On Thin Sets of Primes Expressible as Sumsets

2002/09/11 by Ernie Croot, Christian Elsholtz, Croot, Ernie +1
Mathematics · #11P32 #Advanced Topology and Set Theory #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.CO #math.NT #msc:11P32

paper · pdf · doi:10.48550/arxiv.math/0209137

arxiv created 2002/09/11 · openalex publication_date 2002/09/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that P is an infinite set of primes such that P = A + B + C, where A,B,C are sets with at least two elements. We show that if P(x) > c x/log^d x (where P(x) = the number of elements of P that are <= x), and if A,B,C is a "regular" triple of sets, then either |A+B| <= d, or |B+C| <= d, or |A+C| <= d.

Related

• Primes in Sumsets
• Sumsets in primes containing almost all even positive integers
• Primes of the form n²+n+p have density 1
• Prime Number Sums
• Additive decompositions of sets with restricted prime factors