HMMT 2013 U35

Let $P$ be the number to partition 2013 into an ordered tuple of prime numbers? What is $\log _{2}(P)$ ? If your answer is $A$ and the correct answer is $C$, then your score on this problem will be $\left\lfloor\frac{125}{2}\left(\min \left(\frac{C}{A}, \frac{A}{C}\right)-\frac{3}{5}\right)\right\rfloor$ or zero, whichever is larger.