If we add two whole numbers and get an odd result, we must be adding one even and one odd number.
Since 2 is the only even prime, for an odd number to be the sum of two primes, it would need to be equal to 2 + an odd prime. Since 51 = 2 + 49, and 49 is not prime, we can't write 51 as the sum of two primes.
There is a famous unsolved problem in math known as 'Goldbach's Conjecture', that hypothesizes that every even integer (greater than 2) can be written as the sum of two primes. That's true for every even number anyone has ever tested, but no one has proven if it's true for all even numbers. But it's certainly true for any small even number, including the four even numbers in the answer choices here.
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