On the largest prime factor of integers in short intervals IV

Runbo Li

doi:10.33774/coe-2026-24kjf

Mathematics

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On the largest prime factor of integers in short intervals IV

17 August 2026, Version 1

Working Paper

Runbo Li

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This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

In this short note, by inserting new exponent pairs into previous estimates for exponential sums, we prove that the interval $[x, x+x^{\frac{1}{2}}]$ contains a number with a prime factor larger than $x^{0.744}$ for all sufficiently large $x$.

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