jmc

The prime numbers are $23$ and $29$. Since $29-23=6$, the mean is $\frac{6}{2}=3$ numbers away from $23$ and from $29$. The mean is $\boxed{26}$. We can also find the mean of $23$ and $29$ with $\frac{29+23}{2}=\frac{52}{2}=26$ or just by noticing that the number in the middle of $23$ and $29$ is $26$.