Consecutive primes which are widely digitally delicate

TL;DR

This paper proves that for any positive integer k, there are k consecutive primes such that changing any digit, including leading zeros, makes each prime composite, revealing a new form of digital delicacy.

Contribution

It establishes the existence of arbitrarily long sequences of consecutive primes with a strong digital delicacy property, a novel concept in prime number theory.

Findings

Existence of k consecutive primes with digit-changing digital delicacy for any k

Changing any digit, including leading zeros, makes the prime composite

Demonstrates a new extreme form of prime digit sensitivity

Abstract

We show that for every positive integer $k$, there exist $k$ consecutive primes having the property that if any digit of any one of the primes, including any of the infinitely many leading zero digits, is changed, then that prime becomes composite.