Prove-that-every-even-number-can-be-expressed-as-sum-of-two-primes-or-give-an-counter-example-

Question Number 9049 by Rasheed Soomro last updated on 16/Nov/16

Prove that every even number can be

expressed as sum of two primes or

give an counter example .

Commented by FilupSmith last updated on 16/Nov/16

2 n = p_{1} + p_{2}

p_{n} \in P

all primes are odd except p = 2

∴ 2 n = (2 a + 1) + (2 b + 1)

2 n = 2 a + 2 b + 2

2 n = 2 (a + b + 1) \in E

Commented by FilupSmith last updated on 16/Nov/16

if p = 2, 2 n = p + p = 2 p = 4

2 n = 4

Commented by Rasheed Soomro last updated on 16/Nov/16

All primes are odd, but all odd are

not necessarily primes .

So 2 a + 1 and 2 b + 1 here are not

necessarily prime .

Commented by FilupSmith last updated on 17/Nov/16

I dont understand . am i wrong ?

Commented by mrW last updated on 23/Nov/16

This is the famous {Goldbach}^{'} s

conjecture, one of the most

difficult problems in mathematics .

Facebook Tweet Pin