Understanding Prime Numbers: Definition, Properties, and Python Examples

Prime numbers are the numbers that have only two factors, that are, 1 and the number itself.

Consider an example of number 5, which has only two factors 1 and 5. This means it is a prime number.

Let us take another example of the number 6, which has more than two factors, i.e., 1, 2, 3, and 6. This means 6 is not a prime number.

Now, if we take the example of the number 1, we know that it has only one factor. So, it cannot be a prime number as a prime number should have exactly two factors. This means 1 is neither a prime nor a composite number, it is a unique number.

Prime numbers are the natural numbers (positive integer) greater than 1 with exactly two factors, i.e. 1 and the number itself.

Any whole number greater than 1 that is divisible only by 1 and itself, is defined as a prime number.

Prime Factor

Factors of a number that are prime numbers are called as Prime factors of that number. For example: 2 and 5 are the prime factors of 10.

2 and 3 are the prime factors of 18.

List of Prime Numbers

There are 25 prime numbers from 1 to 100. The complete list of prime numbers from 1 to 100 is given below:

Properties of Prime Numbers

Some of the important properties of prime numbers are given below:

• A prime number is a whole number greater than 1.
• It has exactly two factors, that is, 1 and the number itself.
• There is only one even prime number, that is, 2.
• Any two prime numbers are always co-prime to each other.
• Every number can be expressed as the product of prime numbers.