Hitting a Prime in 2.43 Dice Rolls (On Average)

Noga Alon, Yaakov Malinovsky*

*Corresponding author for this work

Research output: Contribution to journalComment/debate

1 Scopus citations

Abstract

What is the number of rolls of fair six-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 (Formula presented.). This is a solution to a puzzle suggested by DasGupta in the Bulletin of the Institute of Mathematical Statistics, 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.

Original languageEnglish
Pages (from-to)301-303
Number of pages3
JournalAmerican Statistician
Volume77
Issue number3
DOIs
StatePublished - 2023

Funding

FundersFunder number
National Science FoundationDMS-2154082
Bloom's Syndrome Foundation2018267, 2020063

    Keywords

    • Dynamic-programming
    • Prime number theorem
    • Stopping time

    Fingerprint

    Dive into the research topics of 'Hitting a Prime in 2.43 Dice Rolls (On Average)'. Together they form a unique fingerprint.

    Cite this