imc

Because squares of a non-multiple of 3 is always $1(\mathrm{mod}3)$, the only expression always a multiple of $3$ is $\boxed{p^2+26}$. This is excluding when $p\equiv 0(\mathrm{mod}3)$, which only occurs when $p=3$, then $p^2+26=35$ which is still composite.