Hitting a prime by rolling a die with infinitely many faces

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 M of die faces is sufficiently large.