Hitting a prime in 2.43 dice rolls (on average)

2022/09/16 by Alon, Noga, Malinovsky, Yaakov
#11A41 #60G40 #90C39 #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #Other Statistics (stat.OT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2209.07698

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. This is a solution to a puzzle suggested by DasGupta (2017) 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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