Goldbach's conjecture, which has not been proved, states that every even number greater than two is the sum..?

Question

Goldbach's conjecture, which has not been proved, states that every even number greater than two is the sum of two primes. However, the same is not true for every odd number. Which of the following odd numbers is not the sum of two primes?

A- 13
B 33
C- 43
D- 53
E- 73

The person to give me the best answer along with a valid reason to back it up, will get 10 points.

Answer 1

The only way you can add two numbers and get an odd number for the sum is to start with an odd and an even number.

The only even prime number is 2. So, these numbers must be of the form 2 + X, and we want to know for which one X is not prime.

A ... 2 + 11 = 13 ... Since 11 is prime, this isn't the answer.
B ... 2 + 31 = 33 ... Since 33 is prime, this isn't the answer.
C ... 2 + 41 = 43 ... Since 41 is prime, this isn't the answer.
E ... 2 + 71 = 73 ... Since 71 is prime, this isn't the answer.

D ... 2 + 51 = 53 ... However 51 is NOT prime (it's 17 * 3), so this IS the answer to your question -- "D"

Answer 2

a million). 20 = 7 + 13 22 = 3 + 19 24 = 5 + 19 26 = 7 + 19 28 = 11 + 17 30 = 11 + 19 32 = 13 + 19 34 = 17 + 17 36 = 17 + 19 38 = 19 + 19 40 = 17 + 23 2). One such get at the same time is 11.