C# Program - Find all Prime Numbers in a given Interval


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A Prime number is a natural number greater than $$1$$ and divisible by $$1$$ and itself only, for example $$- 2, 3, 5, 7,$$ etc.

Objective: Write a C# code to find all prime numbers in a given internal.

Example: Using function to find prime number

In the below example, a function called primenumber() is created which takes a number as argument and checks it for prime number by dividing it with all natural numbers starting from $$2$$ to $$\frac{N}{2}$$.

using System;

namespace MyApplication { 
   class MyProgram {
    static void primenumber(int MyNum) 
    {
      int n = 0;
      for(int i = 2; i < (MyNum/2+1); i++)
      {
        if(MyNum % i == 0){
          n++;
          break;
        }
      }
      if (n == 0){
        Console.Write(MyNum + " "); 
      }
    }

    static void Main(string[] args) {
      int x = 10;
      int y = 50;
      Console.WriteLine("Prime numbers between "+ x + " and " + y + " are: ");
      for(int i = x; i < y + 1; i++)
      {
        primenumber(i);
      }
    }
  }
}

Output

Prime numbers between 10 and 50 are:
11 13 17 19 23 29 31 37 41 43 47

Example: Optimized Code

  • Instead of checking the divisibility of given number from $$2$$ to $$\frac{N}{2}$$, it is checked till $$\sqrt{N}$$. For a factor larger than $$\sqrt{N}$$, there must the a smaller factor which is already checked in the range of $$2$$ to $$\sqrt{N}$$.
  • Except from $$2$$ and $$3$$, every prime number can be represented into $$6k\pm1$$.

using System;

namespace MyApplication { 
   class MyProgram {
    static void primenumber(int MyNum) 
    {
      int n = 0;
      if (MyNum == 2 || MyNum == 3){
        Console.Write(MyNum + " ");
      } else if (MyNum % 6 == 1 || MyNum % 6 == 5) {
          for(int i = 2; i*i <= MyNum; i++)
          {
            if(MyNum % i == 0){
              n++;
              break;
            }
          }
          if (n == 0){
            Console.Write(MyNum + " ");
          } 
      }
    }

    static void Main(string[] args) { 
      int x = 100;
      int y = 200;
      Console.WriteLine("Prime numbers between "+ x + " and " + y + " are: ");
      for(int i = x; i < y + 1; i++)
      {
        primenumber(i);
      }
    }
  }
}

Output

Prime numbers between 100 and 200 are:
101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 




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