The OEIS A256480 conjecture for prepended-digit primes

Let $b(n)$ be the smallest prime obtained by appending $n$ to a positive-length string of identical decimal digits, or $0$ if no such prime exists.

OEIS A256480 conjecture.

$$b(n)=0$$

if and only if $n$ is even or $n$ is divisible by $5$.

The necessary condition is immediate from the final digit of a prime candidate, while the converse is proposed for all remaining $n$. The supplied text gives no proof or resolution.