Now I'm kondof confused. Must think about this...
Are prime numbers only the natural numbers?
Well, technically, it is defined as a natural number, so yes. However, I believe you could extend the pretext of it to other numbers. For example, above, if you had 0 for Q and T, you would get:
P(S+Ti)-Q(T-Si)=PS=A+Bi=A. So, the factors of A would be P and S. So it makes sense. Take Q=2 and T=5:
P(S+Ti)-Q(T-Si)=P(S+5i)-2(5-Si)=PS+5i-10+2Si=S(P+2i)+5i-10
and P=9, S=3:
3(9+2i)+5i-10=27+6i+5i-10=17+11i
So the factors of 17+11i are (9+2i) and (3+5i) so 17+11i wouldn't be prime by this definition.
But yeah, it's defined as natural (real) numbers only.