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

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 java 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 $\frac{N}{2}$.

public class MyClass {
int n = 0;
for(int i = 2; i < (MyNum/2+1); i++)
{
if(MyNum % i == 0){
n++;
break;
}
}
if (n == 0){
System.out.print(MyNum + " ");
}
}
public static void main(String[] args) {
int x = 10;
int y = 50;
System.out.println("Prime numbers between "+ x + " and " + y + " are: ");
for(int i = x; i < y + 1; 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 $6k\pm1$.

public class MyClass {
int n = 0;
if (MyNum == 2 || MyNum == 3){
System.out.print(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){
System.out.print(MyNum + " ");
}
}
}
public static void main(String[] args) {
int x = 100;
int y = 200;
System.out.println("Prime numbers between "+ x + " and " + y + " are: ");
for(int i = x; i < y + 1; 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