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

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 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
General Mathematics
Statistics, Probability and Uncertainty

Keywords

Dynamic-programming
Prime number theorem
Stopping time

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10.1080/00031305.2023.2179664

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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.",

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AU - Malinovsky, Yaakov

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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.

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KW - Prime number theorem

KW - Stopping time

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Hitting a Prime in 2.43 Dice Rolls (On Average)

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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