Even numbers expressed as the sum of two primes

Can we prove that the even number greater than 2 can be expressed as the sum of two prime numbers....

#NumberTheory

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

This is Goldbach conjecture. No one has proved this conjecture till now. It is million-dollar conjecture.This is the best-known unsolved conjecture. If a person has a correct proof of it, he will be prized 1 million dollars. The proof would be judged by a panel of 6 mathematicians. ( As per the article given in Koshy's book) . Also this is the strong Goldbach conjecture. Go ahead if you know the proof:-)

Keshav Bassi - 5 years, 9 months ago

What have you tried? What are your thoughts?

Calvin Lin Staff - 5 years, 9 months ago

I want to ask that can we prove that the even numbers >2 can be expressed as the sum of prime numbers. Eg: 6=3+3 22=17+5

Prabhav Bansal - 5 years, 9 months ago

That is an interesting question. What have you tried? What are your thoughts? Do you think this is always possible? If yes, why? If no, why not?

Calvin Lin Staff - 5 years, 9 months ago

yes

FAIZAN KHAN - 5 years, 9 months ago

Can you prove this? I am asking for the proof.

Prabhav Bansal - 5 years, 9 months ago

As we know after 2 all prime numbers are only odd. & We also know that sum of 2 odd numbers will always be even. Then what what do u want to know exactly???

FAIZAN KHAN - 5 years, 9 months ago

But this is the converse. Please don't prove the converse.

Prabhav Bansal - 5 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$