Hitting a Prime in 2.43 Dice Rolls (On Average)

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Hitting a Prime in 2.43 Dice Rolls (On Average)

Alon, Noga; Malinovsky, Yaakov

The American statistician, 07/2023, Volume: 77, Issue: 3

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What is the number of rolls of fair six-sided dice until the first time the total sum of all rolls is a prime? We compute the expectation and the variance of this random variable up to an additive error of less than . This is a solution to a puzzle suggested by DasGupta in the Bulletin of the Institute of Mathematical Statistics, where the published solution is incomplete. The proof is simple, combining a basic dynamic programming algorithm with a quick Matlab computation and basic facts about the distribution of primes.

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