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.

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Does over there exist a composite, deficient, weird number that is divisible by the sum of its ideal factors?

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