## Twin Prime

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### Description

Twin prime numbers are two prime numbers whose difference is 2, and both the numbers are prime numbers.

If both the numbers are prime but the difference is not 2, then the pair of the numbers are not twin prime.

The twin prime numbers are (3, 5), (5, 7), (11, 13) etc.

But (2, 3), (7, 11) these pairs are not twin prime as the difference between two is not 2.

### Algorithm

INPUT: Two Numbers

OUTPUT: Whether the numbers are twin prime or not

PROCESS:

Step 1: [Taking the inputs]

Step 2: [Checking for ‘twin prime’]

Set c<-0

[Checking for twin prime]

If absolute value of (m-n)=2 then

[Checking if m is a prime number]

For i=1 to m repeat

If m mod i=0 then

Set c<-c+1

[End of ‘if’]

[End of ‘for’ loop]

[If the 1st number is prime then check for another number]

If c=2 then

Set c<-0

For i=1 to n repeat

If n mod i=0 then

Set c<-c+1

[End of ‘if’]

[End of ‘for’ loop]

[Checking if n is a prime number]

If c=2 then

Print "The numbers are twin prime"

[If the 2nd number is not prime]

Else

Print "The numbers are not twin prime"

[End of ‘if-else’]

[End of ‘if’]

[If the 1st number is not prime]

Else

Print "The numbers are not twin prime"

[End of ‘else’]

[End of ‘if’]

[If the gap is not 2]

Else

Print "The numbers are not twin prime"

[End of ‘Else’]

Step 3: Stop.

## TIME COMPLEXITY:

for(i=1;i<=m;i++)-------------------------------------O(m)

{

if(m%i==0)----------------------------------O(1)

c++;

}

//if the 1st number is prime then check for another number

if(c==2)--------------------------------------------------O(1)

{

c=0;

for(i=1;i<=n;i++)----------------------------O(n)

{

if(n%i==0)--------------------------O(1)

c++;

}

//checking if n is a prime number

if(c==2)----------------------------------------O(1)

printf("The numbers are twin prime");

//if the 2nd number is not prime

else

printf("The numbers are not twin prime");

}

//if the 1st number is not prime

else

printf("The numbers are not twin prime");

The time complexity of this program is O(m+n) where ‘m’ is the first number and ‘n’ is the second number.

## SPACE COMPLEXITY:

The space complexity of this program is O(1) as it requires a constant number of memory spaces for any given input.