The various other prime numbers space all odd number such as \$5, 11, 127,\$ and also \$37\$. So, why is \$2\$ the only prime even number over there is?

Is it due to the fact that it only has 1 and itself the way, also though it"s even? check it the end on this great incubadoradeartistas.com web page one-fourth indigenous the bottom.

You are watching: Is 2 the only even prime number

Why is 2 the only even \$(\$binary\$)\$ number that is prime?

For the same reason that three is the only ternary number the is prime. I beg your pardon is the same factor for which 5 is the just quinary number that is prime. Etc.

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

A (positive) also number is some number \$n\$ such the \$n = 2 cdot k\$ for part (positive) creature \$k\$. A prime number has actually only itself and also \$1\$ together (positive) divisors.

What happens if \$n ot = 2\$ in our definition of also numbers?

Pick a element \$p\$. Speak to a number \$n\$ \$p\$-divisible if \$pmid n\$. Then \$p\$ is the only \$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 not prime: e.g. Factors as \$(1+i)(1-i)\$. The also primes that the Gaussian integers room \$pm 1 pm i\$, back these space all the "same" element in the very same sense the in the integers, \$2\$ and also \$-2\$ room 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 through odd denominator, \$2/7\$ is an even prime. In fact, \$2/n\$ is prime because that every odd essence \$n\$. (but again, these room all the "same" prime)

There are likewise number rings the have distinct even primes that space not the "same" in the sense implied above.

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answer Nov 3 "14 in ~ 2:00
user14972user14972
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A element number is such that it is divisible by only itself and one. Consisting of 1 as a prime number would certainly violate the an essential theory that arithmetic, so in contemporary incubadoradeartistas.comematics that is excluded. 2 is a prime since it is divisible by just two and also one. All the other also numbers are not prime due to the fact that they space all divisible by two. The leaves just the odd numbers. The course, no all odd 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 native prime originates from the Latin native primus which method "first." 2 (2) is the first even number. In other words, the starts every the even numbers. There is more than one odd element number because odd number are never ever divisible by 2.

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reply Mar 26 "17 at 0:32
Carly Brooke SteffenCarly Brooke Steffen
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The number \$2\$ has only two entirety number factors, \$1\$ and itself. That"s pretty much it after this: The various other numbers the are also up from two are all divisible by that number in part way. This is likewise known together the "oddest prime" since it"s the only prime number that"s even, therefore it"s likewise known as the strange one out. I guess now that that"s pretty lot it going come the question about why this can happen.

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answered Nov 3 "14 in ~ 1:45
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