On the largest prime factors of shifted semiprime numbers

2025/12/10 by До Дык Там, Tam, Do Duc
Mathematics · #Analytic Number Theory Research #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2512.09245

Abstract

A natural number n is called semi-prime if it is a product of two primes or a square of a prime. We denote ℙ₂ the set of all semi-primes. Our goal is to prove that for fixed integer number a and sufficiently large x the largest prime factor of number ∏_\substackn∈ ℙ₂
n≤ x(n+a) exceeds x^θ, where θ= 0.5-ε, 0<ε≤ 0.01 is arbitrarily small.

Citations

• On the largest prime factor of n²+1

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