[[Number theory MOC]]
# Prime number

A natural number $n \in \mathbb{N}$ is called **prime** iff it has exactly two divisors in $\mathbb{N}$,
namely one and itself.[^one]  #m/def/num 
The first 25 primes are
$$
\begin{align*}
2,3,4,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97, \dots
\end{align*}
$$
Prime numbers admit generalizations to two different concepts in the setting of a ring:
The [[Irreducible element]] and the [[Prime element]].

[^one]: It follows that $1$ is not prime.


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