# Prime, Composite Numbers and Their Arrangements

Found in topics: Numbers

## What is Prime Number?

Any Natural number greater than 1, which is divisible by 1 and only by itself is called Prime Number.

Example

2, 3, 5, 7, 11 etc.

Note

2 is the smallest Prime Number.

## Arrangement of prime numbers

Prime numbers can be arranged in a line form like shown as below in the diagram.

Arrangement of prime numbers

## What is composite number?

Any Natural number, which is greater than 1 and is not a Prime Number is called a Composite Number.

Example

4, 6, 8, 9, 10 etc.

Note

1 is neither a Prime Number nor Composite Number.

Note

Every number in maths can either be a prime or a composite number except 0 and 1 because 0 and 1 are neither a prime number nor a composite number.

## Arrangement of composite numbers

Composite numbers can be arranged in a rectangular or square form like shown as below in the diagram.

Arrangement of composite numbers

## What are coprimes?

Two numbers are called to be coprime or co-prime if they have only 1 as a common factor.

In other way, we can say if greatest common divisor of two numbers is 1, then the two numbers are coprimes.

Example

(2,3), (14,15), (8,13) etc.

## What is twin prime?

Two numbers are called Twin Prime if they differ by 2 only or we can say that there is only one composite number between them. One prime number can be 2 more or 2 less than another prime number.

Example

(3,5), (29,31), (71,73) etc.

## What are prime triplets?

A set of three consecutive Prime Numbers if the smallest and the largest differ by 6 and must be in the form of (p, p + 2, p + 6) is called a Prime Triplet.

Example

(5,7,11)
Why?
Because, 5, 7 and 11 is in the form of p, p + 2, p + 6
where p = 5
p + 2 = 5 + 2 = 7
and p + 6 = 5 + 6 = 11

## Solved Examples

### 1) Check whether the following numbers are prime numbers or composite numbers. 142, 211, 291, 323, 247

a) 142 is a composite number because it is divisible by 2.
b) 211 is a prime number.
b) 291 is a composite number because it is divisible by 3.
d) 323 is a composite number because it is divisible by 17.
e) 427 is a composite number because it is divisible by 7.

### 2) List all pair of twin primes between 50 and 100.

(59, 61) and (71, 73) are thw twin primes between 50 and 100.

### 3) Find the seven consecutive composite numbers less than 100 and there should be no prime numbers between them.

90, 91, 92, 93, 94, 95, 96

### 4) Write the only prime number between 90 and 100.

97 is the only prime number between 90 and 100.

### 5) Write all even prime numbers between 1 and 100.

2 is the only prime numbers between 1 and 100.

### 6) Write all prime numbers less than 50.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47 are the prime numbers which are less than 50.

### 7) Write all pair of twin primes between 1 and 100.

The following pairs are the twin primes between 1 and 100. (3, 5)
(5, 7)
(11, 13)
(17, 19)
(29, 31)
(41, 43)
(59, 61)
(71, 73)

### 8) Write the total number of prime numbers between 1 and 100.

The total number of prime numbers between 1 and 100 are 25.

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twin
coprime
3
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25
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## Worksheet 2

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### Multiple choice questions

a) 91

b) 97

c) 99

d) 93

a) 97

b) 99

c) 93

d) 98

a) prime

b) composite

c) twin

d) unique

a) consecutive

b) twin

c) unique

d) odd

a) 2

b) 3

c) 1

d) 4

a) 1

b) 2

c) 5

d) 7

a) 41 and 43

b) 71 and 73

c) 53 and 59

d) 11 and 13

a) 3 and 17

b) 17 and 68

c) 14 and 16

d) 13 and 91

a) 8

b) 10

c) 12

d) 6

#### 10) The prime numbers between 70 and 80 are

a) 72, 73, 74

a) 71, 72, 73

a) 71, 74, 79

a) 71, 73, 79

Last updated on: 30-06-2024