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This is a Quantitative Study study.

October 19, 2025Open Access

Primes in almost all short intervals II

Key Points

The study confirms the existence of prime numbers in the interval [n-n^(1/22+ε), n] for almost all n.
It improves the previous exponent related to prime distributions from 1/21.5 to 1/22.
A combination of sieve machinery and Harman's arithmetic information was utilized in the analysis.
The introduction of variable role-reversal significantly contributes to the proof's success.

Abstract

By combining the sieve machinery used in the author's previous paper on this topic and some new arithmetic information in Harman's monograph, the author proves that the interval n-n^1{22+}, n contains prime numbers for almost all n, improving the previous exponent 121. 5 by the author. The use of the variable role-reversal plays a crucial role in the proof.

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Cite This Study

Runbo Li (Fri,) studied this question.

synapsesocial.com/papers/68f43ef4854d1061a58abe59 https://doi.org/https://doi.org/10.33774/coe-2025-jrnjl

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