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# Check if a number is prime or not

Introduction:

In mathematics, a prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, a prime number has only two factors: 1 and itself. Determining whether a given number is prime or not is a common problem in mathematics and computer science.

Problem Statement:

We want to write a program that checks whether a given number is prime or not. The program should take an input number and output whether it is a prime number or not.

Example:

Let's consider an example to understand the concept better. Suppose we have a number 37. We want to check if it is prime or not.

Algorithm:

The algorithm to determine whether a number is prime or not can be explained as follows:

1. Start by checking if the number is less than or equal to 1. If it is, then it is not prime.
2. Check for some base cases where the number is known to be prime (e.g., 2, 3, 5). Return true if the number matches any of these cases.
3. Iterate from n/2 to 2 and check if the number is divisible by any of these values. If it is divisible, then it is not prime.
4. If none of the above conditions are satisfied, then the number is prime.

Pseudocode:

``````function is_prime(n):
if n <= 1:
return false
if n is 2 or 3 or 5:
return true
for i from n/2 to 2:
if n is divisible by i:
return false
return true

function prime_number(number):
if is_prime(number):
print number, "is a prime number"
else:
print number, "is not a prime number"```
```

Explanation:

The program starts by defining a function `is_prime` that takes a number `n` as input. It checks if the number is less than or equal to 1 and returns false in such cases. Then it checks for the base cases where the number is known to be prime (2, 3, and 5) and returns true if the number matches any of these cases. Next, it iterates from `n/2` to 2 and checks if the number is divisible by any of these values. If it is divisible, then it returns false, indicating that the number is not prime. If none of the conditions are satisfied, it returns true, indicating that the number is prime.

The `prime_number` function takes a number as input and calls the `is_prime` function. If the `is_prime` function returns true, it prints that the number is a prime number; otherwise, it prints that the number is not prime.

## Code Solution

Here given code implementation process.

``````//C Program
//Check if a number is prime or not
#include <stdio.h>

int is_prime(int n)
{
if(n<=1)
{
return 0;
}
//Base case
if(n==2 || n ==3 || n==5)
{
return 1;
}
//Check divisibility of a number
for (int i = n/2; i > 1 ; --i)
{
if(n%i == 0)
{
return 0;
}
}

return 1;
}

void prime_number(int number)
{

if(is_prime(number)==1)
{
printf("%d is a prime number\n",number );
}
else
{
printf("%d not a prime number\n",number );
}

}

int main()
{
prime_number(37);
prime_number(46);
return 0;
}```
```

#### Output

``````37 is a prime number
46 not a prime number``````
``````#include<iostream>

using namespace std;
/*
C++ Program
Check if a number is prime or not
*/
class MyNumber {
public:
bool is_prime(int n) {
if (n <= 1) {
return false;
}
//Base case

if (n == 2 || n == 3 || n == 5) {
return true;
}
for (int i = n / 2; i > 1; --i) {
//Check divisibility of a number

if (n % i == 0) {
return false;
}
}
return true;
}
void prime_number(int number) {
if (this->is_prime(number)) {
cout << number << " is a prime number\n";
} else {
cout << number << " number not a prime number\n";
}
}
};
int main() {
MyNumber obj;
//Test case
obj.prime_number(37);
obj.prime_number(46);
return 0;
}```
```

#### Output

``````37 is a prime number
46 number not a prime number``````
``````/*
Java Program
Check if a number is prime or not
*/

public class MyNumber {

public boolean is_prime(int n)
{
if(n<=1)
{
return false;
}
//Base case
if(n==2 || n ==3 || n==5)
{
return true;
}

for (int i = n/2; i > 1 ; --i)
{
//Check divisibility of a number
if(n%i == 0)
{
return false;
}
}

return true;
}

public void prime_number(int number)
{

if(is_prime(number))
{
System.out.print(number+" is a prime number\n");
}
else
{
System.out.print(number+" number not a prime number\n");
}

}

public static void main(String[] args) {

MyNumber obj = new MyNumber();
//Test case
obj.prime_number(37);
obj.prime_number(46);

}
}```
```

#### Output

``````37 is a prime number
46 number not a prime number``````
``````/*
C# Program
Check if a number is prime or not
*/
using System;
public class MyNumber {

public Boolean is_prime(int n) {
if (n <= 1) {
return false;
}
//Base case
if (n == 2 || n == 3 || n == 5) {
return true;
}

for (int i = n / 2; i > 1; --i) {
//Check divisibility of a number
if (n % i == 0) {
return false;
}
}

return true;
}

public void prime_number(int number) {

if (is_prime(number)) {
Console.Write(number + " is a prime number\n");
} else {
Console.Write(number + " number not a prime number\n");
}

}

public static void Main(String[] args) {

MyNumber obj = new MyNumber();
//Test case
obj.prime_number(37);
obj.prime_number(46);

}
}```
```

#### Output

``````37 is a prime number
46 number not a prime number``````
``````# Python 3 Program
# Check if a number is prime or not
class MyNumber :
def is_prime(self, n) :
if (n <= 1) :
return False

#Base case
if (n == 2 or n == 3 or n == 5) :
return True

i = n / 2
while (i > 1) :
#Check divisibility of a number
if (n % i == 0) :
return False

i -= 1

return True

def prime_number(self, number) :
if (self.is_prime(number)) :
print(number ," is a prime number\n")
else :
print(number ," number not a prime number\n")

def main() :
obj = MyNumber()
obj.prime_number(37)
obj.prime_number(46)

if __name__ == "__main__":
main()```
```

#### Output

``````37 is a prime number
46 number not a prime number``````
``````# Ruby Program
# Check if a number is prime or not
class MyNumber
def is_prime(n)
if (n <= 1)
return false
end
#Base case

if (n == 2 or n == 3 or n == 5)
return true
end
i = n / 2
while (i > 1)
#Check divisibility of a number

if (n % i == 0)
return false
end
i -= 1
end
return true
end
def prime_number(number)
if (self.is_prime(number))
print(number ," is a prime number\n")
else
print(number ," number not a prime number\n")
end
end
end
def main()
obj = MyNumber.new()
obj.prime_number(37)
obj.prime_number(46)
end
main()```
```

#### Output

``````37 is a prime number
46 number not a prime number
``````
``````/*
Scala Program
Check if a number is prime or not
*/
class MyNumber {
def is_prime(n: Int): Boolean = {
if (n <= 1) {
return false;
}
//Base case

if (n == 2 || n == 3 || n == 5) {
return true;
}
var i: Int = n / 2;
while (i > 1) {
//Check divisibility of a number

if (n % i == 0) {
return false;
}
i -= 1;
}
return true;
}
def prime_number(number: Int): Unit = {
if (this.is_prime(number)) {
print(s" \$number is a prime number\n");
} else {
print(s" \$number not a prime number\n");
}
}
}
object Main {
def main(args: Array[String]): Unit = {
var obj: MyNumber = new MyNumber();obj.prime_number(37);obj.prime_number(46);
}
}```
```

#### Output

`````` 37 is a prime number
46 not a prime number``````
``````/*
Swift 4 Program
Check if a number is prime or not
*/
class MyNumber {
func is_prime(_ n: Int) -> Bool {
if (n <= 1) {
return false;
}
//Base case

if (n == 2 || n == 3 || n == 5) {
return true;
}
var i: Int = n / 2;
while (i > 1) {
//Check divisibility of a number

if (n % i == 0) {
return false;
}
i -= 1;
}
return true;
}
func prime_number(_ number: Int) {
if (self.is_prime(number)) {
print(number ," is a prime number");
} else {
print(number ," number not a prime number");
}
}
}
func main() {
let obj: MyNumber = MyNumber();
obj.prime_number(37);
obj.prime_number(46);
}
main();```
```

#### Output

``````37  is a prime number
46  number not a prime number``````
``````<?php
/*
Php Program
Check if a number is prime or not
*/
class MyNumber {
public 	function is_prime(\$n) {
if (\$n <= 1) {
return false;
}
//Base case

if (\$n == 2 || \$n == 3 || \$n == 5) {
return true;
}
for (\$i = intval(\$n / 2); \$i > 1; --\$i) {
//Check divisibility of a number

if (\$n % \$i == 0) {
return false;
}
}
return true;
}
public 	function prime_number(\$number) {
if (\$this->is_prime(\$number)) {
echo(\$number ." is a prime number\n");
} else {
echo(\$number ." number not a prime number\n");
}
}
};

function main() {
\$obj = new MyNumber();
//Test case

\$obj->prime_number(37);
\$obj->prime_number(46);
}
main();```
```

#### Output

``````37 is a prime number
46 number not a prime number``````
``````/*
Node Js Program
Check if a number is prime or not
*/
class MyNumber {
is_prime(n) {
if (n <= 1) {
return false;
}
//Base case

if (n == 2 || n == 3 || n == 5) {
return true;
}
for (var i = parseInt( n / 2); i > 1; --i) {
//Check divisibility of a number

if (n % i == 0) {
return false;
}
}
return true;
}
prime_number(number) {
if (this.is_prime(number)) {
process.stdout.write(number + " is a prime number\n");
} else {
process.stdout.write(number + " number not a prime number\n");
}
}
}

function main(args) {
var obj = new MyNumber();
//Test case
obj.prime_number(37);
obj.prime_number(46)
}
main();```
```

#### Output

``````37 is a prime number
46 number not a prime number``````

Resultant Output:

When we run the program with the input numbers 37 and 46, we get the following output:

`37 is a prime number`

`46 is not a prime number`

Explanation of Output:

In the given example, we checked whether the numbers 37 and 46 are prime or not. The output indicates that 37 is a prime number, while 46 is not a prime number.

Time Complexity:

The time complexity of the algorithm is approximately `O(n/2)`, where `n` is the given number. This is because we iterate from `n/2` to 2 to check for divisibility. Therefore, the time complexity can be simplified as `O(n)`.

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