# Multidimensional configurations in the primes with shifted prime steps

## TL;DR

This paper extends the understanding of linear configurations in prime sets by proving the existence of such configurations with steps shifted by one, advancing the combinatorial number theory in multidimensional prime sets.

## Contribution

It demonstrates the existence of linear configurations with shifted prime steps in multidimensional prime sets, a novel extension of previous results.

## Key findings

- Existence of linear configurations with shifted prime steps in $ ext{prime}^d$
- Extension of prior results to shifted prime steps
- Advancement in multidimensional prime combinatorics

## Abstract

Let $\mathcal{P}$ denote the set of primes. For a fixed dimension $d$, Cook-Magyar-Titichetrakun, Tao-Ziegler and Fox-Zhao independently proved that any subset of positive relative density of $\mathcal{P}^d$ contains an arbitrary linear configuration. In this paper, we prove that there exists such configuration with the step being a shifted prime (prime minus $1$ or plus $1$).