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

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

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.



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.


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.


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 $1$ ?


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.

Thanks because that contributing response to starrkingschool.netematics Stack Exchange!

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

But avoid

Asking because that help, clarification, or responding to various other answers.Making statements based upon opinion; ago them increase with recommendations or personal experience.

Use starrkingschool.netJax to style equations. starrkingschool.netJax reference.

See more: How To Make Salt Water For Hermit Crabs, 16, How To Mix Saltwater

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

article Your price Discard

By clicking “Post her Answer”, you agree to our regards to service, privacy policy and cookie policy

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

Does there exist a composite, deficient, strange number that is divisible through the sum of its suitable factors?
site architecture / logo design © 2021 stack Exchange Inc; user contributions licensed under cc by-sa. Rev2021.11.9.40693

your privacy

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