Number is prime or not

Prime numbers are numbers that have only 2 factors. The two factors are 1 and themselves.

For example number = 6

6: 1,2,3,6 => 6 is not a prime

3: 1,3 => 3 is a prime number (3 is divisible by 1 and 3 only)

public class Prime {
  public static void main(String[] args) {
    int n = 3,count=0;

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

    if(count==2){
      System.out.println("Prime");
    }
    else{
      System.out.println("Not a prime");
    }
  }
}

Prime

Here we can also optimize the code by starting the loop from 2 and without using the count variable.

i=2

3: 3

public class Prime {
  public static void main(String[] args) {
    int n = 6;

    for(int i=2;i<n;i++){
      if(n%i==0){
        System.out.println("Not a prime");
        System.exit(0);
      }
    }
    System.out.println("Prime");
  }
}

Not a prime

Take n = 6;

i range from 2 to 5(n-1)

if (n%i ==0)

Not a prime

exit from the code

None of the i values divides the n then it is prime.

Better Approach:

for example number 36

repeating the loop from 2 to 36 will take more time time limit also exceed in coding challenges

better to follow this

36 = 1 * 36

36 = 2 * 18

36 = 3 *12

36 = 4 * 9

36 = 6 * 6

36 = 9 * 4

36 = 12 * 3

36 = 18 * 2

36 = 36 * 1

the square root of 36 is 6

after the 6 * 6 multiplication, all are repeated twice

so only repeat the loop to root(n)

root(36) = 6

public class Prime {
  public static void main(String[] args) {
    int n = 18;
    double val = Math.round(Math.sqrt(n));
    for(int i=2;i<=val;i++){
      if(n%i==0){
        System.out.println("Not a prime");
        System.exit(0);
      }
    }
    System.out.println("Prime");
  }
}

Not a prime

OR

we can write this way also

public class Prime {
  public static void main(String[] args) {
    int n = 29;
    for(int i=2;i*i<n;i++){
      if(n%i==0){
        System.out.println("Not a prime");
        System.exit(0);
      }
    }
    System.out.println("Prime");
  }
}

Prime