Hitting a prime in 2.43 dice rolls (on average)

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https://arxiv.org/abs/2209.07698
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https://doi.org/10.48550/arXiv.2209.07698
http://hdl.handle.net/11603/26187
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2022-09-16
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5 pages
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journal articles
preprints
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Abstract
What is the number of rolls of fair 6-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 10−4 , showing that the expectation is 2.4284.. and the variance is 6.2427... This is a solution of a puzzle suggested a few years ago by DasGupta in the Bulletin of the IMS, 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.