Consecutive primes which are widely digitally delicate and Brier numbers

TL;DR

This paper proves that for any positive integer k, there are k consecutive primes that are both widely digitally delicate and Brier numbers, combining properties previously shown separately.

Contribution

It establishes the existence of k consecutive primes that are simultaneously widely digitally delicate and Brier numbers for any positive integer k.

Findings

Existence of k consecutive primes that are widely digitally delicate and Brier numbers for all k

Extension of previous results combining two prime properties

Use of covering systems and a theorem of D. Shiu

Abstract

Making use of covering systems and a theorem of D. Shiu, the first and second authors showed that for every positive integer $k$, there exist $k$ consecutive widely digitally delicate primes. They also noted that for every positive integer $k$, there exist $k$ consecutive primes which are Brier numbers. We show that for every positive integer $k$, there exist $k$ consecutive primes that are both widely digitally delicate and Brier numbers.