Hitting a prime by rolling a die with infinitely many faces
Number Theory
2023-06-27 v1 Probability
Abstract
Alon and Malinovsky recently proved that it takes on average rolls of fair six-sided dice until the first time the total sum of all rolls arrives at a prime. Naturally, one may extend the scenario to dice with a different number of faces. In this paper, we prove that the expected stopping round in the game of Alon and Malinovsky is approximately when the number of die faces is sufficiently large.
Cite
@article{arxiv.2306.14073,
title = {Hitting a prime by rolling a die with infinitely many faces},
author = {Shane Chern},
journal= {arXiv preprint arXiv:2306.14073},
year = {2023}
}