Hitting a Prime in 2.43 Dice Rolls (On Average)

Noga Alon, Yaakov Malinovsky

Research output: Contribution to journalComment/debatepeer-review

1 Scopus citations


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 (Formula presented.). 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.

Original languageEnglish (US)
Pages (from-to)301-303
Number of pages3
JournalAmerican Statistician
Issue number3
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


  • Dynamic-programming
  • Prime number theorem
  • Stopping time


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