Hitting the Primes for the k-th time takes

k log(k)(1+o(1)) dice rolls (on average)

By Noga Alon, Yaakov Malinovsky, Lucy Martinez, and Doron Zeilberger


.pdf    .tex   

Written: Dec. ,2024


In this paper [arxiv version] by Noga Alon and Yaakov Malinovsky, extended in this paper, by Lucy Martinez and Doron Zeilberger, the expected number of rolls it takes until the running total is a prime (and other interesting kinds of numbers) for the FIRST time. But how long would it take (on average) until you see a prime k times?, for any k. We use computation to give exact values (up to many decimal places) for these numbers for k from 1 to 30 and use human ingenuity to prove that it is asymptotiaclly k*ln(k)*(1+o(1))


Maple package


Sample Input and Output for PRIMESk.txt


Plots of the Probability Density Functions (pdf) of the Random Variable "Reaching a prime for the k-th time" by rolling a fair die for k=20,40,60,80,100


Articles of Doron Zeilberger

Noga Alon's Home Page

Yaakov Malinovsky's Home Page

Lucy Martinez's Home Page

Doron Zeilberger's Home Page