MHB Max 3-Digit Prime Divisor of 2000!/(1000!1000!)

[Albert1]

giving :
(1) $p$ is a divisor of $\dfrac{2000!}{1000!1000!}$
(2) $p$ is a prime
(3) $p$ is a 3-digit number
find $max(p)$

 

[kaliprasad]

giving :
(1) $p$ is a divisor of $\dfrac{2000!}{1000!1000!}$
(2) $p$ is a prime
(3) $p$ is a 3-digit number
find $max(p)$

Spoiler

refer to http://mathhelpboards.com/challenge-questions-puzzles-28/highest-3-digit-prime-factor-17685.html