2. The positive integer 2018 is the product of two primes.
What is the sum of these two primes?
A 1001
B 1010
C 1011
D 1100
E 1101
Solution
C

The prime factorization of 2018 is given by $2018=2 \times 1009$. The sum of the two prime factors is $2+1009=1011$.

NoтE
There is no very quick way to check that 1009 is prime, as this would involve checking that no prime $\leq 29$ is a divisor. [Why is this enough?] Fortunately, the question tells us that 2018 is the product of two primes. We can conclude from this that the second factor 1009 is prime.