The pairs $6h-1$ and $6h+1$ are not twin primes, that is at least one of them is factorizable/decomposable, where $h$ can be found from any of the following equations:
$$ \begin{align} h = 6t_1t_2 +7t_1+5t_2+6\;,\\ h = 6t_1t_2 +5t_1+5t_2+4\;,\\ h = 6t_1t_2 +7t_1+7t_2+8\;.\\ \end{align} $$
Here $h$ is the third integer coordinate of the points of the paraboloids obtained by integer values of $t_1$ and $t_2$, where $t_1$ and $t_2$ belongs to $N\cup\{0\}$.
Now, can you explain how to support the statement cited above, if I am correct. Or else, let me know where I am wrong.