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arXiv · 2306.14073

Hitting a prime by rolling a die with infinitely many faces

Shane Chern
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Abstract

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

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Shane Chern. 2023-06-24. Hitting a prime by rolling a die with infinitely many faces. https://arxiv.org/abs/2306.14073

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