Sequence of 5 Consecutive Non-Primable Numbers by Changing 1 Digit

Theorem
The following sequence of $5$ consecutive positive integers cannot be made into prime numbers by changing just one digit:
 * $872\,894, 872\,895, 872\,896, 872\,897, 872\,898$

Proof
Numbers ending in $0$, $2$, $4$, $6$ and $8$ are not prime because by Divisibility by 2 they are divisible by $2$.

Numbers ending in $0$ and $5$ are not prime because by Divisibility by 5 they are divisible by $5$.

Hence each of $872\,894$, $872\,895$, $872\,896$ and $872\,898$ remain composite when you change any of their digits except the last one.

So we inspect the prime factors of the following, only bothering to check the numbers ending in $1$, $3$, $7$ and $9$:

All we need to do now is to inspect $872\,897$.

The result has been proven.