# Java Program to Check Prime Number

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

### Example: Using conditional statements

In the below example, the number called MyNum is checked for prime number by dividing it with all natural numbers starting from $2$ to $N-1$.

public class MyClass {
public static void main(String[] args) {
int MyNum = 17;
int n = 0;
for(int i = 2; i < MyNum; i++)
{
if(MyNum % i == 0){
n++;
break;
}
}
if (n == 0){
System.out.println(MyNum + " is a prime number.");
} else {
System.out.println(MyNum + " is not a prime number.");
}
}
}

Output

17 is a prime number.

### Example: Using Method

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.println(MyNum + " is a prime number.");
} else {
System.out.println(MyNum + " is not a prime number.");
}
}
public static void main(String[] args) {
}
}

Output

21 is not a prime number.

### 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.println(MyNum + " is a prime number.");
} 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.println(MyNum + " is a prime number.");
} else {
System.out.println(MyNum + " is not a prime number.");
}
} else {
System.out.println(MyNum + " is not a prime number.");
}
}
public static void main(String[] args) {