Reducing the number of prime factors of long κ-tuples

2011/11/08 by C.S. Franze, C. S. Franze, Franze, C. S.
Mathematics · #11N35 #11N36 #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT #msc:11N35 #msc:11N36

paper · pdf · doi:10.48550/arxiv.1111.2003

15 pages, submitted to London Mathematical Society

arxiv created 2011/11/08 · openalex publication_date 2011/11/08 · arxiv updated 2011/11/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that there are infinitely many integers n such that the total number of prime factors of (n+h₁)(n+h₂)...(n+h_κ) is at most (1/2)κlogκ+O(κ), provided κ is sufficiently large.

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