In how many ways can we represent the number $$2003$$ as a sum of two prime numbers? ($$2003$$ Math Kangaroo Problems, Level $$7-8$$, Question \#$$15$$) 
Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers->Knowing Prime and Composite Numbers
If so, $2$ must be one of the prime numbers, and the other must be $2003-2=2001$, which is not prime. Thus, such a representation is impossible. 