(4) 7 Hint: Let the common difference be $d$, from the condition we get: $2 a_{4} \leqslant 2+3 d, d \leqslant a_{4}-3$, so
$$
2 a_{4} \leqslant 2+3 d \leqslant 2+3\left(a_{4}-3\right),
$$

Therefore, $a_{4} \geqslant 7$.
(4) In the arithmetic sequence $\left\{a_{n}\right\}$, if $S_{4} \leqslant 4, S_{5} \geqslant 15$, then the minimum value of $a_{4}$ is
$\qquad$