English

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 2.428492.42849\ldots 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 logM\log M when the number MM 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}
}
R2 v1 2026-06-28T11:13:37.169Z