I"ve heard stories around why the number $1$ is no a prime number nor a composite number, even on in the middle of this awesome starrkingschool.net page.

You are watching: Why is 1 neither prime nor composite

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Anyway, let"s reduced to the chase. Just how come $1$ isn"t a prime number or even a composite number? I want to know from your great-heard-of answers! At least I recognize that a prime number has only 2 factors, $1$ and itself. So, why isn"t this the same for $1$? It has actually a variable of $1$, i beg your pardon is likewise itself, $1$. I desire to hear around this, too.


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Because if it were prime, climate the element factorization of numbers wouldn"t it is in unique. For this reason it"s characterized as not-prime.


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Because $1$ is a unit in $Bbb Z$. In every ring, in certain in every UFD you have actually units and nonunits. It is the nonunits that room factored right into irreducible (=prime) determinants times units, but one doesn"t element units. Distinct factorization is unique up come unit multipliers, since one can add an arbitrary unit times its inverse, and also still gain a an excellent factorization.


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The main handy idea behind primes is to remove all your multiples as composites, check out sieve the Eratosthenes. What would take place if us were to apply this reasoning to the number $1$ ?


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For a number to it is in a prime number it must have two determinants one and it"s self, yet with 1 only 1 times one is 1, so it only has one factor, thus making it no a element number.


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