jmc

The four smallest prime numbers are 2, 3, 5, and 7, with product $2\cdot 3\cdot 5\cdot 7=210$. The four smallest composite numbers are 4, 6, 8, and 9, with product $4\cdot 6\cdot 8\cdot 9=1728$. The positive difference is thus $1728-210=\boxed{1518}$.