ClaimmathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →importance · settledImportance 0.15, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

TopicsNumber theory Probabilistic Collatz dynamics Collatz conjecture

For random odd N, the 2-adic valuation of 3N+1 is geometrically distributed with mean 2.

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Decomposition

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any given value {a \in{\bf N}+1} with probability {2^{-a}}. Such a geometric random variable is twice as likely to be odd as to be even

https://terrytao.wordpress.com/2019/09/10/almost-all-collatz-orbits-attain-almost-bounded-values/extraction 0.85

number of times 2 divides 3N+1 has geometric distribution of mean 2

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Created by extractor · Sep 13, 2026. Every judgment on this page is accompanied by a reasoning trace.