When talking around prime numbers, it seems favor the examples given $(2,3,5,7,11,13,...)$ have the residential or commercial property that they have no factors less than themselves and also greater than one. However $0$ also has this property, so is it prime? If not, why not?

Is zero odd or even?

When talking about even numbers, it seems prefer the examples given $(2,4,6,8,...)$ have the property that, when separating them by $2,$ have a non-zero quotient and a zero remainder; odd numbers $(1,3,5,7,...)$ have actually a non-zero quotient and a remainder the $1.$ So, is $0$ odd? even? neither odd no one even?

Is zero a number?

I"ve heard that every number is either odd or even, but if $0$ is neither odd nor even, go that typical it isn"t also a number?

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edited Dec 28 "18 in ~ 11:57

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If you space willing to accept the integers together numbers, then you should have no problem considering $0$ a number. Because that one willing to specify even numbers as "integer multiples the $2$" climate it"s an in similar way clear that $0$ must be taken into consideration even. I don"t desire to invest a lot of an are here rehashing the evenness that $0$ because there are currently questions devoted to that problem, however fortunately that renders it straightforward to straight you to the answer: Is zero strange or even?

I"ve additionally found some more discussions top top the "numberness that zero" the you might find useful: What's the hard part of zero? , Why do some world state that 'Zero is no a number'?

The question as to whether or no it need to be taken into consideration prime is an ext interesting.

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What have to primes be?

After you learn about divisibility and factorization, this idea arises about breaking number down into smaller components (sort of favor describing issue with smaller and smaller parts). Divisibility provides a partial order top top the nonegative integers. This just way that due to the fact that $12=3cdot 4$, the "smaller parts" 3 and also 4 separating 12, we have the right to record this together $3prec 12$ and also $4prec 12$. Furthermore $2prec 4$ due to the fact that $2$ divides $4$, and so on. Due to the fact that $1$ divides everything, we would certainly say that $1prec n$ for any kind of nonegative essence $n$.

In physics, we room interested in the smallest things from which everything is developed from (the "atoms"!). The idea the atoms has two parts:

they have to all be "small"they should build everything else

Well, us can"t allow $1$ be together a thing, since it would certainly be the only smallest thing, and moreover girlfriend can"t develop anything indigenous $1$ alone. So that is in a sense, also simple.

The next finest candidates space those things just above $1$. What just above means becomes fingerprint if you draw a picture:


This is a kind of Hasse diagram because that the nonnegative integers partially ordered through divisibility. Since the chart is infinite it"s not really a Hasse diagram, and the lines come zero don"t yes, really come from any type of numbers, yet this is great for our purposes.

From the diagram friend can easily see the the primes lied in the very first row above $1$, and so they are "as tiny as possible" without gift $1$, and moreover, everything over them (excepting zero) is built out of miscellaneous combinations of the primes. The gradeschool definition of prime number basically quantities to the fact that naught lies in between $1$ and also $p$ for each prime.

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Zero, paradoxically, is yes, really aloof and nowhere close to the remainder of the primes: that doesn"t it seems to be ~ very small after all. Additionally he is quite useless for building numbers because $0n=0$ for any $n$.

So for reasons favor these, $0$ is not taken into consideration as a prime: the doesn"t make a an excellent "atom."