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Aug 19, 2022 at 7:03 comment added Aditya Guha Roy @BCLC complementing professor Tao's comment: you may look at his blogpost terrytao.wordpress.com/2015/01/04/… or the notes at people.math.ethz.ch/~kowalski/probabilistic-number-theory.pdf for more details on probabilistic number theory.
Aug 6, 2022 at 20:58 comment added Timothy Chow I am reminded of the Dance Marathon Problem, which also features a kind of extreme value problem, and a limit that seems like it should exist, but doesn't.
Aug 6, 2022 at 12:53 history edited Terry Tao CC BY-SA 4.0
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Aug 6, 2022 at 12:48 comment added Terry Tao @BCLC Probabilistic number theory has been a thing for almost a century. en.wikipedia.org/wiki/Probabilistic_number_theory
Aug 6, 2022 at 12:43 history edited Terry Tao CC BY-SA 4.0
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Aug 6, 2022 at 9:34 vote accept Jakub Konieczny
Aug 6, 2022 at 7:07 comment added user196574 On the name of that random variable, it looks like a discrete version of Gumbel and is discussed in arxiv.org/abs/1410.7568 as a candidate extreme-value distribution for data taking integer values.
Aug 6, 2022 at 0:39 comment added BCLC oh using probability to prove a number theory result? or did the question already have some probability in it?
Aug 5, 2022 at 23:43 history edited Terry Tao CC BY-SA 4.0
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Aug 5, 2022 at 23:37 history answered Terry Tao CC BY-SA 4.0