Many ways problem

$T_1$ $T_2$ $T_3$ $T_4$ $T_5$ $T_6$ $T_7$ $T_8$ $T_9$ $T_{10}$ $T_{11}$ $T_{12}$
$1$ $3$ $6$ $10$ $15$ $21$ $28$ $36$ $45$ $55$ $66$ $78$
Looking at the first twelve triangular numbers, we see that only $3$ is prime, the others are all composite numbers (apart from $1$). So our conjecture might be that $3$ is the only triangular number which is prime. How can we go about justifying this?