"Every composite positive integer has at least one prime factor less than the square root of the integer."
Proof by contradiction:
If $p_1, p_2, ..., p_n$ are prime factors of $x$ greater than $\sqrt{x}$. Then the following holds for $∀$ $i,j∈ℕ$ $i,j
Considering two prime factors of $x$, $p_1$ and $p_2$ greater than $\sqrt{x}$ using the same reasoning above we have $p_1p_2 > x$ $CONTRADICTION!$ This means a positive composite integer can only have one (but may not have any) prime factor greater than its square root.
This is only a proof of what I think is right but I still have a weird feeling that I'm missing something because I've not come across a theorem like this before. The first one I wrote above is a very popular one, and if what the answer I gave is valid then how come it is not popular(unless it isn't true).