## What are Prime Numbers?

Every prime number has exactly 2 factors. The numbers that have factors 1 and number itself are known as prime numbers. The prime number is known to be the simplest of a number. Let us see a few examples of prime numbers and the list of prime numbers from 1 to 1000.

For example, let us take a number for example 11. It can be written as 11 × 1 and 1 × 11. There is no other way of writing the number 11. So the factors of number11 are 1 and 11. So, we can say that 11 is a prime number. Similarly, we can say for the numbers 2, 3, 5, 7, 13, 17, … etc can only be written in two forms with a single factor as 1, hence are the prime numbers.

Each prime number is only divisible by the number 1 and itself. This means that number 1 can never be a prime number. So any prime number should have only two factors and the number should be greater than 1.

### History of Prime Numbers

The prime number was discovered by Eratosthenes (275-194 B.C.). Eratosthenes took the example of a sieve to filter out the prime numbers from a list of natural numbers and drain out the composite numbers.

Students can practice this method, by writing the positive integers from the numbers 1 to 1000 and circling the prime numbers, and putting a cross mark to all the composite numbers.

### Properties of Prime Numbers

Some of the properties of prime numbers are:

Every number that is greater than 1 can be divided by at least one prime number.

Every even positive integer greater than the number 2 can be expressed as the sum of two primes.

Except for number 2, all other prime numbers are odd. In other words, we can say that two is the only even prime number.

Two prime numbers are coprime to each other.

## Difference Between Prime Numbers and Composite Numbers

Here’s the list of prime numbers from 1 to 1000. There are a total 168 prime numbers in the list of prime numbers from 1 to 1000.

## List of Prime Numbers Prime Numbers From 1 to 1000

### Composite Numbers

Composite numbers are numbers that have at least one factor other than the number itself and 1. Let’s look at a few examples.

Let us take a number say 4. It can be written as 4 × 1, 1 × 4, and 2 × 2 So the factors of 4 are 1, 2, and 4. Therefore, we can say that 4 is a composite number as it has only 2 factors.

Now, let us take a number, say 6, that can be written as 6 × 1, 1 × 6, 2 × 3, and 3 × 2. So, the factors of number 6 are 1, 2, 3, and 6. Therefore, we can say that number 6 is a composite number.

Let us take a number say 8. The number 8 can be written as 8 × 1, 1 × 8, 2 × 4, and 4 × 2. So the factors of 8 are 1, 2, 4, as well as 8. Therefore, we can say that number 8 is a composite number.

Question 1) Which are the Prime Numbers?

Answer) Prime numbers are known to be the numbers that have only 2 factors: 1 and themselves. For example, the first 5 prime numbers are here 2, 3, 5, 7, and 11. By contrast, numbers with more than 2 factors are known as composite numbers.

Question 2) What are the Prime Numbers From 1 to 1000?

Answer) When a number has more than two factors it is known as a composite number. The first few prime numbers are as follows: 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, and 199, etc.

Question 3) Why is 11 Not a Prime Number?

Answer) For number 11, the answer is that the given number is a prime number as the number 11 has only two distinct divisors that is: 1 and itself (11). As a consequence, 11 is only a multiple of the number 1 and 11.

Question 4) What are the Properties of Prime Numbers?

Answer) Some of the properties of prime numbers are:

Every number that is greater than 1 can be divided by at least one prime number.

Every even positive integer greater than the number 2 can be expressed as the sum of two primes.