2016 AMC 12A Problem 5

Problem 5 of 25Easier

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?

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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.

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