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One of the Most Difficult Unsolved Problem in Mathematics

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Mohammad Hassan Murad:
As mathematicians believe most of the mysteries of Nature are hidden in numbers. Now I shall talk about such a mysterious problem in number theory. At first I begin by quoting one of the most greatest mathematician of England,

The famous problem of which I propose to speak tonight is probably as difficult as any of the unsolved problems of mathematics.
G. H. Hardy on Goldbach's conjecture
What is Goldbach's Conjecture?
The Prussian mathematician Christian Goldbach noticed a pattern in the following sums:
4=2+2,                        6=3+3,                  8=3+5
10=3+7,12=5+7,         14=3+11=7+7,
16=3+13=5+11,          18=5+13=7+11,     20=3+17=7+13
⋮
(Do you see a pattern here?) Based on his observations, Goldbach, in a letter to Euler in 1742, conjectured that every even integer > 2 can be expressed as the sum of two primes. Euler could not prove it, and his conjecture still remains an unsolved problem.

Is Goldbach'ss Conjecture true for all even integer?
If not, up to when it is true?

To know more on this see the following attached file

tany:
Very good post sir..

Saba Fatema:
Mysterious problem...

asitrony:
Dear Sir,

This conjecture is merely useful one! To me it seems very riddle in case of larger or extremely larger numbers but approved for small numbers. Don't keep unsolving the conjecture as comes a great opportunity to invent.

Thanks !

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