-1
$\begingroup$

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.

$\endgroup$

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

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ 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. $\endgroup$ – Ross Millikan Sep 9 '16 at 15:44
  • $\begingroup$ Proof by exhaustion $\endgroup$ – jnyan Sep 9 '16 at 16:05
1
$\begingroup$

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

$\endgroup$
1
$\begingroup$

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 $14=11+3=7+7$.

$\endgroup$
  • $\begingroup$ Okay, That was my initial thought but I didn't know if there was a way to do it through a formal Proof. Like I said really bad at this. $\endgroup$ – ntgoodatmth Sep 9 '16 at 17:07
  • $\begingroup$ 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. $\endgroup$ – Piquito Sep 10 '16 at 18:14

Not the answer you're looking for? Browse other questions tagged or ask your own question.