Proof: to prove the $2$ is the only even primenumber we must prove following:(1) $2$ is an also prime number(2) If over there existed another even primenumber to speak $m$, climate $m=2$

Proof that 1) is obvious.

You are watching: Is two the only even prime number

Proof that 2):Let us assume contrary: there exists another even prime number say $m ≠ 2$. Due to the fact that $m$ is also we have actually that $m = 2k$ because that some positive integer $k$. Thus, we have actually three distinctdivisors that $m$ that room $1$, $2$ and also $m$ Thiscontradicts the an interpretation of prime uneven $m= 2$.

Therefore, $2$ is the only also primenumber.

edited Nov 18 "14 in ~ 7:41

man Marty
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asked Nov 18 "14 in ~ 6:53

Akash PatalwanshiAkash Patalwanshi
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2 answers 2

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Yes, it is sufficient. Although you really shouldn"t speak proof is "obvious" trivial can be better. The problem here is proportionality. One might easily say the the whole trouble was trivial.

In general the best method to gauge what is trivial and what is no is to consider whether your presumption trivializes the totality problem.

It doesn"t take much to describe why 2 is an even prime and it isn"t much more trivial 보다 the second component so you more than likely should.

PS You have actually 4 divisors, $1$ ,$2$, $k$ and $2k$ yet that doesn"t change the problem of your proof.

answered Nov 18 "14 in ~ 7:05

john MartyJohn Marty
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Saying (1) is apparent may no be sufficient to it is in a proof: it is no a proof and also (2) is additionally obvious.

I think it might be fingerprint if you were trying come prove (2) that any type of even positive integer various other than $2$ is no prime. In any type of case because that (2) you could to state the $k\gt 1$.

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reply Nov 18 "14 at 7:09

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