Prove $2$ is only even prime
Andrew Henderson 
Prove that $2$ is the only even prime:
I have tried, this is what I have done. Is this is suffitient?
Proof: To prove that $2$ is the only even prime number we need to prove following: (1) $2$ is an even prime number (2) If there existed another even prime number say $m$, then $m=2$
Proof of 1) is obvious.
Proof of 2): Let us assume contrary: There exists another even prime number say $m ≠ 2$. Since $m$ is even we have that $m = 2k$ for some positive integer $k$. Thus, we have three distinct divisors of $m$ that are $1$, $2$ and $m$ This contradicts the definition of prime unless $m = 2$.
Therefore, $2$ is the only even prime number.
$\endgroup$2 Answers
$\begingroup$Yes, it is sufficient. Although you really shouldn't say proof is "obvious" trivial might be better. The issue here is proportionality. One could easily say that the whole problem was trivial.
In general the best way to gauge what is trivial and what is not is to consider whether your assumption trivializes the whole problem.
It doesn't take much to explain why 2 is an even prime and it isn't much more trivial than the second part so you probably should.
PS You have 4 divisors, $1$ ,$2$, $k$ and $2k$ but that doesn't change the substance of your proof.
$\endgroup$ 2 $\begingroup$Saying (1) is obvious may not be enough to be a proof: it is not a proof and (2) is also obvious.
I think it might be clearer if you were trying to prove (2) that any even positive integer other than $2$ is not prime. In any case for (2) you could to state that $k\gt 1$.
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