Hitting a Prime by Rolling a Die with Infinitely Many Faces

Shane Chern

The American Statistician, 2024, vol. 78, issue 3, 297-303

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 article, 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.

Date: 2024
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DOI: 10.1080/00031305.2023.2290720

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