Prime Number Sums

TL;DR

This paper proves that for any positive integer n, there exists a permutation of the set {1,...,n} such that the sum of each element and its image under the permutation is prime.

Contribution

It introduces a novel permutation construction ensuring prime sums for all elements, expanding understanding of prime-related permutation problems.

Findings

Existence of such permutations for all n

Construction method for the permutations

Implications for prime sum problems

Abstract

We prove that it is always possible to find a permutation $p$ on the set $\{1,...,n\}$ such that $c+p(c)$ is prime for all $c \in \{1,...,n\}.$