The reversible-prime conjecture in every base

Fix a base $b\geq 2$ and let $\overleftarrow{n}$ denote the integer obtained by reversing the base-$b$ digits of $n$. A reversible prime is a prime number whose digital reverse is also prime. Reversible-prime conjecture. For every base $b\geq 2$, there are infinitely many reversible primes; that is, infinitely many prime numbers $p$ such that $\overleftarrow{p}$ is also prime. This is one of two long-standing conjectures about digital reversals mentioned in the paper and is described as currently out of reach.