Prime Numbers and Their properties

Prime Numbers and Their properties

In mathematics, there are various types of numbers such as natural numbers, whole numbers, real numbers, and so on. Similarly, a prime number is a type of number which consists of exactly two factors, the number itself and the number 1. For example, number 5 consists of two factors, 1 and 5, thus ‘5’ is a prime number. The great Greek mathematician Euclid proposed the term of a prime number. Some of the examples of it are as follows: 3, 5, 7, 11, 13, 17, 19, 23, etc. The number ‘1’ is not considered to be a composite of prime numbers because it consists of only one factor. In this article, we will try to cover some related topics such as its properties of it, carry out the comparison from real numbers, and do a detailed analysis about them. 

Real Numbers

The numbers which are found in the mathematical world except the complex numbers can be defined as real numbers. It includes numbers such as rational numbers, irrational numbers, fractions, positive integers along negative. The real numbers are denoted with the help of the alphabet ‘r’. Every function of the numbers mentioned above will automatically be the function of real numbers. For example, rational numbers are used to represent any fraction, integers are used to calculate the length or measure temperature, numbers that are natural are used to count objects. In the next few sections, we will cover the types of real numbers, comparison between real and prime numbers. 

Types of Real numbers 

As mentioned above, numbers that are found in the mathematical world except the complex numbers can be defined as real numbers. Therefore, we can assume that there are numerous types of real numbers. The following are the types of real numbers.

  • The numbers which can be expressed in the form of p/q or a/b or x/y where the q is not equivalent to zero can be defined as the rational number. 
  • The numbers which cannot be expressed in the form of a simple fraction can be defined as irrational numbers. 
  • A type of number which consists of every integer that is positive and 0 can be regarded as the whole number.
  • The types of numbers which are used for counting and ordering are known as natural numbers.
  • Any number which can be represented without a fraction can be defined as the integers. 

Some Important Properties of Prime Numbers 

The prime numbers are the types of numbers that consist of only two factors, 1 and the number itself. The following are the properties of prime numbers.

  • A prime number exactly contains two factors. For example, let us consider the number ‘3’, if we calculate the factors of it we will find that there are two factors, 1 and 3 itself. Therefore, 3 is a prime number. 
  • There is a very unique number ‘2’ which is an even prime number. Except, the number two there are no even numbers that are prime. 
  • Whenever you talk about the prime number, we must not forget that two numbers which are prime are always coprime to one another. 

Some Differences Between Prime Numbers and Real Numbers

  1. A prime number is a type of number which consists of exactly two factors, the number itself and the number 1 whereas real numbers are the numbers that contain each and every type of number except complex numbers.
  2. Some examples of Prime numbers are as follows: 3, 7, 9, 13, 17, etc. Some examples of Real numbers are as follows: Rational numbers, irrational numbers, and many more. 

If you want to learn about prime numbers and real numbers in a detailed, fun, and interactive manner, visit Cuemath. 

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