1. Which of the following cannot be written as the sum of two prime numbers?
A 5
B 7
C 9
D 10
E 11
Solution: $\mathbf{E}$
If the odd number 11 is the sum of two prime numbers, it must be the sum of the only even prime, 2 , and an odd prime. But $11=2+9$ and 9 is not prime. So 11 is not the sum of two prime numbers. On the other hand, $5=2+3,7=2+5,9=2+7$ and $10=3+7$. Therefore, these are all the sum of two prime numbers.