# What Are Prime Numbers In Maths

## What Are Prime Numbers In Maths

What are prime numbers in mathematics - In mathematics, numbers are classified in many bases. But in the number system of mathematics, on the basis of factors, the number has been classified as three types.

Composite Number

Prime Number

Co-prime Number

In this mathematical article, we will study prime numbers in detail. But before that let us take brief information about composite numbers and co-prime numbers as well.

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CLASSIFICATION OF NUMBERS ON THE BASIS OF FACTORS

### What Are Prime Numbers In Maths?

A number which is divisible by 1 and any number other than itself is called a composite number. Such a number has 2, 3 or more factors. For example – 4, 6, 8, 9, 10 etc.

#### Form of Factors of Some Composite Numbers

4 = 2 × 2, 1 × 4

6 = 2 × 3, 1 × 6

8 = 2 × 2 × 2, 1 × 8

18 = 2 × 3 × 3, 1 × 18

#### What Are Prime Numbers Called?

A number which is not divisible by any natural number other than 1 and itself is called a prime number. Such a number has only 2 factors. Eg – 2, 3, 5, 7, 11 etc.

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2 = 2 × 1

3 = 3 × 1

7 = 7 × 1

19 = 19 × 1

31 = 31 × 1

### What Are Co-Prime Numbers Called?

Co-prime means a number which is divisible by the same number at the same time. It means – Those two numbers of a pair whose HCF is only 1 are called co-prime numbers. like -

(7,13) = 1

(17, 19) = 1

(41, 47) = 1

Any two consecutive numbers are also called co-prime numbers. like -

(41, 42)

(17, 18)

(36, 37)

Some special things related to numbers 0, 1 and 2

The numbers 0 and 1, based on mathematical principles, are neither composite nor prime.

2 is the smallest prime number.

2 is the only even prime number.

A pair with 0 as a co-prime number has only 1 or –1.

### STUDY OF PRIME NUMBERS

#### What Is The Mathematical Definition Of A Prime Number?

Prime numbers are those positive and integer numbers which cannot be divided by any other natural number except 1 and the same number.

Prime numbers are also called prime numbers. It does not have 1 in its factorization and any number other than that number itself.

For example,

23 = 1 × 23

37 = 1 × 37

59 = 1 × 59

If we pay attention to any one number in these examples, then we will understand its definition easily.

For example, 37 is a prime number, which cannot be divided by any number other than 1 and 37 itself. Hence, 1 × 37 is its factor. Only 1 and 37 itself is its coefficient.

### SOME IMPORTANT FACTS RELATED TO PRIME NUMBERS

Prime numbers are always greater than 1.

They are always in positive and integer form.

The method of finding the prime number is called factorisation.

It has only 2 factors.

2 is the smallest unit of prime number.

All prime numbers except 2 are odd.

0 and 1 are not considered prime numbers.

The number of prime numbers is infinite.

As of now discovered, 82589933 is the largest prime number.

The definition of prime number applies only to natural numbers.

There is no fixed rule for prime numbers, they have to be derived by definition.

### LIST OF PRIME NUMBERS IN THE NUMBER SERIES FROM 1 TO 100

The total number of prime numbers in the natural numbers from 1 to 100 is only 25.

2 3 5 7 11

97 13 17 19 23

29 31 37 41 43

47 53 59 61 67

71 73 79 83 89

#### Law Of Prime Numbers – How To Find Prime Numbers?

Well, there is no fixed or written rule for prime numbers. But still, there are 2 methods by which a prime number can be found. Most of these methods prove to be correct.

#### FIRST METHOD OF FINDING PRIME NUMBER

For prime numbers, 2 formulas are used in the first method.

6n + 1

6n – 1

The first 13 prime numbers can be found from these 2 formulas. Here n can be 1, 2, 3… etc. Let us understand this with some examples.

6 × 1 + 1 = 7 6 × 1 – 1 = 5

6 × 2 + 1 = 13 6 × 2 – 1 = 11

6 × 3 + 1 = 19 6 × 3 – 1 = 17

6 × 4 + 1 = 25 6 × 4 – 1 = 23

6 × 5 + 1 = 31 6 × 5 – 1 = 29

#### SECOND METHOD OF FINDING PRIME NUMBERS

This method is not like a written formula, but just a trick. This is done to find only the first 39 numbers greater than 40.

Its formula is: n2 + n + 41

Here n = 1, 2, 3 ... 39. Let us see some examples of this as well.

(0)2 + 0 + 0 = 41

(1)2 + 1 + 41 = 43

(2)2 + 2 + 41 = 47

(3)2 + 3 + 41 = 53

(4)2 + 4 + 41 = 61

(5)2 + 5 + 41 = 71