C# Program to check if a number is prime or not

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. To check if a number is prime in C#, we need to verify that it has exactly two divisors.

Algorithm

To determine if a number is prime, we use a for loop to check all numbers from 1 to the given number. We count how many divisors exist by checking if the remainder is zero when dividing the number by each potential divisor −

for (int i = 1; i <= n; i++) {
    if (n % i == 0) {
        count++;
    }
}

If the count equals 2, the number is prime because it's only divisible by 1 and itself.

Using Basic Prime Check

Example

using System;

namespace Demo {
    class MyApplication {
        public static void Main() {
            int n = 5, a = 0;
            for (int i = 1; i <= n; i++) {
                if (n % i == 0) {
                    a++;
                }
            }
            if (a == 2) {
                Console.WriteLine("{0} is a Prime Number", n);
            } else {
                Console.WriteLine("{0} is Not a Prime Number", n);
            }
        }
    }
}

The output of the above code is −

5 is a Prime Number

Using Optimized Prime Check

For better performance, we can optimize by checking divisors only up to the square root of the number −

Example

using System;

class Program {
    public static void Main() {
        int[] numbers = {2, 4, 17, 25, 29};
        
        foreach (int num in numbers) {
            if (IsPrime(num)) {
                Console.WriteLine("{0} is a Prime Number", num);
            } else {
                Console.WriteLine("{0} is Not a Prime Number", num);
            }
        }
    }
    
    static bool IsPrime(int n) {
        if (n <= 1) return false;
        if (n == 2) return true;
        if (n % 2 == 0) return false;
        
        for (int i = 3; i * i <= n; i += 2) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }
}

The output of the above code is −

2 is a Prime Number
4 is Not a Prime Number
17 is a Prime Number
25 is Not a Prime Number
29 is a Prime Number

Using Method with Special Cases

Example

using System;

class PrimeChecker {
    public static void Main() {
        int[] testNumbers = {1, 2, 3, 9, 13, 100};
        
        foreach (int number in testNumbers) {
            Console.WriteLine("{0}: {1}", number, CheckPrime(number) ? "Prime" : "Not Prime");
        }
    }
    
    static bool CheckPrime(int n) {
        if (n <= 1) return false;
        if (n <= 3) return true;
        if (n % 2 == 0 || n % 3 == 0) return false;
        
        for (int i = 5; i * i <= n; i += 6) {
            if (n % i == 0 || n % (i + 2) == 0) {
                return false;
            }
        }
        return true;
    }
}

The output of the above code is −

1: Not Prime
2: Prime
3: Prime
9: Not Prime
13: Prime
100: Not Prime

Comparison of Methods

Conclusion

Prime number checking in C# can be implemented using various approaches, from basic divisor counting to optimized algorithms. The square root optimization significantly improves performance for large numbers by reducing the number of iterations required.