Прості числа (зв'язок із теорією чисел)

Natural numbers are very social, you know? They love to form relationships with one another. (And thus it becomes our job, as number theorists, to discover those relationships.)

One of the fundamental relationships among the natural numbers is called divisibility. Well, what is it? Easy. If a natural number $a$ divides another natural number $b$ without reminder, we say that $b$ is divisible by $a$. For example, $100$ is divisible by $5$, but $9$ is not. We also say $5$ is a divisor of $100$. Well, $100$ has other divisors too, for example, $10$, $20$ etc.

In terms of divisibility, there is an elite class of natural numbers, each of which accepts only $1$ and itself as its divisors. We named these numbers primes. For example, $5$ is a prime. What are its divisors? $1$ and $5$ only. Therefore, $5$ is indeed a prime.

List of first a few primes: $$2,3,5,7,11,13,17,19,23,29,31,37,41,43,47$$