I"ve heard stories about why the number $1$ is no a element number no one a composite number, also on in the center of this awesome mmsanotherstage2019.comematics page.

You are watching: Are there any numbers that are neither prime nor composite

Just scroll under to the middle to read around it. It"s a little bit short.

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



Because if it to be prime, then the element factorization of number wouldn"t be unique. For this reason it"s characterized as not-prime.


Because $1$ is a unit in $Bbb Z$. In every ring, in particular in every UFD you have units and also nonunits. That is the nonunits that space factored into irreducible (=prime) components times units, yet one doesn"t element units. Distinct factorization is distinctive up to unit multipliers, since one can include an arbitrarily unit times its inverse, and still gain a great factorization.


The main practical idea behind primes is to remove all their multiples together composites, watch sieve that Eratosthenes. What would take place if we were to apply this reasoning to the number $1$ ?


For a number to it is in a element number that must have two components one and it"s self, however with 1 only 1 times one is 1, so it only has actually one factor, therefore making it not a prime number.

Thanks because that contributing response to mmsanotherstage2019.comematics Stack Exchange!

Please be sure to answer the question. Provide details and share her research!

But avoid

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

Use mmsanotherstage2019.comJax to format equations. mmsanotherstage2019.comJax reference.

See more: 2004 Chevy Cavalier Gas Tank Size Of Gas Tank 2004 Chevy Cavalier

To discover more, view our advice on writing great answers.

write-up Your prize Discard

By click “Post your Answer”, friend agree come our terms of service, privacy policy and also cookie policy

Not the price you're feather for? Browse other questions tagged elementary-number-theory or ask your own question.

Does over there exist a composite, deficient, weird number that is divisible by the sum of its ideal factors?
site style / logo design © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.11.16.40760

her privacy

By click “Accept all cookies”, girlfriend agree stack Exchange have the right to store cookies on your device and disclose details in accordance through our Cookie Policy.