Hitting a Prime in 2.43 Dice Rolls (On Average)

Noga Alon; Yaakov Malinovsky

doi:10.1080/00031305.2023.2179664

Hitting a Prime in 2.43 Dice Rolls (On Average)

Noga Alon, Yaakov Malinovsky

Mathematics

Research output: Contribution to journal › Comment/debate › peer-review

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 language	English (US)
Pages (from-to)	301-303
Number of pages	3
Journal	American Statistician
Volume	77
Issue number	3
DOIs	https://doi.org/10.1080/00031305.2023.2179664
State	Published - 2023

All Science Journal Classification (ASJC) codes

Statistics and Probability
Mathematics(all)
Statistics, Probability and Uncertainty

Keywords

Dynamic-programming
Prime number theorem
Stopping time

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10.1080/00031305.2023.2179664

Cite this

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title = "Hitting a Prime in 2.43 Dice Rolls (On Average)",

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.",

keywords = "Dynamic-programming, Prime number theorem, Stopping time",

author = "Noga Alon and Yaakov Malinovsky",

note = "Funding Information: Research of Noga Alon is supported in part by NSF grant DMS-2154082 and by BSF grant 2018267. Research of Yaakov Malinovsky is supported in part by BSF grant 2020063. We wish to thank the Editor, the Associate Editor and the two referees for helpful comments and suggestions. Publisher Copyright: {\textcopyright} 2023 American Statistical Association.",

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TY - JOUR

T1 - Hitting a Prime in 2.43 Dice Rolls (On Average)

AU - Alon, Noga

AU - Malinovsky, Yaakov

N1 - Funding Information: Research of Noga Alon is supported in part by NSF grant DMS-2154082 and by BSF grant 2018267. Research of Yaakov Malinovsky is supported in part by BSF grant 2020063. We wish to thank the Editor, the Associate Editor and the two referees for helpful comments and suggestions. Publisher Copyright: © 2023 American Statistical Association.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Dynamic-programming

KW - Prime number theorem

KW - Stopping time

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DO - 10.1080/00031305.2023.2179664

M3 - Comment/debate

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VL - 77

SP - 301

EP - 303

JO - American Statistician

JF - American Statistician

IS - 3

ER -

Hitting a Prime in 2.43 Dice Rolls (On Average)

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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