The number that has only two factors that are 1 and the number itself is defined as a prime number. Let us take an example, consider a number, let’s say ‘3’ which contains two factors 1 and the number itself, thus ‘3’ is a prime number. But all real numbers are not prime numbers. For example, 1 which is a real number but not a prime number because it has only one factor that is the number itself. These kinds of numbers are regarded as unique numbers and it will be interesting to learn about them.
Properties of Prime Numbers
There are a lot of important properties of prime numbers. Some of them are as follows:
- It is a whole number greater than 1.
- It has exactly two factors, 1 and the number itself.
- There is only one even prime number amongst all real numbers that is 2.
- There are various numbers which can’t be expressed as the product of prime numbers.
- Any two prime numbers are always coprime to one another.
What Are Real Numbers?
Any number that we can think of except the complex numbers are regarded as real numbers. Real numbers include rational numbers, irrational numbers, positive integers, and negative integers, etc. The set of real numbers is symbolized by the capital letter R. The multiplication and addition of two real numbers will always form into a real number. This property is known as closure property. The sum and product of two or more than two real numbers always remain the same even after changing the orders of numbers. This is known as commutative property. There are various other properties of real numbers as well.
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Subsets of Real Numbers:
Real numbers are of various types. Only the complex numbers are excluded from this category. The following are the subsets of real numbers:
- Natural numbers: The numbers that are positive counting makes the set of natural numbers. For example, 1,2,3 ….
- Whole Numbers: All natural numbers including 0 makes the set of whole numbers. For example, 0,1,2,3…
- Rational Numbers: Any number that can be written in the form of p divided by q where p and q are positive integers and q is not equal to zero is known as a rational number. For example, -3, -6 etc.
- Irrational Numbers: They are the types of real numbers which cannot be represented as a simple fraction. For example, √2, √6 etc.
- Integers: Every positive number, negative numbers and zero make up to the set of integers. For example, -3, -2, -1, 1,2,3,0 etc.
History of Real Numbers and Prime Numbers
Since ancient times, these numbers have been the topic of curiosity. The Greek mathematicians around 500 BC led by the very famous scientist Aristotle realized the need for irrationality and started working on it. Indian and Chinese mathematicians around the Middle Ages brought the acceptance of zero, prime numbers, negative numbers, and integers. In the 17th century, Descartes introduced the term real to describe roots of a polynomial and distinguished it from the imaginary ones. We can see that, now-a-days various scientists use their time in finding out different prime numbers with mystical properties. Euclid proposed a theorem on prime numbers that there are indefinite kinds of these numbers. There was a great polymath named Eratosthenes. He designed a unique and a smart way to determine all the prime numbers. This method of determining prime numbers is known as the Sieve of Eratosthenes