I know that in general, it is difficult to tell whether a knot is prime or not. However, the Wikipedia page has established that the trefoil knot and the figure 8 knot are prime knots.
I've managed to draw the Seifert circles for these two knots and obtained the genus of their Seifert surfaces.
For the trefoil knot, I got $g(S_1)=(3-2+1)/2=1$ and for the figure 8 knot, I got $g(S_2)=(4-2+1)/2=3/2$. I know I'm supposed to use Seifert's Theorem that $g(K\#L)=g(K)+g(L)$ somehow, but what can I do?