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Z. Yang

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Preprint Jul 2026

An improvement on the largest prime factors of consecutive integers

Let $P^+(n)$ denote the largest prime factor of $n$. One of Erd\H{o}s and Tur\'an's conjectures asserts that the asymptotic density of integers $n$ satisfying $P^+(n)<P^+(n+1)$ is 1/2. In this paper, we prove that this density is larger than 0.280, which improves the previous result 0.2017 by L\"u and Wang (2025). We a...

Z. Yang · 1 citation