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Hitting a prime by rolling a die with infinitely many faces

2023/06/24 by Shane Chern, Chern, Shane
Computer Science · Mathematics · #11A41 #60C05 #Artificial Intelligence in Games #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2306.14073

openalex publication_date 2023/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Alon and Malinovsky recently proved that it takes on average 2.42849… 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 log M when the number M of die faces is sufficiently large.

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