## 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.

**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.

#### Factors Of Some Prime Numbers

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

#### CONCLUSION OF THIS ARTICLE ON PRIME NUMBERS

Prime numbers are those numbers which have the ability to represent the factorization of any non-zero natural number. These factors can be of the same type. Hence it is also called the Fundamental Theorem of Arithmetic.

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