# 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.

### Method 1: Using conditional statements

In the example below, 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.");
}
}
}
```

The above code will give the following output:

```17 is a prime number.
```

### Method 2: Using Method

In the example below, 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 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) {
}
}
```

The above code will give the following output:

```21 is not a prime number.
```

### Method 3: Optimized Code

• Instead of checking the divisibility of given number from 2 to N/2, it is checked till square root of N. For a factor larger than square root of N, there must the a smaller factor which is already checked in the range of 2 to square root of N.
• Except from 2 and 3, every prime number can be represented into 6k ± 1.
```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) {
```21 is not a prime number.