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C# Program to Check If a Number Is a Prime or Not

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Prime number

C# program to check if a number is a prime or not has been shown here. A positive number $n$ is called a prime, if it does not have any divisor except $1$ and $n$. For example if $n = 13$, it is prime but if $n = 10$, it is not prime as $10$ is divisible by $2$ and $5$ apart from $1$ and $10$. The algorithm, pseudocode and time complexity of the program have been shown below.






1. Algorithm to check if a number is a prime or not


1. Take a positive number n as input.

2. Check for each i $\in$ [2, $\sqrt{n}$], if n is divisible by i

3. If step 2 is true for atleast one i, then n is not a prime.

4. If step 2 is false for each i, then n is a prime.




2. Pseudocode to check if a number is a prime or not


Input : A postive number $n$

Output : $n$ is a prime or not a prime

1. Procedure checkPrime($n$):

2. $flag \leftarrow 0$

3. Repeat for $i \in [2, \sqrt{n}]$:

4. If $n \mod i$ = 0:

5. $flag \leftarrow 1$

6. break

7. If $n = 1$

8. Return "not a prime"

9. Else:

10. If $flag = 1$:

11. Return "not a prime"

12. Else:

13. Return "a prime"

14. End Procedure





3. Time complexity to check if a number is a prime or not


Time Complexity: O($\sqrt{n}$)

Where n is the input number.





4. C# Program & output to check if a number is a prime or not using iteration

Code has been copied
/*********************************
	 alphabetacoder.com
C# program to check if a number 
is a prime or not using iteration
***********************************/

using System;

namespace CheckPrime {
    class Program {
        static void Main(string[] args) {
            // declare variables
            int n, i, flag = 0;

            // take input of the number
            Console.Write("Enter the number = ");
            n = Convert.ToInt32(Console.ReadLine());

            // check if n is a prime or not
            // If n has divisor between 2 and
            // square root of n, then 
            // n is not prime else n is prime
            for (i = 2; i <= Math.Sqrt(n); i++) {
                if (n % i == 0) {
                    flag = 1; // mark as not prime
                    break; // exit from loop
                }
            }

            // dispay the result
            if (n == 0 || n == 1)
                Console.Write(n + " is neither a prime nor a composite!");
            else {
                if (flag == 0)
                    Console.Write(n + " is a prime!");
                else
                    Console.Write(n + " is not a prime!");
            }
        }
    }
}

Output

Enter the number = 101

101 is a prime!




5. C# Program & output to check if a number is a prime or not using recursion

Code has been copied
/*********************************
	alphabetacoder.com
C# program to check if a number 
is a prime or not using recursion
***********************************/

using System;

namespace CheckPrime {
    class Program {
        // recursive function to check 
        // if a number is prime or not
        // check divisor upto sqrt(num)
        static int check_prime(int num, int i) {
            // return 1, as num is prime
            if (i > Math.Sqrt(num))
                return 1;
            // return 0, as num is not prime
            if (num % i == 0)
                return 0;
            // call function
            return check_prime(num, i + 1);
        }

        static void Main(string[] args) {
            // declare variables
            int n;

            // take input of the number
            Console.Write("Enter the number = ");
            n = Convert.ToInt32(Console.ReadLine());

            //check if n is a prime or not
            // by calling the function
            // if the function returns 1, 
            // it is considered prime else
            // it is considered not prime
            if (n == 0 || n == 1)
                Console.Write(n + " is neither a prime nor a composite!");
            else {
                if (check_prime(n, 2) == 1)
                    Console.Write(n + " is a prime!");
                else
                    Console.Write(n + " is not a prime!");
            }
        }
    }
}

Output

Enter the number = 37

37 is a prime!




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