Basically, a prime number is a natural number that has only two divisors or factors: 1 and the same number. That is, the number that can be divided by one and by the same number is a prime.
The first prime number is 2, and there are 25 prime numbers between 1 and 100, they are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.
Let’s look at a simple example:
As we said, 2 is prime because it can be divided by 1 and 2, respectively. So is 3 (it can divide by itself and by 1, but not by 2) and 5 (it can divide by itself and by 1, but not by 2, not by 3, not by 4).
Now why is 4 not a prime number? Very easy, because 4 can be divided by itself, by 1, but also by 2 since 4/2 = 2 and therefore does not fulfill the characteristic that would make it a prime.
The property for a number to be prime (again, the ability to be only divisible by 1 by itself) is known as primality. As a curiosity you should know that all the only prime numbers are odd except 2, this is quite obvious since from 4 all of them can be divided, at least, by 2 because they are even.
The Prime numbers they are useful for finding the factors of any natural number. A factor is the number that a natural number can be divided into. Think of this as “is divisible by.” Example:
The factors of 14 are 14, 7, 2, 1, since 2 x 7 = 14, and 1 x 14 = 14.
Currently, the mathematical community is inclined not to consider 1 in the list of prime numbers. This was already defined by a convention where it is tried to emphasize that prime numbers only have two factors, the number itself and 1. Therefore, 1 is not considered a prime number, since it only has one factor, 1.
But this was not always the case, in fact until the 19th century mathematicians mostly considered it a cousin. Many mathematical works are still valid despite considering 1 as a prime number as several huge lists of published primes beginning with 1.
Prime numbers have many applications in advanced mathematics, especially when used as factors of other numbers. Numbers that are not prime can be divided into prime factors. For example, the factors of 12 in 4 x 3, can be divided into prime factors like this, 2 x 2 x 3.