IMC 2017 Q4
4. Which of the following is not the sum of two primes?
- A 5
- B 7
- C 9
- D 11
- E 13
Intermediate Mathematical Challenge 2017, Question 4. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 11
All primes except 2 are odd. So the sum of a pair of primes cannot be odd, and so cannot be prime, unless one of the pair is 2. We note that 5 = 2 + 3; 7 = 2 + 5; 9 = 2 +7; 13 = 2 + 11. However, 11 = 2 + 9 and so it is not the sum of two primes, as 9 is not prime.
Solution © UK Mathematics Trust, from the IMC 2017 solutions. Longer versions with investigations: Solutions and investigations (PDF).