Hitting a prime in 2.43 dice rolls (on average)
Probability
2023-01-25 v4 Number Theory
Other Statistics
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.
Keywords
Cite
@article{arxiv.2209.07698,
title = {Hitting a prime in 2.43 dice rolls (on average)},
author = {Noga Alon and Yaakov Malinovsky},
journal= {arXiv preprint arXiv:2209.07698},
year = {2023}
}