Number theory · Oct 6, 2026

Independent largest prime factors of consecutive integers

Resolves the Erdős–Pomerance joint Dickman conjecture: the logarithmic sizes of the largest prime factors of n and n+1n+1 are asymptotically independent in ordinary natural density. In particular, the integers satisfying P+(n)<P+(n+1)P^+(n)\lt P^+(n+1) have density 1/2.

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