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.
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.