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.


number-theory
re-superstructure
cite
monitor
edited Nov 18 "14 in ~ 7:41
*

man Marty
3,48811 yellow badge1616 silver badges4242 bronze badges
asked Nov 18 "14 in ~ 6:53
*

Akash PatalwanshiAkash Patalwanshi
2,92511 yellow badge1414 silver badges3838 bronze badges
$\endgroup$
add a comment |

2 answers 2


active earliest Votes
5
$\begingroup$
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.


re-publishing
cite
monitor
answered Nov 18 "14 in ~ 7:05
*

john MartyJohn Marty
3,48811 gold badge1616 silver- badges4242 bronze badges
$\endgroup$
2
include a comment |
1
$\begingroup$
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 $k\gt 1$.


share
point out
monitor
reply Nov 18 "14 at 7:09
*

HenryHenry
136k99 gold badges108108 silver badges216216 bronze badges
$\endgroup$
add a comment |

your Answer


Thanks for contributing solution to snucongo.orgematics ridge Exchange!

Please be certain to answer the question. Provide details and also share your research!

But avoid

Asking because that help, clarification, or responding to other answers.Making statements based on opinion; earlier them up with references or personal experience.

Use snucongo.orgJax to format equations. Snucongo.orgJax reference.

To discover more, check out our advice on writing an excellent answers.

See more: Mineral Crystals Of Quartz Biotite Mica And Amphibole Are Produced Primarily By The


Draft saved
Draft discarded

Sign increase or log in


sign up using Google
sign up using Facebook
authorize up using Email and Password
submit

Post as a guest


name
email Required, but never shown


Post as a guest


surname
email

Required, however never shown


write-up Your answer Discard

By click “Post her Answer”, girlfriend agree come our regards to service, privacy policy and also cookie plan


Not the price you're looking for? Browse various other questions tagged number-theory or questioning your own question.


Featured ~ above Meta
associated
0
Proof the 2 and also 3 are the only siamese twins that exist!
5
Maximum amount of divisors the the number $n^m+m^n$
3
Prove the the equation $x^2+7x=-12$ has precisely two distinctive solutions in $\snucongo.orgbbZp$, because that every element $p$.
4
Prove that there exists a hopeful integer $a$ such that $n|a^2-a$
4
show that just finitely plenty of positive integers $n$ have actually the residential property that for every $m$ for which $1
5
let $n=apq+1$. Prove the if $pq \ | \ \phi(n)$ then $n$ is prime.
4
A element number divides only the molecule
0
An boundless sequence a for which element divisors the $a_i^2+1$ space in the collection $S$
hot Network questions more hot inquiries

question feed
subscribe to RSS
inquiry feed To subscribe to this RSS feed, copy and paste this URL right into your RSS reader.


*

snucongo.orgematics
firm
ridge Exchange Network
site architecture / logo © 2021 stack Exchange Inc; user contributions licensed under cc by-sa. Rev2021.9.17.40238


snucongo.orgematics ridge Exchange works ideal with JavaScript permitted
*

her privacy

By clicking “Accept every cookies”, you agree stack Exchange can store cookie on your maker and disclose info in accordance through our Cookie Policy.