Prime numbers are numbers that are only divisible by two divisors: one and itself. The number one is not a prime number. There are multiple types of primes numbers but they all have this in common. In theory, there are an infinite amount of prime numbers and there will always be another larger prime number then the largest one we know today. The following is the example of the first fifty prime numbers in order:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29,

31, 37, 41, 43, 47, 53, 59, 61, 67, 71,

73, 79, 83, 89, 97, 101, 103, 107, 109, 113,

127, 131, 137, 139, 149, 151, 157, 163, 167, 173,

179, 181, 191, 193, 197, 199, 211, 223, 227, 229,

233, 239, 241, 251, 257, 263, 269, 271, 277, 281

To find prime numbers you only need to try dividing by all of the whole numbers between one and the number itself. The example is as follows:

Is 7 a prime number? Yes

7 2 = 3.5

7 3 = 2.3333…

7 4 = 1.75

7 5 = 1.4

7 6 = 1.16666…

As you can see, if you are trying to solve a very large number you might want to cut down on the amount of work that you need to do. There are two simple tips that you can use to to cut down on how much work you have to do to find a if a number is prime or not is by dividing the number by only prime numbers and no numbers more then half of that number. So the work to figuring out if seven is a prime number reduces to the following:

Is 7 a prime number? Yes

7 2 = 3.5

7 3 = 2.3333…

The reasoning behind why theses two methods work is simple. If you take a number and divide it by two, there is no way a number higher then that number will be divisible by two and be a whole number as the result. The reasoning for why the prime numbers to divide by is simple. If you find a number that is not prime, the prime number that is divisible by that number is also divisible by the number you are trying to solve.

With prime numbers there are also many other types of primes. These are only the most simple to remember of the many there are out there.

Balanced Primes

These are primes which are the average of the previous and following primes.

Emirps

When you are able to reverse the numbers of a prime to create another prime number.

Even Prime

The only even prime is two.

Odd Primes

This is determined by any prime number greater then two which is essently every prime but two.

Repunit Primes

These are prime numbers that only have the digit one used in them.