n C r denotes the number of combinations of n things taking r at a time.

2000C1000 = 2000*1999*.......*1001/1000! 
=> 2000C1000 = 2^(500) {odds from 1001 to 2000}/500!
As odds cannot be multiple of 2, next possibility is 3.
Maximum prime between 500 and 667 is the largest 3-digit
prime factor of 2000 C 1000
The required number is 661.