# Show that every even integer greater than 2 can be written as a sum of two primes up to n less than or equal to 30 [closed]

Suppose $n$ is an even integer less than or equal to $30$.

$n= p_1 +p_2$

^^Is that legal? and if so where do I proceed from there.

P.S I am new to this forum and I am taking a number theory class. I switched from math major to math minor because I cannot write a proof to save my life.

Any help/ tips/ would be appreciated.

## closed as unclear what you're asking by Peter Franek, Shailesh, Parcly Taxel, Leucippus, user296602 Sep 10 '16 at 4:55

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• First you need to clearly state what you are trying to prove. I believe it is "Show that all even numbers greater than $2$ and less than $30$ can be expressed as the sum of two primes." Your title is not clear at all. – Ross Millikan Sep 9 '16 at 15:44
• Proof by exhaustion – jnyan Sep 9 '16 at 16:05

There are only thirteen even numbers between $2$ and $30$, so the easiest way to prove this is to show such a sum for each one. $$4=2+2\\6=3+3$$ Continue
In general you have Golbach Conjecture but for $n$ even less than or equal to $30$ you have to verify it . An example is $$4=2+2\\6=3+3\\8=5+3\\10=7+3\\12=7+5\\14=7+7\\16=13+3\\18=11+7\\20=13+7\\22=17+5\\24=19+5\\26=13+13\\28=23+5\\30=19+11$$ Notice that the examples are not unique, for instance $14=11+3=7+7$.
• I think at a table with the primes $2,3,5,....,23$ ($29$ is excluded obviously) and take all the possible sums of two of them giving even numbers. I feel that if you get a strictly formal proof, then you have in hand Golbach conjecture in general. – Piquito Sep 10 '16 at 18:14