$\begin{aligned} 4 &=& 2+2 \\ 5&=&2+3 \\ 6&=&3+3 \end{aligned}$

The above shows that the first 3 positive integers larger than 3 can be expressed as the sum of 2 prime numbers .

Is it true that we can express
**
any
**
positive integer larger than 3 as the sum of 2 prime numbers?

Yes, it is true
No, it is not true

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

Relevant wiki: Prime NumbersAll primes except 2 are odd. If the claim of all positive integer larger than 3 is a sum of two primes is true, then for any prime larger than 3 to be odd, one of the two primes must be 2. This also means that subsequent primes must be 2 apart. It is true for 5 and 7 but not true for 11, 17, 23 and so on. Therefore, $\boxed{\text{no, it is not true.}}$ .