On the Largest Prime Factor of Integers in Short Intervals

Q: What type of study is this?

This is a Quantitative Study study.

Runbo Li

doi:10.20944/preprints202504.1212.v2

October 16, 2025Open Access

On the Largest Prime Factor of Integers in Short Intervals

View Full Paper

Ask AI

Bookmark

Share

Key Points

The study shows that for large integers, the interval contains an integer with a prime factor larger than x^(51/53-ε), establishing a new bound.
The result improves previous findings by Jia and Liu (2000), setting the γ value at 2/53 for a key mathematical exercise.
The framework for this analysis centers on the distribution of prime factors within specified integer intervals and its implications.
Findings may influence further research in number theory, especially regarding properties of primes in specific contexts.

Ask about this paper

Answers are grounded in this paper and cite their sources.

Implication

Analysis reveals that large integers have prime factors exceeding specific bounds, highlighting prime distribution.

Abstract

The author sharpens a result of Jia and Liu (2000), showing that for sufficiently large \( x \), the interval \( [x, x+x1/2+ε] \) contains an integer with a prime factor larger than \( x51/53-ε \). This gives a solution with \( γ = 2/53 \) to the Exercise 5.1 in Harman's monograph.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Runbo Li (2025) studied this question.

synapsesocial.com/papers/68f43f09854d1061a58ac90b https://doi.org/10.20944/preprints202504.1212.v2

View Full Paper

Ask AI

Bookmark

Share

On the Largest Prime Factor of Integers in Short Intervals

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

On the Largest Prime Factor of Integers in Short Intervals

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading