The other prime numbers room all odd numbers such as \$5, 11, 127,\$ and also \$37\$. So, why is \$2\$ the just prime also number there is?

Is it due to the fact that it only has actually 1 and itself the way, even though it"s even? inspect it out on this excellent brickandmortarphilly.com page one-fourth from the bottom.

You are watching: Is 2 the only even prime number

Why is two the only also \$(\$binary\$)\$ number that is prime?

For the same factor that 3 is the only ternary number the is prime. Which is the same reason for which 5 is the only quinary number that is prime. Etc.

Because every also number various other than 2 is obviously divisible by 2 and also so by an interpretation cannot be prime.

A (positive) even number is part number \$n\$ such that \$n = 2 cdot k\$ for part (positive) essence \$k\$. A prime number has only itself and \$1\$ together (positive) divisors.

What wake up if \$n ot = 2\$ in our meaning of even numbers?

Pick a element \$p\$. Call a number \$n\$ \$p\$-divisible if \$pmid n\$. Climate \$p\$ is the just \$p\$-divisible prime, trivially. In particular, \$2\$ is the just \$2\$-divisible, or even, prime.

In the integers, \$-2\$ is another even prime.

For variety, in the Gaussian integers, \$2\$ is no prime: e.g. Determinants as \$(1+i)(1-i)\$. The even primes the the Gaussian integers space \$pm 1 pm i\$, back these space all the "same" prime in the very same sense the in the integers, \$2\$ and also \$-2\$ space the "same" prime.

(I specify "even" in a number ar to be tantamount to its share being even)

In the ring of every rational numbers v odd denominator, \$2/7\$ is an also prime. In fact, \$2/n\$ is prime because that every odd creature \$n\$. (but again, these space all the "same" prime)

There are also number rings that have distinct even primes that are not the "same" in the feeling implied above.

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reply Nov 3 "14 in ~ 2:00
user14972user14972
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A element number is such that it is divisible through only itself and also one. Including 1 as a element number would violate the fundamental theory the arithmetic, so in modern brickandmortarphilly.comematics the is excluded. Two is a prime since it is divisible by just two and also one. All the other also numbers space not prime since they are all divisible through two. The leaves only the strange numbers. Of course, not all weird numbers space prime (e.g. Ripe is divisible by three).

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answered january 28 "15 at 8:36

Michael LeeMichael Lee
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The indigenous prime comes from the Latin word primus which means "first." 2 (2) is the very first even number. In other words, that starts all the also numbers. There is much more than one odd prime number since odd number are never ever divisible by 2.

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answer Mar 26 "17 in ~ 0:32
Carly Brooke SteffenCarly Brooke Steffen
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The number \$2\$ has only two whole number factors, \$1\$ and itself. That"s pretty lot it after this: The various other numbers that are even up native two are all divisible by the number in part way. This is additionally known together the "oddest prime" since it"s the only prime number that"s even, for this reason it"s additionally known together the strange one out. Ns guess now that that"s pretty much it going to the question around why this deserve to happen.

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answer Nov 3 "14 in ~ 1:45
brickandmortarphilly.comsterbrickandmortarphilly.comster
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