Question

Prove that for every even natural number greater than 2 is the sum of two prime numbers, then every odd natural number greater than 5 is the sum of 3 primes

Answer 1

@eliassaab can u help me?

Answer 2

This is an unsolved problem, I think.
http://en.wikipedia.org/wiki/Goldbach%27s_conjecture

Answer 3

nooooo like u just assume every even natural number greater than 2 is the sum of two prime numbers

Answer 4

Basically, all you're going to do here is look at whatever number is 3 less than that odd number. It will be an even number, which means it is the sum of two primes. Those two primes + 3 will give you your odd number, which is all you need, since 3 is a prime number.

Assume every even number greater than 2 is the sum of two prime numbers.
Let m be an odd number greater than 5.
m = 3 + n where n is an even number greater than 2.
n is the sum of two prime numbers, p and q, so
m = 3 + p + q
Since 3 is prime, m is equal to the sum of three prime numbers.
Therefore, if all even numbers greater then 2 are the sum of two prime numbers, then all odd numbers greater than 5 are the sum of three prime numbers.
QED

Answer 5

AWEEESSSOOMMMMMEEEEEEEEEEEEEEE

Answer 6

You're awesome.

Answer 7

ummmm not really cant solve a thing on my own and i am majoring in math

Answer 8

Haha I majored in math myself. Writing proofs is a hard skill to learn.

Answer 9

The problem should have been asked more clearly like that
If every even number greater than 2 can be written as the sum of two prime number,
then every odd number greater than 5 can be written as the sum of three prime number.

The way, I read the problem, was that one has to prove both statements. Of course, as I said before, the first one is an unsolved problem.

Answer 10

Yeah, it could have been stated more clearly. "Prove the implication" would have done it.