One of the most famous unsolved problems in mathematics is the conjecture made by Christian Goldbach in the letter to Leonhard Euler in 1742. Conjecture made in this letter is now known as Goldbach's Conjecture. Conjecture is as given:
Every even integer greater than 2 can be expressed as sum of two (not necessarily distinct) prime numbers. Presently, it is not known if the conjecture is true or false, though most mathematicians believe it to be true.
(a) Explain one way to prove that Goldbach's Conjecture is false.
(b) Prove the given:
If there exists the odd integer greater than five which is not sum of 3 prime numbers, then Goldbach's Conjecture is false.