# Prime Numbers up to 100

The prime numbers up to 100 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, 97. In this article, we will learn more about prime numbers and we will look at how we can find these numbers.

We will represent them on a grid for easy visualization.

##### ALGEBRA

Relevant for…

Learning about the prime numbers up to 100.

See table of numbers

##### ALGEBRA

Relevant for…

Learning about the prime numbers up to 100.

See table of numbers

## Definition of prime numbers

Prime numbers are defined as the numbers that are only divisible by themselves and by 1. This means that if we try to divide them by any other number, the result will not be a whole number. So if we divide a prime number by another number that is not 1 or itself, we will get a remainder.

### EXAMPLES

• 10 is not a prime number since we can divide it by 1, 2, 5 and 10 without getting a remainder.
• 5 is a prime number since we can only divide it by 1 and 5 without getting a remainder.
• 7 is a prime number since we can only divide it by 1 and 7 without getting a remainder.
• 12 is not a prime number since we can divide it by 1, 2, 3, 4, 6 and 12 without getting a remainder.

## Is 1 a prime number?

Another definition of prime numbers is that a prime number must have exactly two factors to be considered a prime number.

The number 1 only has one factor which is itself, therefore, the number 1 is not considered a prime number. If 1 were to be considered a prime number, we would have to redefine some mathematical properties.

## Prime numbers up to 100

To facilitate visualization, we are going to create a table with the prime numbers up to 100.

Let’s start with 2. 2 is a prime number, but all multiples of 2 will be composite numbers since they are divisible by 2. So, we cross out all multiples of 2 from the table.

The next prime number is 3. In the same way, all multiples of 3 will be composite since they are divisible by 3, so we cross them out.

After 3 we have 5. We cross out all multiples of 5 since they are composite numbers.

Then, we have the prime number 7 and we cross out all its multiples.

The next prime number is 11, so we cross out all its multiples 22, 33, 44, 55, 66, 77, 88, 99. All these numbers have already been crossed out, so we finish crossing out all the composite numbers.

This is the list of prime numbers up to 100: 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.

You don’t need to memorize all of these numbers, but it would be helpful if you memorize small prime numbers like 2, 3, 5, 7, 11, 13.

## How many prime numbers are there?

The Greek mathematician Eratosthenes (3rd century BC) came up with a simple method to find all prime numbers up to any certain number. This process is called the sieve of Eratosthenes.

We know that between 1 and 100 there are 25 prime numbers. Also, it has been known since ancient times that there are an infinite number of prime numbers in total, so it is impossible to list all of them.

The largest known prime number as of November 2020 is 282,589,933 − 1. This number was found through computational numerical methods.

Euclid made a proof that there is no single largest prime number and many mathematicians and enthusiasts have continued to search for ever-larger prime numbers.

## Examples of prime numbers

The following are some easy prime number examples and exercises:

### EXAMPLES

• Is 12 a prime number?

Answer: 12 can be divided by 1, 2, 3, 4, 6, and 12 without leaving any remainders. This number is divisible for more than 2 numbers, so it is not a prime number.

• Is 17 a prime number?

Answer: 17 can be divided by 1 and 17 without leaving any remainders. It cannot be divided by 2, 3, 4, 5, 6, 7 or 8 without leaving a remainder. This number is only divisible for 2 numbers, so it is a prime number.

• Is 25 a prime number?

Answer: 25 can be divided by 1, 5, and 25 without leaving any remainders. This number is divisible for more than 2 numbers, so it is not a prime number.

• Is 29 a prime number?

Answer: 29 can be divided by 1 and 29 without leaving any remainders. It cannot be divided by 2, 3, 4, 5, 6, 7, 8, 9, 10, or 11 without leaving a remainder. This number is only divisible for 2 numbers, so it is a prime number.  