Prove that if every even natural number greater than 2 is a sum of two prime numbers ( Goldbach conjucture), then every odd number greater than 5 is a sum of three prime numbers.

Proof:

1. Let every number in the Set of Natural numbers greater than 2 be ‘m’

2. m = 2 + 2n [ 2n => Even number]

3. But based on the Goldbach conjucture, m is a sum of 2 primes.

Let p and q be the two primes

m = (2 + 2n) = p + q

4. Let O be the odd number greater than 5

O = m + 3

Note : Since m is greater than 2, so O > 5

5. But m is a sum of 2 primes, so O can be expressed as a sum of 2 primes + 3.

Also, 3 is a prime!

O = p + q + 3

O is expressed as sum of 3 primes.