Question

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?

an odd integer greater than $2$ that can be written as the sum of two prime numbers

an odd integer greater than $2$ that cannot be written as the sum of two prime numbers

an even integer greater than $2$ that can be written as the sum of two numbers that are not prime

an even integer greater than $2$ that can be written as the sum of two prime numbers

an even integer greater than $2$ that cannot be written as the sum of two prime numbers

Solution:

A counterexample must satisfy the hypothesis of being an even integer greater than $2$ while failing the conclusion that it can be written as the sum of two prime numbers.

Thus, the correct answer is E.

2016 AMC 12A Problem 5

Solution:

Problem 5 in Other Years