Superpolynomial-size conjecture for smallest palindromic quotient representations

Let $N$ be a natural number for which there exist palindromic numbers $A$ and $B$ with $N=A/B$, and measure the size of a solution by the length of the relevant base-$2$ representations. Superpolynomial-size conjecture. The size of the smallest solution to $N=A/B$ in palindromes $A,B$, if it exists, is not bounded by any polynomial in $N$.

The source proves an explicit upper bound for the smallest solution when one exists, but conjectures that no polynomial bound in $N$ is possible.