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2016 AMC 12A Question 5

AMC12 · 2016 AMC 12A

Question 5

Goldbach’s conjecture states that every even integer greater than $2$ can be written as the sum of two prime numbers (for example, $2016=13+2003$). So far, no one has been able to prove that the conjecture is true, and no one has found a counterexample to show that the conjecture is false. What would a counterexample consist of?
  1. an odd integer greater than $2$ that can be written as the
    sum of two prime numbers
  2. an odd integer greater than $2$ that cannot be written as the
    sum of two prime numbers
  3. an even integer greater than $2$ that can be written as the
    sum of two numbers that are not prime
  4. an even integer greater than $2$ that can be written as the
    sum of two prime numbers
  5. an even integer greater than $2$ that cannot
    be written as the sum of two prime numbers