Infinite partial sumsets in the primes

TL;DR

This paper proves the existence of infinite sets of natural numbers whose pairwise sums, in a specific order, are always prime, revealing new structures within prime number theory.

Contribution

It introduces the first construction of infinite sets with pairwise sums forming primes under a particular ordering, advancing understanding of prime sumsets.

Findings

Existence of infinite sets with prime-sum properties

Construction method for such sets

Implications for additive number theory

Abstract

We show that there exist infinite sets $A = \{a_1,a_2,\dots\}$ and $B = \{b_1,b_2,\dots\}$ of natural numbers such that $a_i+b_j$ is prime whenever $1 \leq i < j$.