks

    Contact information:
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    Phone: 410-455-3021


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    Albin O. Kuhn Library & Gallery
    University of Maryland, Baltimore County
    1000 Hilltop Circle
    Baltimore, MD 21250
    www.umbc.edu/scholarworks

    Contact information:
    Email: scholarworks-group@umbc.edu
    Phone: 410-455-3021


    If you wish to submit a copyright complaint or withdrawal request, please email mdsoar-help@umd.edu.