On the Largest Prime Factor of Integers in Short Intervals

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.